""" This code is automatically generated. Never edit it manually. For details of generating the code see `rubi_parsing_guide.md` in `parsetools`. """ from sympy.external import import_module matchpy = import_module("matchpy") if matchpy: from matchpy import Pattern, ReplacementRule, CustomConstraint, is_match from sympy.integrals.rubi.utility_function import ( Int, Sum, Set, With, Module, Scan, MapAnd, FalseQ, ZeroQ, NegativeQ, NonzeroQ, FreeQ, NFreeQ, List, Log, PositiveQ, PositiveIntegerQ, NegativeIntegerQ, IntegerQ, IntegersQ, ComplexNumberQ, PureComplexNumberQ, RealNumericQ, PositiveOrZeroQ, NegativeOrZeroQ, FractionOrNegativeQ, NegQ, Equal, Unequal, IntPart, FracPart, RationalQ, ProductQ, SumQ, NonsumQ, Subst, First, Rest, SqrtNumberQ, SqrtNumberSumQ, LinearQ, Sqrt, ArcCosh, Coefficient, Denominator, Hypergeometric2F1, Not, Simplify, FractionalPart, IntegerPart, AppellF1, EllipticPi, EllipticE, EllipticF, ArcTan, ArcCot, ArcCoth, ArcTanh, ArcSin, ArcSinh, ArcCos, ArcCsc, ArcSec, ArcCsch, ArcSech, Sinh, Tanh, Cosh, Sech, Csch, Coth, LessEqual, Less, Greater, GreaterEqual, FractionQ, IntLinearcQ, Expand, IndependentQ, PowerQ, IntegerPowerQ, PositiveIntegerPowerQ, FractionalPowerQ, AtomQ, ExpQ, LogQ, Head, MemberQ, TrigQ, SinQ, CosQ, TanQ, CotQ, SecQ, CscQ, Sin, Cos, Tan, Cot, Sec, Csc, HyperbolicQ, SinhQ, CoshQ, TanhQ, CothQ, SechQ, CschQ, InverseTrigQ, SinCosQ, SinhCoshQ, LeafCount, Numerator, NumberQ, NumericQ, Length, ListQ, Im, Re, InverseHyperbolicQ, InverseFunctionQ, TrigHyperbolicFreeQ, InverseFunctionFreeQ, RealQ, EqQ, FractionalPowerFreeQ, ComplexFreeQ, PolynomialQ, FactorSquareFree, PowerOfLinearQ, Exponent, QuadraticQ, LinearPairQ, BinomialParts, TrinomialParts, PolyQ, EvenQ, OddQ, PerfectSquareQ, NiceSqrtAuxQ, NiceSqrtQ, Together, PosAux, PosQ, CoefficientList, ReplaceAll, ExpandLinearProduct, GCD, ContentFactor, NumericFactor, NonnumericFactors, MakeAssocList, GensymSubst, KernelSubst, ExpandExpression, Apart, SmartApart, MatchQ, PolynomialQuotientRemainder, FreeFactors, NonfreeFactors, RemoveContentAux, RemoveContent, FreeTerms, NonfreeTerms, ExpandAlgebraicFunction, CollectReciprocals, ExpandCleanup, AlgebraicFunctionQ, Coeff, LeadTerm, RemainingTerms, LeadFactor, RemainingFactors, LeadBase, LeadDegree, Numer, Denom, hypergeom, Expon, MergeMonomials, PolynomialDivide, BinomialQ, TrinomialQ, GeneralizedBinomialQ, GeneralizedTrinomialQ, FactorSquareFreeList, PerfectPowerTest, SquareFreeFactorTest, RationalFunctionQ, RationalFunctionFactors, NonrationalFunctionFactors, Reverse, RationalFunctionExponents, RationalFunctionExpand, ExpandIntegrand, SimplerQ, SimplerSqrtQ, SumSimplerQ, BinomialDegree, TrinomialDegree, CancelCommonFactors, SimplerIntegrandQ, GeneralizedBinomialDegree, GeneralizedBinomialParts, GeneralizedTrinomialDegree, GeneralizedTrinomialParts, MonomialQ, MonomialSumQ, MinimumMonomialExponent, MonomialExponent, LinearMatchQ, PowerOfLinearMatchQ, QuadraticMatchQ, CubicMatchQ, BinomialMatchQ, TrinomialMatchQ, GeneralizedBinomialMatchQ, GeneralizedTrinomialMatchQ, QuotientOfLinearsMatchQ, PolynomialTermQ, PolynomialTerms, NonpolynomialTerms, PseudoBinomialParts, NormalizePseudoBinomial, PseudoBinomialPairQ, PseudoBinomialQ, PolynomialGCD, PolyGCD, AlgebraicFunctionFactors, NonalgebraicFunctionFactors, QuotientOfLinearsP, QuotientOfLinearsParts, QuotientOfLinearsQ, Flatten, Sort, AbsurdNumberQ, AbsurdNumberFactors, NonabsurdNumberFactors, SumSimplerAuxQ, Prepend, Drop, CombineExponents, FactorInteger, FactorAbsurdNumber, SubstForInverseFunction, SubstForFractionalPower, SubstForFractionalPowerOfQuotientOfLinears, FractionalPowerOfQuotientOfLinears, SubstForFractionalPowerQ, SubstForFractionalPowerAuxQ, FractionalPowerOfSquareQ, FractionalPowerSubexpressionQ, Apply, FactorNumericGcd, MergeableFactorQ, MergeFactor, MergeFactors, TrigSimplifyQ, TrigSimplify, TrigSimplifyRecur, Order, FactorOrder, Smallest, OrderedQ, MinimumDegree, PositiveFactors, Sign, NonpositiveFactors, PolynomialInAuxQ, PolynomialInQ, ExponentInAux, ExponentIn, PolynomialInSubstAux, PolynomialInSubst, Distrib, DistributeDegree, FunctionOfPower, DivideDegreesOfFactors, MonomialFactor, FullSimplify, FunctionOfLinearSubst, FunctionOfLinear, NormalizeIntegrand, NormalizeIntegrandAux, NormalizeIntegrandFactor, NormalizeIntegrandFactorBase, NormalizeTogether, NormalizeLeadTermSigns, AbsorbMinusSign, NormalizeSumFactors, SignOfFactor, NormalizePowerOfLinear, SimplifyIntegrand, SimplifyTerm, TogetherSimplify, SmartSimplify, SubstForExpn, ExpandToSum, UnifySum, UnifyTerms, UnifyTerm, CalculusQ, FunctionOfInverseLinear, PureFunctionOfSinhQ, PureFunctionOfTanhQ, PureFunctionOfCoshQ, IntegerQuotientQ, OddQuotientQ, EvenQuotientQ, FindTrigFactor, FunctionOfSinhQ, FunctionOfCoshQ, OddHyperbolicPowerQ, FunctionOfTanhQ, FunctionOfTanhWeight, FunctionOfHyperbolicQ, SmartNumerator, SmartDenominator, SubstForAux, ActivateTrig, ExpandTrig, TrigExpand, SubstForTrig, SubstForHyperbolic, InertTrigFreeQ, LCM, SubstForFractionalPowerOfLinear, FractionalPowerOfLinear, InverseFunctionOfLinear, InertTrigQ, InertReciprocalQ, DeactivateTrig, FixInertTrigFunction, DeactivateTrigAux, PowerOfInertTrigSumQ, PiecewiseLinearQ, KnownTrigIntegrandQ, KnownSineIntegrandQ, KnownTangentIntegrandQ, KnownCotangentIntegrandQ, KnownSecantIntegrandQ, TryPureTanSubst, TryTanhSubst, TryPureTanhSubst, AbsurdNumberGCD, AbsurdNumberGCDList, ExpandTrigExpand, ExpandTrigReduce, ExpandTrigReduceAux, NormalizeTrig, TrigToExp, ExpandTrigToExp, TrigReduce, FunctionOfTrig, AlgebraicTrigFunctionQ, FunctionOfHyperbolic, FunctionOfQ, FunctionOfExpnQ, PureFunctionOfSinQ, PureFunctionOfCosQ, PureFunctionOfTanQ, PureFunctionOfCotQ, FunctionOfCosQ, FunctionOfSinQ, OddTrigPowerQ, FunctionOfTanQ, FunctionOfTanWeight, FunctionOfTrigQ, FunctionOfDensePolynomialsQ, FunctionOfLog, PowerVariableExpn, PowerVariableDegree, PowerVariableSubst, EulerIntegrandQ, FunctionOfSquareRootOfQuadratic, SquareRootOfQuadraticSubst, Divides, EasyDQ, ProductOfLinearPowersQ, Rt, NthRoot, AtomBaseQ, SumBaseQ, NegSumBaseQ, AllNegTermQ, SomeNegTermQ, TrigSquareQ, RtAux, TrigSquare, IntSum, IntTerm, Map2, ConstantFactor, SameQ, ReplacePart, CommonFactors, MostMainFactorPosition, FunctionOfExponentialQ, FunctionOfExponential, FunctionOfExponentialFunction, FunctionOfExponentialFunctionAux, FunctionOfExponentialTest, FunctionOfExponentialTestAux, stdev, rubi_test, If, IntQuadraticQ, IntBinomialQ, RectifyTangent, RectifyCotangent, Inequality, Condition, Simp, SimpHelp, SplitProduct, SplitSum, SubstFor, SubstForAux, FresnelS, FresnelC, Erfc, Erfi, Gamma, FunctionOfTrigOfLinearQ, ElementaryFunctionQ, Complex, UnsameQ, _SimpFixFactor, SimpFixFactor, _FixSimplify, FixSimplify, _SimplifyAntiderivativeSum, SimplifyAntiderivativeSum, _SimplifyAntiderivative, SimplifyAntiderivative, _TrigSimplifyAux, TrigSimplifyAux, Cancel, Part, PolyLog, D, Dist, Sum_doit, PolynomialQuotient, Floor, PolynomialRemainder, Factor, PolyLog, CosIntegral, SinIntegral, LogIntegral, SinhIntegral, CoshIntegral, Rule, Erf, PolyGamma, ExpIntegralEi, ExpIntegralE, LogGamma , UtilityOperator, Factorial, Zeta, ProductLog, DerivativeDivides, HypergeometricPFQ, IntHide, OneQ, Null, rubi_exp as exp, rubi_log as log, Discriminant, Negative, Quotient ) from sympy.core.add import Add from sympy.core.mod import Mod from sympy.core.mul import Mul from sympy.core import EulerGamma from sympy.core.numbers import (Float, I, Integer) from sympy.core.power import Pow from sympy.core.singleton import S from sympy.functions.elementary.complexes import (Abs, sign) from sympy.functions.elementary.miscellaneous import sqrt from sympy.integrals.integrals import Integral from sympy.logic.boolalg import (And, Or) from sympy.simplify.simplify import simplify from sympy.integrals.rubi.symbol import WC from sympy.core.symbol import symbols, Symbol from sympy.functions import (sin, cos, tan, cot, csc, sec, sqrt, erf) from sympy.functions.elementary.hyperbolic import (acosh, asinh, atanh, acoth, acsch, asech, cosh, sinh, tanh, coth, sech, csch) from sympy.functions.elementary.trigonometric import (atan, acsc, asin, acot, acos, asec, atan2) from sympy.core.numbers import pi as Pi A_, B_, C_, F_, G_, H_, a_, b_, c_, d_, e_, f_, g_, h_, i_, j_, k_, l_, m_, n_, p_, q_, r_, t_, u_, v_, s_, w_, x_, y_, z_ = [WC(i) for i in 'ABCFGHabcdefghijklmnpqrtuvswxyz'] a1_, a2_, b1_, b2_, c1_, c2_, d1_, d2_, n1_, n2_, e1_, e2_, f1_, f2_, g1_, g2_, n1_, n2_, n3_, Pq_, Pm_, Px_, Qm_, Qr_, Qx_, jn_, mn_, non2_, RFx_, RGx_ = [WC(i) for i in ['a1', 'a2', 'b1', 'b2', 'c1', 'c2', 'd1', 'd2', 'n1', 'n2', 'e1', 'e2', 'f1', 'f2', 'g1', 'g2', 'n1', 'n2', 'n3', 'Pq', 'Pm', 'Px', 'Qm', 'Qr', 'Qx', 'jn', 'mn', 'non2', 'RFx', 'RGx']] i, ii, Pqq, Q, R, r, C, k, u = symbols('i ii Pqq Q R r C k u') _UseGamma = False ShowSteps = False StepCounter = None def hyperbolic(): from sympy.integrals.rubi.constraints import cons33, cons170, cons8, cons29, cons50, cons127, cons96, cons1118, cons178, cons1490, cons19, cons89, cons167, cons3, cons95, cons168, cons87, cons1491, cons247, cons249, cons91, cons1444, cons150, cons1861, cons2, cons1492, cons1441, cons810, cons1493, cons1494, cons1456, cons1442, cons64, cons1269, cons1495, cons812, cons813, cons4, cons1362, cons130, cons40, cons139, cons746, cons65, cons1496, cons198, cons1497, cons5, cons55, cons13, cons598, cons1498, cons20, cons1499, cons378, cons148, cons491, cons1500, cons70, cons71, cons825, cons826, cons1501, cons1503, cons1257, cons1504, cons58, cons152, cons1505, cons1506, cons685, cons369, cons1507, cons358, cons68, cons856, cons25, cons1508, cons56, cons14, cons820, cons1133, cons1134, cons1135, cons1509, cons821, cons530, cons1267, cons1512, cons21, cons1573, cons1574, cons1575, cons1576, cons1577, cons1578, cons1579, cons1580, cons1581, cons1045, cons1582, cons1646, cons1738, cons1647, cons586, cons466, cons1685, cons1410, cons1686, cons1687, cons1862, cons1863, cons1690, cons814, cons815, cons557, cons1864, cons1865, cons27, cons1693, cons1866, cons1101, cons1867, cons1868, cons1397, cons1869, cons1695, cons1870, cons965, cons1871, cons1872, cons210, cons1702, cons1013, cons1553, cons1703, cons1704, cons211, cons226, cons1701, cons1873, cons1705, cons1706, cons1874, cons1708, cons1709, cons1875, cons1876, cons1877, cons1878, cons1879, cons1880, cons1881, cons1882, cons1883, cons1884, cons1885, cons1886, cons1887, cons1888, cons1722, cons1889, cons1890, cons1891, cons1725, cons1892, cons165, cons340, cons164, cons629, cons73, cons1727, cons1728, cons1729, cons90, cons1730, cons1458, cons465, cons1731, cons1480, cons1732, cons1893, cons36, cons37, cons1476, cons1483, cons1735 pattern5646 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons8, cons29, cons50, cons127, cons33, cons170) rule5646 = ReplacementRule(pattern5646, replacement5646) pattern5647 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons8, cons29, cons50, cons127, cons33, cons170) rule5647 = ReplacementRule(pattern5647, replacement5647) pattern5648 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*sinh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons8, cons29, cons50, cons127, cons33, cons96) rule5648 = ReplacementRule(pattern5648, replacement5648) pattern5649 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*cosh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons8, cons29, cons50, cons127, cons33, cons96) rule5649 = ReplacementRule(pattern5649, replacement5649) pattern5650 = Pattern(Integral(sinh(x_*WC('f', S(1)) + WC('e', S(0)))/(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons127, cons1118) rule5650 = ReplacementRule(pattern5650, replacement5650) pattern5651 = Pattern(Integral(cosh(x_*WC('f', S(1)) + WC('e', S(0)))/(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons127, cons1118) rule5651 = ReplacementRule(pattern5651, replacement5651) pattern5652 = Pattern(Integral(sinh(x_*WC('f', S(1)) + WC('e', S(0)))/(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons127, cons178) rule5652 = ReplacementRule(pattern5652, replacement5652) pattern5653 = Pattern(Integral(cosh(x_*WC('f', S(1)) + WC('e', S(0)))/(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons127, cons178) rule5653 = ReplacementRule(pattern5653, replacement5653) pattern5654 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons8, cons29, cons50, cons127, cons19, cons1490) rule5654 = ReplacementRule(pattern5654, replacement5654) pattern5655 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons8, cons29, cons50, cons127, cons19, cons1490) rule5655 = ReplacementRule(pattern5655, replacement5655) pattern5656 = Pattern(Integral((WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons3, cons8, cons29, cons50, cons127, cons89, cons167) rule5656 = ReplacementRule(pattern5656, replacement5656) pattern5657 = Pattern(Integral((WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons3, cons8, cons29, cons50, cons127, cons89, cons167) rule5657 = ReplacementRule(pattern5657, replacement5657) pattern5658 = Pattern(Integral((WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons3, cons8, cons29, cons50, cons127, cons95, cons167, cons168) rule5658 = ReplacementRule(pattern5658, replacement5658) pattern5659 = Pattern(Integral((WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons3, cons8, cons29, cons50, cons127, cons95, cons167, cons168) rule5659 = ReplacementRule(pattern5659, replacement5659) pattern5660 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*sinh(x_*WC('f', S(1)) + WC('e', S(0)))**n_, x_), cons8, cons29, cons50, cons127, cons19, cons87, cons167, cons1491) rule5660 = ReplacementRule(pattern5660, replacement5660) pattern5661 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*cosh(x_*WC('f', S(1)) + WC('e', S(0)))**n_, x_), cons8, cons29, cons50, cons127, cons19, cons87, cons167, cons1491) rule5661 = ReplacementRule(pattern5661, replacement5661) pattern5662 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*sinh(x_*WC('f', S(1)) + WC('e', S(0)))**n_, x_), cons8, cons29, cons50, cons127, cons19, cons87, cons167, cons33, cons247) rule5662 = ReplacementRule(pattern5662, replacement5662) pattern5663 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*cosh(x_*WC('f', S(1)) + WC('e', S(0)))**n_, x_), cons8, cons29, cons50, cons127, cons19, cons87, cons167, cons33, cons247) rule5663 = ReplacementRule(pattern5663, replacement5663) pattern5664 = Pattern(Integral((WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons3, cons8, cons29, cons50, cons127, cons95, cons167, cons249) rule5664 = ReplacementRule(pattern5664, replacement5664) pattern5665 = Pattern(Integral((WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons3, cons8, cons29, cons50, cons127, cons95, cons167, cons249) rule5665 = ReplacementRule(pattern5665, replacement5665) pattern5666 = Pattern(Integral((WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons3, cons8, cons29, cons50, cons127, cons89, cons91, cons1444) rule5666 = ReplacementRule(pattern5666, replacement5666) pattern5667 = Pattern(Integral((WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons3, cons8, cons29, cons50, cons127, cons89, cons91, cons1444) rule5667 = ReplacementRule(pattern5667, replacement5667) pattern5668 = Pattern(Integral((WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons3, cons8, cons29, cons50, cons127, cons95, cons91, cons1444, cons168) rule5668 = ReplacementRule(pattern5668, replacement5668) pattern5669 = Pattern(Integral((WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons3, cons8, cons29, cons50, cons127, cons95, cons91, cons1444, cons168) rule5669 = ReplacementRule(pattern5669, replacement5669) pattern5670 = Pattern(Integral((a_ + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons150, cons1861) rule5670 = ReplacementRule(pattern5670, replacement5670) pattern5671 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons150, cons1492) rule5671 = ReplacementRule(pattern5671, replacement5671) pattern5672 = Pattern(Integral((a_ + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1441, cons87) rule5672 = ReplacementRule(pattern5672, replacement5672) pattern5673 = Pattern(Integral((a_ + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1441, cons810, cons1493) rule5673 = ReplacementRule(pattern5673, replacement5673) pattern5674 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1494, cons87) rule5674 = ReplacementRule(pattern5674, replacement5674) pattern5675 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1456, cons87) rule5675 = ReplacementRule(pattern5675, replacement5675) pattern5676 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1494, cons810, cons1493) rule5676 = ReplacementRule(pattern5676, replacement5676) pattern5677 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1456, cons810, cons1493) rule5677 = ReplacementRule(pattern5677, replacement5677) pattern5678 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1442, cons64) rule5678 = ReplacementRule(pattern5678, replacement5678) pattern5679 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons64) rule5679 = ReplacementRule(pattern5679, replacement5679) pattern5680 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1442, cons64) rule5680 = ReplacementRule(pattern5680, replacement5680) pattern5681 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons64) rule5681 = ReplacementRule(pattern5681, replacement5681) pattern5682 = Pattern(Integral((a_ + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1442, cons1495, cons64) rule5682 = ReplacementRule(pattern5682, replacement5682) pattern5683 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons1495, cons64) rule5683 = ReplacementRule(pattern5683, replacement5683) pattern5684 = Pattern(Integral(u_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(v_))**WC('n', S(1)), x_), cons2, cons3, cons19, cons4, cons812, cons813) rule5684 = ReplacementRule(pattern5684, replacement5684) pattern5685 = Pattern(Integral(u_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(v_))**WC('n', S(1)), x_), cons2, cons3, cons19, cons4, cons812, cons813) rule5685 = ReplacementRule(pattern5685, replacement5685) pattern5686 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons4, cons1362) rule5686 = ReplacementRule(pattern5686, replacement5686) pattern5687 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons4, cons1362) rule5687 = ReplacementRule(pattern5687, replacement5687) pattern5688 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**WC('p', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons4, cons130) rule5688 = ReplacementRule(pattern5688, replacement5688) pattern5689 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**WC('p', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons4, cons130) rule5689 = ReplacementRule(pattern5689, replacement5689) pattern5690 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons40, cons150, cons139, cons746) rule5690 = ReplacementRule(pattern5690, replacement5690) pattern5691 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons40, cons150, cons139, cons746) rule5691 = ReplacementRule(pattern5691, replacement5691) pattern5692 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons65, cons150, cons1496) rule5692 = ReplacementRule(pattern5692, replacement5692) pattern5693 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons65, cons150, cons1496) rule5693 = ReplacementRule(pattern5693, replacement5693) pattern5694 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons65, cons198) rule5694 = ReplacementRule(pattern5694, replacement5694) pattern5695 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons65, cons198) rule5695 = ReplacementRule(pattern5695, replacement5695) pattern5696 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons1497) rule5696 = ReplacementRule(pattern5696, replacement5696) pattern5697 = Pattern(Integral((a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons1497) rule5697 = ReplacementRule(pattern5697, replacement5697) pattern5698 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**WC('p', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons130) rule5698 = ReplacementRule(pattern5698, replacement5698) pattern5699 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**WC('p', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons130) rule5699 = ReplacementRule(pattern5699, replacement5699) pattern5700 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons40, cons55, cons13, cons139, cons598) rule5700 = ReplacementRule(pattern5700, replacement5700) pattern5701 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons40, cons55, cons13, cons139, cons598) rule5701 = ReplacementRule(pattern5701, replacement5701) pattern5702 = Pattern(Integral(x_**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons40, cons150, cons33, cons139, cons1498) rule5702 = ReplacementRule(pattern5702, replacement5702) pattern5703 = Pattern(Integral(x_**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons40, cons150, cons33, cons139, cons1498) rule5703 = ReplacementRule(pattern5703, replacement5703) pattern5704 = Pattern(Integral(x_**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons65, cons20, cons150, cons1496) rule5704 = ReplacementRule(pattern5704, replacement5704) pattern5705 = Pattern(Integral(x_**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons65, cons20, cons150, cons1496) rule5705 = ReplacementRule(pattern5705, replacement5705) pattern5706 = Pattern(Integral(x_**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons19, cons65, cons198) rule5706 = ReplacementRule(pattern5706, replacement5706) pattern5707 = Pattern(Integral(x_**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**p_*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons19, cons65, cons198) rule5707 = ReplacementRule(pattern5707, replacement5707) pattern5708 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**WC('p', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons1499) rule5708 = ReplacementRule(pattern5708, replacement5708) pattern5709 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(a_ + x_**n_*WC('b', S(1)))**WC('p', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons1499) rule5709 = ReplacementRule(pattern5709, replacement5709) pattern5710 = Pattern(Integral(sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons87, cons167) rule5710 = ReplacementRule(pattern5710, replacement5710) pattern5711 = Pattern(Integral(cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons87, cons167) rule5711 = ReplacementRule(pattern5711, replacement5711) pattern5712 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons378, cons167, cons148) rule5712 = ReplacementRule(pattern5712, replacement5712) pattern5713 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons378, cons167, cons148) rule5713 = ReplacementRule(pattern5713, replacement5713) pattern5714 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons40, cons198) rule5714 = ReplacementRule(pattern5714, replacement5714) pattern5715 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons40, cons198) rule5715 = ReplacementRule(pattern5715, replacement5715) pattern5716 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons40, cons491) rule5716 = ReplacementRule(pattern5716, With5716) pattern5717 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons40, cons491) rule5717 = ReplacementRule(pattern5717, With5717) pattern5718 = Pattern(Integral(sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons4, cons1500) rule5718 = ReplacementRule(pattern5718, replacement5718) pattern5719 = Pattern(Integral(cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons4, cons1500) rule5719 = ReplacementRule(pattern5719, replacement5719) pattern5720 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons4, cons130) rule5720 = ReplacementRule(pattern5720, replacement5720) pattern5721 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons4, cons130) rule5721 = ReplacementRule(pattern5721, replacement5721) pattern5722 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons40, cons70, cons71) rule5722 = ReplacementRule(pattern5722, replacement5722) pattern5723 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons40, cons70, cons71) rule5723 = ReplacementRule(pattern5723, replacement5723) pattern5724 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70) rule5724 = ReplacementRule(pattern5724, replacement5724) pattern5725 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70) rule5725 = ReplacementRule(pattern5725, replacement5725) pattern5726 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*sinh(u_))**WC('p', S(1)), x_), cons2, cons3, cons5, cons825, cons826) rule5726 = ReplacementRule(pattern5726, replacement5726) pattern5727 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*cosh(u_))**WC('p', S(1)), x_), cons2, cons3, cons5, cons825, cons826) rule5727 = ReplacementRule(pattern5727, replacement5727) pattern5728 = Pattern(Integral(sinh(x_**n_*WC('d', S(1)))/x_, x_), cons29, cons4, cons1501) rule5728 = ReplacementRule(pattern5728, replacement5728) pattern5729 = Pattern(Integral(cosh(x_**n_*WC('d', S(1)))/x_, x_), cons29, cons4, cons1501) rule5729 = ReplacementRule(pattern5729, replacement5729) pattern5730 = Pattern(Integral(sinh(c_ + x_**n_*WC('d', S(1)))/x_, x_), cons8, cons29, cons4, cons1500) rule5730 = ReplacementRule(pattern5730, replacement5730) pattern5731 = Pattern(Integral(cosh(c_ + x_**n_*WC('d', S(1)))/x_, x_), cons8, cons29, cons4, cons1500) rule5731 = ReplacementRule(pattern5731, replacement5731) pattern5732 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons40, CustomConstraint(With5732)) rule5732 = ReplacementRule(pattern5732, replacement5732) pattern5733 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons40, CustomConstraint(With5733)) rule5733 = ReplacementRule(pattern5733, replacement5733) pattern5734 = Pattern(Integral((e_*x_)**m_*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons40, CustomConstraint(With5734)) rule5734 = ReplacementRule(pattern5734, replacement5734) pattern5735 = Pattern(Integral((e_*x_)**m_*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons40, CustomConstraint(With5735)) rule5735 = ReplacementRule(pattern5735, replacement5735) pattern5736 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons150, cons33, cons1503) rule5736 = ReplacementRule(pattern5736, replacement5736) pattern5737 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons150, cons33, cons1503) rule5737 = ReplacementRule(pattern5737, replacement5737) pattern5738 = Pattern(Integral((x_*WC('e', S(1)))**m_*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons150, cons33, cons96) rule5738 = ReplacementRule(pattern5738, replacement5738) pattern5739 = Pattern(Integral((x_*WC('e', S(1)))**m_*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons150, cons33, cons96) rule5739 = ReplacementRule(pattern5739, replacement5739) pattern5740 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons19, cons150) rule5740 = ReplacementRule(pattern5740, replacement5740) pattern5741 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons19, cons150) rule5741 = ReplacementRule(pattern5741, replacement5741) pattern5742 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons378, cons1257, cons148, cons1504) rule5742 = ReplacementRule(pattern5742, replacement5742) pattern5743 = Pattern(Integral(x_**WC('m', S(1))*cosh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons378, cons1257, cons148, cons1504) rule5743 = ReplacementRule(pattern5743, replacement5743) pattern5744 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons19, cons4, cons58, cons13, cons148) rule5744 = ReplacementRule(pattern5744, replacement5744) pattern5745 = Pattern(Integral(x_**WC('m', S(1))*cosh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons19, cons4, cons58, cons13, cons148) rule5745 = ReplacementRule(pattern5745, replacement5745) pattern5746 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons152, cons13, cons148, cons1505) rule5746 = ReplacementRule(pattern5746, replacement5746) pattern5747 = Pattern(Integral(x_**WC('m', S(1))*cosh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons152, cons13, cons148, cons1505) rule5747 = ReplacementRule(pattern5747, replacement5747) pattern5748 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons152, cons13, cons148, cons1506, cons685) rule5748 = ReplacementRule(pattern5748, replacement5748) pattern5749 = Pattern(Integral(x_**WC('m', S(1))*cosh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons152, cons13, cons148, cons1506, cons685) rule5749 = ReplacementRule(pattern5749, replacement5749) pattern5750 = Pattern(Integral((x_*WC('e', S(1)))**m_*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons40, cons150, cons369) rule5750 = ReplacementRule(pattern5750, With5750) pattern5751 = Pattern(Integral((x_*WC('e', S(1)))**m_*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons40, cons150, cons369) rule5751 = ReplacementRule(pattern5751, With5751) pattern5752 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons50, cons19, cons40, cons150, cons148) rule5752 = ReplacementRule(pattern5752, replacement5752) pattern5753 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons50, cons19, cons40, cons150, cons148) rule5753 = ReplacementRule(pattern5753, replacement5753) pattern5754 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons19, cons4, cons58, cons13, cons139, cons1507) rule5754 = ReplacementRule(pattern5754, replacement5754) pattern5755 = Pattern(Integral(x_**WC('m', S(1))*cosh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons19, cons4, cons58, cons13, cons139, cons1507) rule5755 = ReplacementRule(pattern5755, replacement5755) pattern5756 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons152, cons13, cons139, cons1507, cons1505) rule5756 = ReplacementRule(pattern5756, replacement5756) pattern5757 = Pattern(Integral(x_**WC('m', S(1))*cosh(x_**n_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons152, cons13, cons139, cons1507, cons1505) rule5757 = ReplacementRule(pattern5757, replacement5757) pattern5758 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons40, cons198, cons20) rule5758 = ReplacementRule(pattern5758, replacement5758) pattern5759 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons40, cons198, cons20) rule5759 = ReplacementRule(pattern5759, replacement5759) pattern5760 = Pattern(Integral((x_*WC('e', S(1)))**m_*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons40, cons198, cons369) rule5760 = ReplacementRule(pattern5760, With5760) pattern5761 = Pattern(Integral((x_*WC('e', S(1)))**m_*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons40, cons198, cons369) rule5761 = ReplacementRule(pattern5761, With5761) pattern5762 = Pattern(Integral((x_*WC('e', S(1)))**m_*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons40, cons198, cons358) rule5762 = ReplacementRule(pattern5762, replacement5762) pattern5763 = Pattern(Integral((x_*WC('e', S(1)))**m_*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons40, cons198, cons358) rule5763 = ReplacementRule(pattern5763, replacement5763) pattern5764 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons40, cons491) rule5764 = ReplacementRule(pattern5764, With5764) pattern5765 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons40, cons491) rule5765 = ReplacementRule(pattern5765, With5765) pattern5766 = Pattern(Integral((e_*x_)**m_*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons40, cons491) rule5766 = ReplacementRule(pattern5766, replacement5766) pattern5767 = Pattern(Integral((e_*x_)**m_*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons40, cons491) rule5767 = ReplacementRule(pattern5767, replacement5767) pattern5768 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons40, cons68, cons856, cons25) rule5768 = ReplacementRule(pattern5768, replacement5768) pattern5769 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons40, cons68, cons856, cons25) rule5769 = ReplacementRule(pattern5769, replacement5769) pattern5770 = Pattern(Integral((e_*x_)**m_*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons40, cons68, cons856, cons25) rule5770 = ReplacementRule(pattern5770, replacement5770) pattern5771 = Pattern(Integral((e_*x_)**m_*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons40, cons68, cons856, cons25) rule5771 = ReplacementRule(pattern5771, replacement5771) pattern5772 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons19, cons4, cons1508) rule5772 = ReplacementRule(pattern5772, replacement5772) pattern5773 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))), x_), cons8, cons29, cons50, cons19, cons4, cons1508) rule5773 = ReplacementRule(pattern5773, replacement5773) pattern5774 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons130) rule5774 = ReplacementRule(pattern5774, replacement5774) pattern5775 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons130) rule5775 = ReplacementRule(pattern5775, replacement5775) pattern5776 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70, cons71, cons20) rule5776 = ReplacementRule(pattern5776, replacement5776) pattern5777 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70, cons71, cons20) rule5777 = ReplacementRule(pattern5777, replacement5777) pattern5778 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons70) rule5778 = ReplacementRule(pattern5778, replacement5778) pattern5779 = Pattern(Integral((x_*WC('e', S(1)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons70) rule5779 = ReplacementRule(pattern5779, replacement5779) pattern5780 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*sinh(u_))**WC('p', S(1)), x_), cons2, cons3, cons50, cons19, cons5, cons825, cons826) rule5780 = ReplacementRule(pattern5780, replacement5780) pattern5781 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*cosh(u_))**WC('p', S(1)), x_), cons2, cons3, cons50, cons19, cons5, cons825, cons826) rule5781 = ReplacementRule(pattern5781, replacement5781) pattern5782 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1))*cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons19, cons4, cons5, cons55, cons56) rule5782 = ReplacementRule(pattern5782, replacement5782) pattern5783 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))*cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons19, cons4, cons5, cons55, cons56) rule5783 = ReplacementRule(pattern5783, replacement5783) pattern5784 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1))*cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons5, cons95, cons1503, cons56) rule5784 = ReplacementRule(pattern5784, replacement5784) pattern5785 = Pattern(Integral(x_**WC('m', S(1))*sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))*cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons5, cons95, cons1503, cons56) rule5785 = ReplacementRule(pattern5785, replacement5785) pattern5786 = Pattern(Integral(sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons14) rule5786 = ReplacementRule(pattern5786, replacement5786) pattern5787 = Pattern(Integral(cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons14) rule5787 = ReplacementRule(pattern5787, replacement5787) pattern5788 = Pattern(Integral(sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0)))**n_, x_), cons2, cons3, cons8, cons87, cons167) rule5788 = ReplacementRule(pattern5788, replacement5788) pattern5789 = Pattern(Integral(cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0)))**n_, x_), cons2, cons3, cons8, cons87, cons167) rule5789 = ReplacementRule(pattern5789, replacement5789) pattern5790 = Pattern(Integral(sinh(v_)**WC('n', S(1)), x_), cons150, cons820, cons1133) rule5790 = ReplacementRule(pattern5790, replacement5790) pattern5791 = Pattern(Integral(cosh(v_)**WC('n', S(1)), x_), cons150, cons820, cons1133) rule5791 = ReplacementRule(pattern5791, replacement5791) pattern5792 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons1134) rule5792 = ReplacementRule(pattern5792, replacement5792) pattern5793 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons1134) rule5793 = ReplacementRule(pattern5793, replacement5793) pattern5794 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons1135) rule5794 = ReplacementRule(pattern5794, replacement5794) pattern5795 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons1135) rule5795 = ReplacementRule(pattern5795, replacement5795) pattern5796 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons168, cons1134) rule5796 = ReplacementRule(pattern5796, replacement5796) pattern5797 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons168, cons1134) rule5797 = ReplacementRule(pattern5797, replacement5797) pattern5798 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons168, cons1135) rule5798 = ReplacementRule(pattern5798, replacement5798) pattern5799 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons168, cons1135) rule5799 = ReplacementRule(pattern5799, replacement5799) pattern5800 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons96, cons1134) rule5800 = ReplacementRule(pattern5800, replacement5800) pattern5801 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons96, cons1134) rule5801 = ReplacementRule(pattern5801, replacement5801) pattern5802 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons96, cons1135) rule5802 = ReplacementRule(pattern5802, replacement5802) pattern5803 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**m_*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons33, cons96, cons1135) rule5803 = ReplacementRule(pattern5803, replacement5803) pattern5804 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons1509) rule5804 = ReplacementRule(pattern5804, replacement5804) pattern5805 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons1509) rule5805 = ReplacementRule(pattern5805, replacement5805) pattern5806 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*sinh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0)))**n_, x_), cons2, cons3, cons8, cons29, cons50, cons19, cons87, cons167) rule5806 = ReplacementRule(pattern5806, replacement5806) pattern5807 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*cosh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0)))**n_, x_), cons2, cons3, cons8, cons29, cons50, cons19, cons87, cons167) rule5807 = ReplacementRule(pattern5807, replacement5807) pattern5808 = Pattern(Integral(u_**WC('m', S(1))*sinh(v_)**WC('n', S(1)), x_), cons19, cons150, cons70, cons820, cons821) rule5808 = ReplacementRule(pattern5808, replacement5808) pattern5809 = Pattern(Integral(u_**WC('m', S(1))*cosh(v_)**WC('n', S(1)), x_), cons19, cons150, cons70, cons820, cons821) rule5809 = ReplacementRule(pattern5809, replacement5809) pattern5810 = Pattern(Integral((x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons2, cons3, cons50, cons127, cons64) rule5810 = ReplacementRule(pattern5810, replacement5810) pattern5811 = Pattern(Integral((x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))), x_), cons2, cons3, cons50, cons127, cons64) rule5811 = ReplacementRule(pattern5811, replacement5811) pattern5812 = Pattern(Integral((WC('c', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons50, cons127, cons95, cons167, cons170) rule5812 = ReplacementRule(pattern5812, replacement5812) pattern5813 = Pattern(Integral((WC('c', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons50, cons127, cons95, cons167, cons170) rule5813 = ReplacementRule(pattern5813, replacement5813) pattern5814 = Pattern(Integral((WC('c', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons50, cons127, cons95, cons91, cons170) rule5814 = ReplacementRule(pattern5814, replacement5814) pattern5815 = Pattern(Integral((WC('c', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons50, cons127, cons95, cons91, cons170) rule5815 = ReplacementRule(pattern5815, replacement5815) pattern5816 = Pattern(Integral((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons530) rule5816 = ReplacementRule(pattern5816, replacement5816) pattern5817 = Pattern(Integral((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons530) rule5817 = ReplacementRule(pattern5817, replacement5817) pattern5818 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons33, cons170) rule5818 = ReplacementRule(pattern5818, replacement5818) pattern5819 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons33, cons170) rule5819 = ReplacementRule(pattern5819, replacement5819) pattern5820 = Pattern(Integral(S(1)/((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))*(x_*WC('d', S(1)) + WC('c', S(0)))**S(2)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267) rule5820 = ReplacementRule(pattern5820, replacement5820) pattern5821 = Pattern(Integral(S(1)/((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))*(x_*WC('d', S(1)) + WC('c', S(0)))**S(2)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267) rule5821 = ReplacementRule(pattern5821, replacement5821) pattern5822 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_/(a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons33, cons96, cons1512) rule5822 = ReplacementRule(pattern5822, replacement5822) pattern5823 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_/(a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons33, cons96, cons1512) rule5823 = ReplacementRule(pattern5823, replacement5823) pattern5824 = Pattern(Integral(S(1)/((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))*(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267) rule5824 = ReplacementRule(pattern5824, replacement5824) pattern5825 = Pattern(Integral(S(1)/((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))*(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267) rule5825 = ReplacementRule(pattern5825, replacement5825) pattern5826 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_/(a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1267, cons21) rule5826 = ReplacementRule(pattern5826, replacement5826) pattern5827 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_/(a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1267, cons21) rule5827 = ReplacementRule(pattern5827, replacement5827) pattern5828 = Pattern(Integral((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons1573) rule5828 = ReplacementRule(pattern5828, replacement5828) pattern5829 = Pattern(Integral((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons1573) rule5829 = ReplacementRule(pattern5829, replacement5829) pattern5830 = Pattern(Integral((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1267, cons198) rule5830 = ReplacementRule(pattern5830, replacement5830) pattern5831 = Pattern(Integral((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**m_, x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1267, cons198) rule5831 = ReplacementRule(pattern5831, replacement5831) pattern5832 = Pattern(Integral((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons1574, cons33, cons170) rule5832 = ReplacementRule(pattern5832, With5832) pattern5833 = Pattern(Integral((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1267, cons1574, cons33, cons170) rule5833 = ReplacementRule(pattern5833, With5833) pattern5834 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons64) rule5834 = ReplacementRule(pattern5834, replacement5834) pattern5835 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/(a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons64) rule5835 = ReplacementRule(pattern5835, replacement5835) pattern5836 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))/(a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269) rule5836 = ReplacementRule(pattern5836, replacement5836) pattern5837 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))/(a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269) rule5837 = ReplacementRule(pattern5837, replacement5837) pattern5838 = Pattern(Integral((a_ + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons198, cons64) rule5838 = ReplacementRule(pattern5838, replacement5838) pattern5839 = Pattern(Integral((a_ + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**n_*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons1269, cons198, cons64) rule5839 = ReplacementRule(pattern5839, replacement5839) pattern5840 = Pattern(Integral(u_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*tanh(v_))**WC('n', S(1)), x_), cons2, cons3, cons19, cons4, cons812, cons813) rule5840 = ReplacementRule(pattern5840, replacement5840) pattern5841 = Pattern(Integral(u_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/tanh(v_))**WC('n', S(1)), x_), cons2, cons3, cons19, cons4, cons812, cons813) rule5841 = ReplacementRule(pattern5841, replacement5841) pattern5842 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*tanh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons4, cons1362) rule5842 = ReplacementRule(pattern5842, replacement5842) pattern5843 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/tanh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons4, cons1362) rule5843 = ReplacementRule(pattern5843, replacement5843) pattern5844 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons5, cons1575, cons40) rule5844 = ReplacementRule(pattern5844, replacement5844) pattern5845 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons5, cons1575, cons40) rule5845 = ReplacementRule(pattern5845, replacement5845) pattern5846 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons1497) rule5846 = ReplacementRule(pattern5846, replacement5846) pattern5847 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons1497) rule5847 = ReplacementRule(pattern5847, replacement5847) pattern5848 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*tanh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70, cons71) rule5848 = ReplacementRule(pattern5848, replacement5848) pattern5849 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/tanh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70, cons71) rule5849 = ReplacementRule(pattern5849, replacement5849) pattern5850 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))*tanh(u_))**WC('p', S(1)), x_), cons2, cons3, cons5, cons825, cons826) rule5850 = ReplacementRule(pattern5850, replacement5850) pattern5851 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/tanh(u_))**WC('p', S(1)), x_), cons2, cons3, cons5, cons825, cons826) rule5851 = ReplacementRule(pattern5851, replacement5851) pattern5852 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1576, cons40) rule5852 = ReplacementRule(pattern5852, replacement5852) pattern5853 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1576, cons40) rule5853 = ReplacementRule(pattern5853, replacement5853) pattern5854 = Pattern(Integral(x_**WC('m', S(1))*tanh(x_**n_*WC('d', S(1)) + WC('c', S(0)))**S(2), x_), cons8, cons29, cons19, cons4, cons1577) rule5854 = ReplacementRule(pattern5854, replacement5854) pattern5855 = Pattern(Integral(x_**WC('m', S(1))/tanh(x_**n_*WC('d', S(1)) + WC('c', S(0)))**S(2), x_), cons8, cons29, cons19, cons4, cons1577) rule5855 = ReplacementRule(pattern5855, replacement5855) pattern5856 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1578) rule5856 = ReplacementRule(pattern5856, replacement5856) pattern5857 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1578) rule5857 = ReplacementRule(pattern5857, replacement5857) pattern5858 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons1499) rule5858 = ReplacementRule(pattern5858, replacement5858) pattern5859 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/tanh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons1499) rule5859 = ReplacementRule(pattern5859, replacement5859) pattern5860 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))*tanh(u_))**WC('p', S(1)), x_), cons2, cons3, cons50, cons19, cons5, cons825, cons826) rule5860 = ReplacementRule(pattern5860, replacement5860) pattern5861 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/tanh(u_))**WC('p', S(1)), x_), cons2, cons3, cons50, cons19, cons5, cons825, cons826) rule5861 = ReplacementRule(pattern5861, replacement5861) pattern5862 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))))**WC('p', S(1))*tanh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0)))**WC('q', S(1)), x_), cons2, cons3, cons5, cons33, cons87, cons1579, cons1580) rule5862 = ReplacementRule(pattern5862, replacement5862) pattern5863 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))))**WC('p', S(1))*(S(1)/tanh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))))**WC('q', S(1)), x_), cons2, cons3, cons5, cons33, cons87, cons1579, cons1580) rule5863 = ReplacementRule(pattern5863, replacement5863) pattern5864 = Pattern(Integral(tanh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1)), x_), cons2, cons3, cons8, cons4, cons1581) rule5864 = ReplacementRule(pattern5864, replacement5864) pattern5865 = Pattern(Integral((S(1)/tanh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons4, cons1581) rule5865 = ReplacementRule(pattern5865, replacement5865) pattern5866 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))*tanh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons1045) rule5866 = ReplacementRule(pattern5866, replacement5866) pattern5867 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))/tanh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons1045) rule5867 = ReplacementRule(pattern5867, replacement5867) pattern5868 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*tanh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons1582) rule5868 = ReplacementRule(pattern5868, replacement5868) pattern5869 = Pattern(Integral((x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*(S(1)/tanh(x_**S(2)*WC('c', S(1)) + x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons1582) rule5869 = ReplacementRule(pattern5869, replacement5869) pattern5870 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/cosh(x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons64) rule5870 = ReplacementRule(pattern5870, replacement5870) pattern5871 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/sinh(x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons64) rule5871 = ReplacementRule(pattern5871, replacement5871) pattern5872 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/cosh(x_*WC('b', S(1)) + WC('a', S(0)))**S(2), x_), cons2, cons3, cons8, cons29, cons33, cons170) rule5872 = ReplacementRule(pattern5872, replacement5872) pattern5873 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))/sinh(x_*WC('b', S(1)) + WC('a', S(0)))**S(2), x_), cons2, cons3, cons8, cons29, cons33, cons170) rule5873 = ReplacementRule(pattern5873, replacement5873) pattern5874 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons89, cons167, cons1646) rule5874 = ReplacementRule(pattern5874, replacement5874) pattern5875 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons89, cons167, cons1646) rule5875 = ReplacementRule(pattern5875, replacement5875) pattern5876 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons95, cons167, cons1646, cons168) rule5876 = ReplacementRule(pattern5876, replacement5876) pattern5877 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons95, cons167, cons1646, cons168) rule5877 = ReplacementRule(pattern5877, replacement5877) pattern5878 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons89, cons91) rule5878 = ReplacementRule(pattern5878, replacement5878) pattern5879 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons89, cons91) rule5879 = ReplacementRule(pattern5879, replacement5879) pattern5880 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons95, cons91, cons168) rule5880 = ReplacementRule(pattern5880, replacement5880) pattern5881 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**m_*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons95, cons91, cons168) rule5881 = ReplacementRule(pattern5881, replacement5881) pattern5882 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons19, cons4, cons25) rule5882 = ReplacementRule(pattern5882, replacement5882) pattern5883 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**n_, x_), cons2, cons3, cons8, cons29, cons19, cons4, cons25) rule5883 = ReplacementRule(pattern5883, replacement5883) pattern5884 = Pattern(Integral((a_ + WC('b', S(1))/cosh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons530) rule5884 = ReplacementRule(pattern5884, replacement5884) pattern5885 = Pattern(Integral((a_ + WC('b', S(1))/sinh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons530) rule5885 = ReplacementRule(pattern5885, replacement5885) pattern5886 = Pattern(Integral((a_ + WC('b', S(1))/cosh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons198, cons64) rule5886 = ReplacementRule(pattern5886, replacement5886) pattern5887 = Pattern(Integral((a_ + WC('b', S(1))/sinh(x_*WC('f', S(1)) + WC('e', S(0))))**WC('n', S(1))*(x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons198, cons64) rule5887 = ReplacementRule(pattern5887, replacement5887) pattern5888 = Pattern(Integral(u_**WC('m', S(1))*(S(1)/cosh(v_))**WC('n', S(1)), x_), cons19, cons4, cons812, cons813) rule5888 = ReplacementRule(pattern5888, replacement5888) pattern5889 = Pattern(Integral(u_**WC('m', S(1))*(S(1)/sinh(v_))**WC('n', S(1)), x_), cons19, cons4, cons812, cons813) rule5889 = ReplacementRule(pattern5889, replacement5889) pattern5890 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons1738) rule5890 = ReplacementRule(pattern5890, replacement5890) pattern5891 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons1738) rule5891 = ReplacementRule(pattern5891, replacement5891) pattern5892 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons5, cons1575, cons40) rule5892 = ReplacementRule(pattern5892, replacement5892) pattern5893 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons5, cons1575, cons40) rule5893 = ReplacementRule(pattern5893, replacement5893) pattern5894 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons1497) rule5894 = ReplacementRule(pattern5894, replacement5894) pattern5895 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons1497) rule5895 = ReplacementRule(pattern5895, replacement5895) pattern5896 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/cosh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70, cons71) rule5896 = ReplacementRule(pattern5896, replacement5896) pattern5897 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/sinh(u_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons70, cons71) rule5897 = ReplacementRule(pattern5897, replacement5897) pattern5898 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/cosh(u_))**WC('p', S(1)), x_), cons2, cons3, cons5, cons825, cons826) rule5898 = ReplacementRule(pattern5898, replacement5898) pattern5899 = Pattern(Integral((WC('a', S(0)) + WC('b', S(1))/sinh(u_))**WC('p', S(1)), x_), cons2, cons3, cons5, cons825, cons826) rule5899 = ReplacementRule(pattern5899, replacement5899) pattern5900 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1576, cons40) rule5900 = ReplacementRule(pattern5900, replacement5900) pattern5901 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1576, cons40) rule5901 = ReplacementRule(pattern5901, replacement5901) pattern5902 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1578) rule5902 = ReplacementRule(pattern5902, replacement5902) pattern5903 = Pattern(Integral(x_**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons4, cons5, cons1578) rule5903 = ReplacementRule(pattern5903, replacement5903) pattern5904 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/cosh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons1499) rule5904 = ReplacementRule(pattern5904, replacement5904) pattern5905 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/sinh(x_**n_*WC('d', S(1)) + WC('c', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons19, cons4, cons5, cons1499) rule5905 = ReplacementRule(pattern5905, replacement5905) pattern5906 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/cosh(u_))**WC('p', S(1)), x_), cons2, cons3, cons50, cons19, cons5, cons825, cons826) rule5906 = ReplacementRule(pattern5906, replacement5906) pattern5907 = Pattern(Integral((e_*x_)**WC('m', S(1))*(WC('a', S(0)) + WC('b', S(1))/sinh(u_))**WC('p', S(1)), x_), cons2, cons3, cons50, cons19, cons5, cons825, cons826) rule5907 = ReplacementRule(pattern5907, replacement5907) pattern5908 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))))**p_*sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons5, cons33, cons87, cons1579, cons1647) rule5908 = ReplacementRule(pattern5908, replacement5908) pattern5909 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))))**p_*cosh(x_**WC('n', S(1))*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons5, cons33, cons87, cons1579, cons1647) rule5909 = ReplacementRule(pattern5909, replacement5909) pattern5910 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1))*cosh(x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons4, cons64, cons586) rule5910 = ReplacementRule(pattern5910, replacement5910) pattern5911 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))*cosh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons64, cons586) rule5911 = ReplacementRule(pattern5911, replacement5911) pattern5912 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1))*cosh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons466) rule5912 = ReplacementRule(pattern5912, replacement5912) pattern5913 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons466) rule5913 = ReplacementRule(pattern5913, replacement5913) pattern5914 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/tanh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('p', S(1))*cosh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons19, cons466) rule5914 = ReplacementRule(pattern5914, replacement5914) pattern5915 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons1685, cons33, cons170) rule5915 = ReplacementRule(pattern5915, replacement5915) pattern5916 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*(S(1)/tanh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons1685, cons33, cons170) rule5916 = ReplacementRule(pattern5916, replacement5916) pattern5917 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('n', S(1))/cosh(x_*WC('b', S(1)) + WC('a', S(0)))**S(2), x_), cons2, cons3, cons8, cons29, cons4, cons64, cons586) rule5917 = ReplacementRule(pattern5917, replacement5917) pattern5918 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/tanh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))/sinh(x_*WC('b', S(1)) + WC('a', S(0)))**S(2), x_), cons2, cons3, cons8, cons29, cons4, cons64, cons586) rule5918 = ReplacementRule(pattern5918, replacement5918) pattern5919 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))**p_/cosh(x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons19, cons1410) rule5919 = ReplacementRule(pattern5919, replacement5919) pattern5920 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))**p_, x_), cons2, cons3, cons8, cons29, cons19, cons4, cons1410) rule5920 = ReplacementRule(pattern5920, replacement5920) pattern5921 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/tanh(x_*WC('b', S(1)) + WC('a', S(0))))**p_/sinh(x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons19, cons1410) rule5921 = ReplacementRule(pattern5921, replacement5921) pattern5922 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*(S(1)/tanh(x_*WC('b', S(1)) + WC('a', S(0))))**p_, x_), cons2, cons3, cons8, cons29, cons19, cons4, cons1410) rule5922 = ReplacementRule(pattern5922, replacement5922) pattern5923 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons64, cons1686) rule5923 = ReplacementRule(pattern5923, With5923) pattern5924 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*(S(1)/tanh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons4, cons5, cons64, cons1686) rule5924 = ReplacementRule(pattern5924, With5924) pattern5925 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons33, cons87) rule5925 = ReplacementRule(pattern5925, replacement5925) pattern5926 = Pattern(Integral((x_*WC('d', S(1)) + WC('c', S(0)))**WC('m', S(1))*(S(1)/sinh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('n', S(1))*(S(1)/cosh(x_*WC('b', S(1)) + WC('a', S(0))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons378, cons33, cons170, cons1687) rule5926 = ReplacementRule(pattern5926, With5926) pattern5927 = Pattern(Integral(F_**v_*G_**w_*u_**WC('m', S(1)), x_), cons19, cons4, cons5, cons1862, cons1863, cons1690, cons814, cons815) rule5927 = ReplacementRule(pattern5927, replacement5927) pattern5928 = Pattern(Integral((a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons586) rule5928 = ReplacementRule(pattern5928, replacement5928) pattern5929 = Pattern(Integral((a_ + WC('b', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons586) rule5929 = ReplacementRule(pattern5929, replacement5929) pattern5930 = Pattern(Integral((a_ + WC('b', S(1))*tanh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))/cosh(x_*WC('d', S(1)) + WC('c', S(0)))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons586) rule5930 = ReplacementRule(pattern5930, replacement5930) pattern5931 = Pattern(Integral((a_ + WC('b', S(1))/tanh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))/sinh(x_*WC('d', S(1)) + WC('c', S(0)))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons586) rule5931 = ReplacementRule(pattern5931, replacement5931) pattern5932 = Pattern(Integral((a_ + WC('b', S(1))/cosh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*tanh(x_*WC('d', S(1)) + WC('c', S(0)))/cosh(x_*WC('d', S(1)) + WC('c', S(0))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons586) rule5932 = ReplacementRule(pattern5932, replacement5932) pattern5933 = Pattern(Integral((a_ + WC('b', S(1))/sinh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))/(sinh(x_*WC('d', S(1)) + WC('c', S(0)))*tanh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons586) rule5933 = ReplacementRule(pattern5933, replacement5933) pattern5934 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))**WC('q', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons557, cons20) rule5934 = ReplacementRule(pattern5934, replacement5934) pattern5935 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*cosh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))**WC('q', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons557, cons20) rule5935 = ReplacementRule(pattern5935, replacement5935) pattern5936 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))**WC('q', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons557) rule5936 = ReplacementRule(pattern5936, replacement5936) pattern5937 = Pattern(Integral(F_**(x_*WC('b', S(1)) + WC('a', S(0)))*G_**(x_*WC('d', S(1)) + WC('c', S(0)))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons1864, cons1865, cons557, cons27, cons1693) rule5937 = ReplacementRule(pattern5937, replacement5937) pattern5938 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*sinh(x_*WC('e', S(1)) + WC('d', S(0))), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1866) rule5938 = ReplacementRule(pattern5938, replacement5938) pattern5939 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*cosh(x_*WC('e', S(1)) + WC('d', S(0))), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1866) rule5939 = ReplacementRule(pattern5939, replacement5939) pattern5940 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1867, cons89, cons167) rule5940 = ReplacementRule(pattern5940, replacement5940) pattern5941 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1867, cons89, cons167) rule5941 = ReplacementRule(pattern5941, replacement5941) pattern5942 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons4, cons1868, cons586, cons1397) rule5942 = ReplacementRule(pattern5942, replacement5942) pattern5943 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons4, cons1868, cons586, cons1397) rule5943 = ReplacementRule(pattern5943, replacement5943) pattern5944 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1869, cons89, cons91, cons1444) rule5944 = ReplacementRule(pattern5944, replacement5944) pattern5945 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1869, cons89, cons91, cons1444) rule5945 = ReplacementRule(pattern5945, replacement5945) pattern5946 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons4, cons25) rule5946 = ReplacementRule(pattern5946, replacement5946) pattern5947 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons4, cons25) rule5947 = ReplacementRule(pattern5947, replacement5947) pattern5948 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*tanh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons87) rule5948 = ReplacementRule(pattern5948, replacement5948) pattern5949 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/tanh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons87) rule5949 = ReplacementRule(pattern5949, replacement5949) pattern5950 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/cosh(x_*WC('e', S(1)) + WC('d', S(0))))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1695, cons89, cons91) rule5950 = ReplacementRule(pattern5950, replacement5950) pattern5951 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/sinh(x_*WC('e', S(1)) + WC('d', S(0))))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1695, cons89, cons91) rule5951 = ReplacementRule(pattern5951, replacement5951) pattern5952 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/cosh(x_*WC('e', S(1)) + WC('d', S(0))))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons4, cons1870, cons1504, cons965) rule5952 = ReplacementRule(pattern5952, replacement5952) pattern5953 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/sinh(x_*WC('e', S(1)) + WC('d', S(0))))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons4, cons1870, cons1504, cons965) rule5953 = ReplacementRule(pattern5953, replacement5953) pattern5954 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/cosh(x_*WC('e', S(1)) + WC('d', S(0))))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1871, cons89, cons167, cons1646) rule5954 = ReplacementRule(pattern5954, replacement5954) pattern5955 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/sinh(x_*WC('e', S(1)) + WC('d', S(0))))**n_, x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons1871, cons89, cons167, cons1646) rule5955 = ReplacementRule(pattern5955, replacement5955) pattern5956 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/cosh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons87) rule5956 = ReplacementRule(pattern5956, replacement5956) pattern5957 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/sinh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons87) rule5957 = ReplacementRule(pattern5957, replacement5957) pattern5958 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/cosh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons25) rule5958 = ReplacementRule(pattern5958, replacement5958) pattern5959 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(S(1)/sinh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons25) rule5959 = ReplacementRule(pattern5959, replacement5959) pattern5960 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(f_ + WC('g', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1872, cons198) rule5960 = ReplacementRule(pattern5960, replacement5960) pattern5961 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(f_ + WC('g', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1702, cons198) rule5961 = ReplacementRule(pattern5961, replacement5961) pattern5962 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(f_ + WC('g', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1013, cons198) rule5962 = ReplacementRule(pattern5962, replacement5962) pattern5963 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(f_ + WC('g', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1872, cons152, cons1553) rule5963 = ReplacementRule(pattern5963, replacement5963) pattern5964 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(f_ + WC('g', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1702, cons152, cons1553) rule5964 = ReplacementRule(pattern5964, replacement5964) pattern5965 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(f_ + WC('g', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0))))**WC('n', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1013, cons152, cons1553) rule5965 = ReplacementRule(pattern5965, replacement5965) pattern5966 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(h_ + WC('i', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0))))/(f_ + WC('g', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons211, cons226, cons1872, cons1703, cons1704) rule5966 = ReplacementRule(pattern5966, replacement5966) pattern5967 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*(h_ + WC('i', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0))))/(f_ + WC('g', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons211, cons226, cons1701, cons1873, cons1705) rule5967 = ReplacementRule(pattern5967, replacement5967) pattern5968 = Pattern(Integral(F_**(u_*WC('c', S(1)))*G_**v_, x_), cons1101, cons8, cons4, cons1863, cons812, cons813) rule5968 = ReplacementRule(pattern5968, replacement5968) pattern5969 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*x_**WC('m', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons33, cons170, cons150) rule5969 = ReplacementRule(pattern5969, With5969) pattern5970 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*x_**WC('m', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons33, cons170, cons150) rule5970 = ReplacementRule(pattern5970, With5970) pattern5971 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*cosh(x_*WC('g', S(1)) + WC('f', S(0)))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons530) rule5971 = ReplacementRule(pattern5971, replacement5971) pattern5972 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*x_**WC('p', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**WC('m', S(1))*cosh(x_*WC('g', S(1)) + WC('f', S(0)))**WC('n', S(1)), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons1706) rule5972 = ReplacementRule(pattern5972, replacement5972) pattern5973 = Pattern(Integral(F_**((x_*WC('b', S(1)) + WC('a', S(0)))*WC('c', S(1)))*G_**(x_*WC('e', S(1)) + WC('d', S(0)))*H_**(x_*WC('e', S(1)) + WC('d', S(0))), x_), cons1101, cons2, cons3, cons8, cons29, cons50, cons530, cons1863, cons1874) rule5973 = ReplacementRule(pattern5973, replacement5973) pattern5974 = Pattern(Integral(F_**u_*sinh(v_)**WC('n', S(1)), x_), cons1101, cons1708, cons1709, cons150) rule5974 = ReplacementRule(pattern5974, replacement5974) pattern5975 = Pattern(Integral(F_**u_*cosh(v_)**WC('n', S(1)), x_), cons1101, cons1708, cons1709, cons150) rule5975 = ReplacementRule(pattern5975, replacement5975) pattern5976 = Pattern(Integral(F_**u_*sinh(v_)**WC('m', S(1))*cosh(v_)**WC('n', S(1)), x_), cons1101, cons1708, cons1709, cons530) rule5976 = ReplacementRule(pattern5976, replacement5976) pattern5977 = Pattern(Integral(sinh(WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**WC('p', S(1)), x_), cons8, cons1875) rule5977 = ReplacementRule(pattern5977, replacement5977) pattern5978 = Pattern(Integral(cosh(WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**WC('p', S(1)), x_), cons8, cons1875) rule5978 = ReplacementRule(pattern5978, replacement5978) pattern5979 = Pattern(Integral(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons5, cons1876, cons56) rule5979 = ReplacementRule(pattern5979, replacement5979) pattern5980 = Pattern(Integral(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons5, cons1876, cons56) rule5980 = ReplacementRule(pattern5980, replacement5980) pattern5981 = Pattern(Integral(sqrt(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))), x_), cons2, cons3, cons8, cons4, cons1877) rule5981 = ReplacementRule(pattern5981, replacement5981) pattern5982 = Pattern(Integral(sqrt(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))), x_), cons2, cons3, cons8, cons4, cons1877) rule5982 = ReplacementRule(pattern5982, replacement5982) pattern5983 = Pattern(Integral(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons4, cons130, cons1878) rule5983 = ReplacementRule(pattern5983, replacement5983) pattern5984 = Pattern(Integral(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons4, cons130, cons1878) rule5984 = ReplacementRule(pattern5984, replacement5984) pattern5985 = Pattern(Integral(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons4, cons1879) rule5985 = ReplacementRule(pattern5985, replacement5985) pattern5986 = Pattern(Integral(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons4, cons1879) rule5986 = ReplacementRule(pattern5986, replacement5986) pattern5987 = Pattern(Integral(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons148, cons1880) rule5987 = ReplacementRule(pattern5987, replacement5987) pattern5988 = Pattern(Integral(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons148, cons1880) rule5988 = ReplacementRule(pattern5988, replacement5988) pattern5989 = Pattern(Integral(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons139, cons1507, cons1881) rule5989 = ReplacementRule(pattern5989, replacement5989) pattern5990 = Pattern(Integral(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons139, cons1507, cons1881) rule5990 = ReplacementRule(pattern5990, replacement5990) pattern5991 = Pattern(Integral(sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons5, cons1880) rule5991 = ReplacementRule(pattern5991, replacement5991) pattern5992 = Pattern(Integral(cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons4, cons5, cons1880) rule5992 = ReplacementRule(pattern5992, replacement5992) pattern5993 = Pattern(Integral(x_**WC('m', S(1))*sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1882, cons56, cons68) rule5993 = ReplacementRule(pattern5993, replacement5993) pattern5994 = Pattern(Integral(x_**WC('m', S(1))*cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1882, cons56, cons68) rule5994 = ReplacementRule(pattern5994, replacement5994) pattern5995 = Pattern(Integral(x_**WC('m', S(1))*sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons19, cons4, cons130, cons1883) rule5995 = ReplacementRule(pattern5995, replacement5995) pattern5996 = Pattern(Integral(x_**WC('m', S(1))*cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons19, cons4, cons130, cons1883) rule5996 = ReplacementRule(pattern5996, replacement5996) pattern5997 = Pattern(Integral(x_**WC('m', S(1))*sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons19, cons4, cons1884, cons68) rule5997 = ReplacementRule(pattern5997, replacement5997) pattern5998 = Pattern(Integral(x_**WC('m', S(1))*cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons19, cons4, cons1884, cons68) rule5998 = ReplacementRule(pattern5998, replacement5998) pattern5999 = Pattern(Integral(x_**WC('m', S(1))*sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons1885, cons13, cons148, cons68) rule5999 = ReplacementRule(pattern5999, replacement5999) pattern6000 = Pattern(Integral(x_**WC('m', S(1))*cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons1885, cons13, cons148, cons68) rule6000 = ReplacementRule(pattern6000, replacement6000) pattern6001 = Pattern(Integral(x_**WC('m', S(1))*sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons1886, cons13, cons139, cons1507, cons68) rule6001 = ReplacementRule(pattern6001, replacement6001) pattern6002 = Pattern(Integral(x_**WC('m', S(1))*cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons1886, cons13, cons139, cons1507, cons68) rule6002 = ReplacementRule(pattern6002, replacement6002) pattern6003 = Pattern(Integral(x_**WC('m', S(1))*sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1885) rule6003 = ReplacementRule(pattern6003, replacement6003) pattern6004 = Pattern(Integral(x_**WC('m', S(1))*cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1885) rule6004 = ReplacementRule(pattern6004, replacement6004) pattern6005 = Pattern(Integral((S(1)/cosh(WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons8, cons1875) rule6005 = ReplacementRule(pattern6005, replacement6005) pattern6006 = Pattern(Integral((S(1)/sinh(WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons8, cons1875) rule6006 = ReplacementRule(pattern6006, replacement6006) pattern6007 = Pattern(Integral(S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons4, cons1887) rule6007 = ReplacementRule(pattern6007, replacement6007) pattern6008 = Pattern(Integral(S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons4, cons1887) rule6008 = ReplacementRule(pattern6008, replacement6008) pattern6009 = Pattern(Integral((S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons4, cons5, cons1888, cons1647) rule6009 = ReplacementRule(pattern6009, replacement6009) pattern6010 = Pattern(Integral((S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons4, cons5, cons1888, cons1647) rule6010 = ReplacementRule(pattern6010, replacement6010) pattern6011 = Pattern(Integral((S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons148, cons1722, cons1889) rule6011 = ReplacementRule(pattern6011, replacement6011) pattern6012 = Pattern(Integral((S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons148, cons1722, cons1889) rule6012 = ReplacementRule(pattern6012, replacement6012) pattern6013 = Pattern(Integral((S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons139, cons1880) rule6013 = ReplacementRule(pattern6013, replacement6013) pattern6014 = Pattern(Integral((S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons4, cons13, cons139, cons1880) rule6014 = ReplacementRule(pattern6014, replacement6014) pattern6015 = Pattern(Integral((S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons4, cons5, cons1880) rule6015 = ReplacementRule(pattern6015, replacement6015) pattern6016 = Pattern(Integral((S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons4, cons5, cons1880) rule6016 = ReplacementRule(pattern6016, replacement6016) pattern6017 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons8, cons1890) rule6017 = ReplacementRule(pattern6017, replacement6017) pattern6018 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons8, cons1890) rule6018 = ReplacementRule(pattern6018, replacement6018) pattern6019 = Pattern(Integral(x_**WC('m', S(1))/cos(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons19, cons4, cons1891) rule6019 = ReplacementRule(pattern6019, replacement6019) pattern6020 = Pattern(Integral(x_**WC('m', S(1))/sin(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))), x_), cons2, cons3, cons8, cons19, cons4, cons1891) rule6020 = ReplacementRule(pattern6020, replacement6020) pattern6021 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1725, cons68, cons1647) rule6021 = ReplacementRule(pattern6021, replacement6021) pattern6022 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1725, cons68, cons1647) rule6022 = ReplacementRule(pattern6022, replacement6022) pattern6023 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons13, cons148, cons1722, cons1892) rule6023 = ReplacementRule(pattern6023, replacement6023) pattern6024 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons13, cons148, cons1722, cons1892) rule6024 = ReplacementRule(pattern6024, replacement6024) pattern6025 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons13, cons139, cons1885) rule6025 = ReplacementRule(pattern6025, replacement6025) pattern6026 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**p_, x_), cons2, cons3, cons8, cons19, cons4, cons13, cons139, cons1885) rule6026 = ReplacementRule(pattern6026, replacement6026) pattern6027 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/cosh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1885) rule6027 = ReplacementRule(pattern6027, replacement6027) pattern6028 = Pattern(Integral(x_**WC('m', S(1))*(S(1)/sinh(WC('a', S(0)) + WC('b', S(1))*log(x_**WC('n', S(1))*WC('c', S(1)))))**WC('p', S(1)), x_), cons2, cons3, cons8, cons19, cons4, cons5, cons1885) rule6028 = ReplacementRule(pattern6028, replacement6028) pattern6029 = Pattern(Integral(log(x_*WC('b', S(1)))**WC('p', S(1))*sinh(x_*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons13, cons165) rule6029 = ReplacementRule(pattern6029, replacement6029) pattern6030 = Pattern(Integral(log(x_*WC('b', S(1)))**WC('p', S(1))*cosh(x_*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons13, cons165) rule6030 = ReplacementRule(pattern6030, replacement6030) pattern6031 = Pattern(Integral(log(x_*WC('b', S(1)))**WC('p', S(1))*sinh(x_**n_*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons340, cons165) rule6031 = ReplacementRule(pattern6031, replacement6031) pattern6032 = Pattern(Integral(log(x_*WC('b', S(1)))**WC('p', S(1))*cosh(x_**n_*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons340, cons165) rule6032 = ReplacementRule(pattern6032, replacement6032) pattern6033 = Pattern(Integral(x_**WC('m', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))*sinh(x_**WC('n', S(1))*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons19, cons4, cons55, cons13, cons165) rule6033 = ReplacementRule(pattern6033, replacement6033) pattern6034 = Pattern(Integral(x_**WC('m', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))*cosh(x_**WC('n', S(1))*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons19, cons4, cons55, cons13, cons165) rule6034 = ReplacementRule(pattern6034, replacement6034) pattern6035 = Pattern(Integral(x_**m_*log(x_*WC('b', S(1)))**WC('p', S(1))*sinh(x_**WC('n', S(1))*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons164, cons165, cons629) rule6035 = ReplacementRule(pattern6035, replacement6035) pattern6036 = Pattern(Integral(x_**m_*log(x_*WC('b', S(1)))**WC('p', S(1))*cosh(x_**WC('n', S(1))*WC('a', S(1))*log(x_*WC('b', S(1)))**WC('p', S(1))), x_), cons2, cons3, cons164, cons165, cons629) rule6036 = ReplacementRule(pattern6036, replacement6036) pattern6037 = Pattern(Integral(sinh(WC('a', S(1))/(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1)), x_), cons2, cons8, cons29, cons150) rule6037 = ReplacementRule(pattern6037, replacement6037) pattern6038 = Pattern(Integral(cosh(WC('a', S(1))/(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1)), x_), cons2, cons8, cons29, cons150) rule6038 = ReplacementRule(pattern6038, replacement6038) pattern6039 = Pattern(Integral(sinh((x_*WC('b', S(1)) + WC('a', S(0)))*WC('e', S(1))/(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons150, cons73) rule6039 = ReplacementRule(pattern6039, replacement6039) pattern6040 = Pattern(Integral(cosh((x_*WC('b', S(1)) + WC('a', S(0)))*WC('e', S(1))/(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons150, cons73) rule6040 = ReplacementRule(pattern6040, replacement6040) pattern6041 = Pattern(Integral(sinh(u_)**WC('n', S(1)), x_), cons150, cons1727) rule6041 = ReplacementRule(pattern6041, With6041) pattern6042 = Pattern(Integral(cosh(u_)**WC('n', S(1)), x_), cons150, cons1727) rule6042 = ReplacementRule(pattern6042, With6042) pattern6043 = Pattern(Integral(WC('u', S(1))*sinh(v_)**WC('p', S(1))*sinh(w_)**WC('q', S(1)), x_), cons1690) rule6043 = ReplacementRule(pattern6043, replacement6043) pattern6044 = Pattern(Integral(WC('u', S(1))*cosh(v_)**WC('p', S(1))*cosh(w_)**WC('q', S(1)), x_), cons1690) rule6044 = ReplacementRule(pattern6044, replacement6044) pattern6045 = Pattern(Integral(sinh(v_)**WC('p', S(1))*sinh(w_)**WC('q', S(1)), x_), cons557, cons1728) rule6045 = ReplacementRule(pattern6045, replacement6045) pattern6046 = Pattern(Integral(cosh(v_)**WC('p', S(1))*cosh(w_)**WC('q', S(1)), x_), cons557, cons1728) rule6046 = ReplacementRule(pattern6046, replacement6046) pattern6047 = Pattern(Integral(x_**WC('m', S(1))*sinh(v_)**WC('p', S(1))*sinh(w_)**WC('q', S(1)), x_), cons1729, cons1728) rule6047 = ReplacementRule(pattern6047, replacement6047) pattern6048 = Pattern(Integral(x_**WC('m', S(1))*cosh(v_)**WC('p', S(1))*cosh(w_)**WC('q', S(1)), x_), cons1729, cons1728) rule6048 = ReplacementRule(pattern6048, replacement6048) pattern6049 = Pattern(Integral(WC('u', S(1))*sinh(v_)**WC('p', S(1))*cosh(w_)**WC('p', S(1)), x_), cons1690, cons40) rule6049 = ReplacementRule(pattern6049, replacement6049) pattern6050 = Pattern(Integral(sinh(v_)**WC('p', S(1))*cosh(w_)**WC('q', S(1)), x_), cons557, cons1728) rule6050 = ReplacementRule(pattern6050, replacement6050) pattern6051 = Pattern(Integral(x_**WC('m', S(1))*sinh(v_)**WC('p', S(1))*cosh(w_)**WC('q', S(1)), x_), cons1729, cons1728) rule6051 = ReplacementRule(pattern6051, replacement6051) pattern6052 = Pattern(Integral(sinh(v_)*tanh(w_)**WC('n', S(1)), x_), cons89, cons90, cons1730) rule6052 = ReplacementRule(pattern6052, replacement6052) pattern6053 = Pattern(Integral((S(1)/tanh(w_))**WC('n', S(1))*cosh(v_), x_), cons89, cons90, cons1730) rule6053 = ReplacementRule(pattern6053, replacement6053) pattern6054 = Pattern(Integral((S(1)/tanh(w_))**WC('n', S(1))*sinh(v_), x_), cons89, cons90, cons1730) rule6054 = ReplacementRule(pattern6054, replacement6054) pattern6055 = Pattern(Integral(cosh(v_)*tanh(w_)**WC('n', S(1)), x_), cons89, cons90, cons1730) rule6055 = ReplacementRule(pattern6055, replacement6055) pattern6056 = Pattern(Integral((S(1)/cosh(w_))**WC('n', S(1))*sinh(v_), x_), cons89, cons90, cons1730) rule6056 = ReplacementRule(pattern6056, replacement6056) pattern6057 = Pattern(Integral((S(1)/sinh(w_))**WC('n', S(1))*cosh(v_), x_), cons89, cons90, cons1730) rule6057 = ReplacementRule(pattern6057, replacement6057) pattern6058 = Pattern(Integral((S(1)/sinh(w_))**WC('n', S(1))*sinh(v_), x_), cons89, cons90, cons1730) rule6058 = ReplacementRule(pattern6058, replacement6058) pattern6059 = Pattern(Integral((S(1)/cosh(w_))**WC('n', S(1))*cosh(v_), x_), cons89, cons90, cons1730) rule6059 = ReplacementRule(pattern6059, replacement6059) pattern6060 = Pattern(Integral((a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))*cosh(x_*WC('d', S(1)) + WC('c', S(0))))**WC('n', S(1))*(x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons19, cons4, cons1362) rule6060 = ReplacementRule(pattern6060, replacement6060) pattern6061 = Pattern(Integral(x_**WC('m', S(1))*(a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))**S(2))**n_, x_), cons2, cons3, cons8, cons29, cons1458, cons152, cons170, cons465, cons1731) rule6061 = ReplacementRule(pattern6061, replacement6061) pattern6062 = Pattern(Integral(x_**WC('m', S(1))*(a_ + WC('b', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))**S(2))**n_, x_), cons2, cons3, cons8, cons29, cons1480, cons152, cons170, cons465, cons1731) rule6062 = ReplacementRule(pattern6062, replacement6062) pattern6063 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh((c_ + x_*WC('d', S(1)))**n_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons13) rule6063 = ReplacementRule(pattern6063, replacement6063) pattern6064 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*cosh((c_ + x_*WC('d', S(1)))**n_*WC('b', S(1)) + WC('a', S(0)))**WC('p', S(1)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons4, cons64, cons13) rule6064 = ReplacementRule(pattern6064, replacement6064) pattern6065 = Pattern(Integral((x_*WC('g', S(1)) + WC('f', S(0)))**WC('m', S(1))/(WC('a', S(0)) + WC('b', S(1))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2) + WC('c', S(1))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons64, cons1480, cons1732) rule6065 = ReplacementRule(pattern6065, replacement6065) pattern6066 = Pattern(Integral((x_*WC('g', S(1)) + WC('f', S(0)))**WC('m', S(1))/((b_ + WC('c', S(1))*tanh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2)), x_), cons3, cons8, cons29, cons50, cons127, cons210, cons64) rule6066 = ReplacementRule(pattern6066, replacement6066) pattern6067 = Pattern(Integral((x_*WC('g', S(1)) + WC('f', S(0)))**WC('m', S(1))/((WC('a', S(1))/cosh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2) + WC('b', S(0)) + WC('c', S(1))*tanh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2))*cosh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons64, cons1480, cons1732) rule6067 = ReplacementRule(pattern6067, replacement6067) pattern6068 = Pattern(Integral((x_*WC('g', S(1)) + WC('f', S(0)))**WC('m', S(1))/((c_ + WC('b', S(1))/tanh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2)), x_), cons3, cons8, cons29, cons50, cons127, cons210, cons64) rule6068 = ReplacementRule(pattern6068, replacement6068) pattern6069 = Pattern(Integral((x_*WC('g', S(1)) + WC('f', S(0)))**WC('m', S(1))/((WC('a', S(1))/sinh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2) + WC('b', S(1))/tanh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2) + WC('c', S(0)))*sinh(x_*WC('e', S(1)) + WC('d', S(0)))**S(2)), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons210, cons64, cons1480, cons1732) rule6069 = ReplacementRule(pattern6069, replacement6069) pattern6070 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))/(a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons64) rule6070 = ReplacementRule(pattern6070, replacement6070) pattern6071 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))/(a_ + WC('b', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons64) rule6071 = ReplacementRule(pattern6071, replacement6071) pattern6072 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))**n_/(a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons64, cons87, cons167, cons1441) rule6072 = ReplacementRule(pattern6072, replacement6072) pattern6073 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))**n_/(a_ + WC('b', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons64, cons87, cons167, cons1267) rule6073 = ReplacementRule(pattern6073, replacement6073) pattern6074 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))**n_/(a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons64, cons87, cons167, cons1442) rule6074 = ReplacementRule(pattern6074, replacement6074) pattern6075 = Pattern(Integral((x_*WC('f', S(1)) + WC('e', S(0)))**WC('m', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))**n_/(a_ + WC('b', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons64, cons87, cons167, cons1269) rule6075 = ReplacementRule(pattern6075, replacement6075) pattern6076 = Pattern(Integral((A_ + WC('B', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))))*(x_*WC('f', S(1)) + WC('e', S(0)))/(a_ + WC('b', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0))))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons36, cons37, cons1893) rule6076 = ReplacementRule(pattern6076, replacement6076) pattern6077 = Pattern(Integral((A_ + WC('B', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))))*(x_*WC('f', S(1)) + WC('e', S(0)))/(a_ + WC('b', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0))))**S(2), x_), cons2, cons3, cons8, cons29, cons50, cons127, cons36, cons37, cons1476) rule6077 = ReplacementRule(pattern6077, replacement6077) pattern6078 = Pattern(Integral((a_ + WC('b', S(1))*tanh(v_))**WC('n', S(1))*(S(1)/cosh(v_))**WC('m', S(1)), x_), cons2, cons3, cons152, cons1553, cons1483) rule6078 = ReplacementRule(pattern6078, replacement6078) pattern6079 = Pattern(Integral((a_ + WC('b', S(1))/tanh(v_))**WC('n', S(1))*(S(1)/sinh(v_))**WC('m', S(1)), x_), cons2, cons3, cons152, cons1553, cons1483) rule6079 = ReplacementRule(pattern6079, replacement6079) pattern6080 = Pattern(Integral(WC('u', S(1))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1))*sinh(x_*WC('d', S(1)) + WC('c', S(0)))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons530) rule6080 = ReplacementRule(pattern6080, replacement6080) pattern6081 = Pattern(Integral(WC('u', S(1))*cosh(x_*WC('b', S(1)) + WC('a', S(0)))**WC('m', S(1))*cosh(x_*WC('d', S(1)) + WC('c', S(0)))**WC('n', S(1)), x_), cons2, cons3, cons8, cons29, cons530) rule6081 = ReplacementRule(pattern6081, replacement6081) pattern6082 = Pattern(Integral(S(1)/(cosh(c_ + x_*WC('d', S(1)))*cosh(x_*WC('b', S(1)) + WC('a', S(0)))), x_), cons2, cons3, cons8, cons29, cons1735, cons73) rule6082 = ReplacementRule(pattern6082, replacement6082) pattern6083 = Pattern(Integral(S(1)/(sinh(c_ + x_*WC('d', S(1)))*sinh(x_*WC('b', S(1)) + WC('a', S(0)))), x_), cons2, cons3, cons8, cons29, cons1735, cons73) rule6083 = ReplacementRule(pattern6083, replacement6083) pattern6084 = Pattern(Integral(tanh(c_ + x_*WC('d', S(1)))*tanh(x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons8, cons29, cons1735, cons73) rule6084 = ReplacementRule(pattern6084, replacement6084) pattern6085 = Pattern(Integral(S(1)/(tanh(c_ + x_*WC('d', S(1)))*tanh(x_*WC('b', S(1)) + WC('a', S(0)))), x_), cons2, cons3, cons8, cons29, cons1735, cons73) rule6085 = ReplacementRule(pattern6085, replacement6085) pattern6086 = Pattern(Integral((WC('a', S(1))*cosh(v_) + WC('b', S(1))*sinh(v_))**WC('n', S(1))*WC('u', S(1)), x_), cons2, cons3, cons4, cons1267) rule6086 = ReplacementRule(pattern6086, replacement6086) return [rule5646, rule5647, rule5648, rule5649, rule5650, rule5651, rule5652, rule5653, rule5654, rule5655, rule5656, rule5657, rule5658, rule5659, rule5660, rule5661, rule5662, rule5663, rule5664, rule5665, rule5666, rule5667, rule5668, rule5669, rule5670, rule5671, rule5672, rule5673, rule5674, rule5675, rule5676, rule5677, rule5678, rule5679, rule5680, rule5681, rule5682, rule5683, rule5684, rule5685, rule5686, rule5687, rule5688, rule5689, rule5690, rule5691, rule5692, rule5693, rule5694, rule5695, rule5696, rule5697, rule5698, rule5699, rule5700, rule5701, rule5702, rule5703, rule5704, rule5705, rule5706, rule5707, rule5708, rule5709, rule5710, rule5711, rule5712, rule5713, rule5714, rule5715, rule5716, rule5717, rule5718, rule5719, rule5720, rule5721, rule5722, rule5723, rule5724, rule5725, rule5726, rule5727, rule5728, rule5729, rule5730, rule5731, rule5732, rule5733, rule5734, rule5735, rule5736, rule5737, rule5738, rule5739, rule5740, rule5741, rule5742, rule5743, rule5744, rule5745, rule5746, rule5747, rule5748, rule5749, rule5750, rule5751, rule5752, rule5753, rule5754, rule5755, rule5756, rule5757, rule5758, rule5759, rule5760, rule5761, rule5762, rule5763, rule5764, rule5765, rule5766, rule5767, rule5768, rule5769, rule5770, rule5771, rule5772, rule5773, rule5774, rule5775, rule5776, rule5777, rule5778, rule5779, rule5780, rule5781, rule5782, rule5783, rule5784, rule5785, rule5786, rule5787, rule5788, rule5789, rule5790, rule5791, rule5792, rule5793, rule5794, rule5795, rule5796, rule5797, rule5798, rule5799, rule5800, rule5801, rule5802, rule5803, rule5804, rule5805, rule5806, rule5807, rule5808, rule5809, rule5810, rule5811, rule5812, rule5813, rule5814, rule5815, rule5816, rule5817, rule5818, rule5819, rule5820, rule5821, rule5822, rule5823, rule5824, rule5825, rule5826, rule5827, rule5828, rule5829, rule5830, rule5831, rule5832, rule5833, rule5834, rule5835, rule5836, rule5837, rule5838, rule5839, rule5840, rule5841, rule5842, rule5843, rule5844, rule5845, rule5846, rule5847, rule5848, rule5849, rule5850, rule5851, rule5852, rule5853, rule5854, rule5855, rule5856, rule5857, rule5858, rule5859, rule5860, rule5861, rule5862, rule5863, rule5864, rule5865, rule5866, rule5867, rule5868, rule5869, rule5870, rule5871, rule5872, rule5873, rule5874, rule5875, rule5876, rule5877, rule5878, rule5879, rule5880, rule5881, rule5882, rule5883, rule5884, rule5885, rule5886, rule5887, rule5888, rule5889, rule5890, rule5891, rule5892, rule5893, rule5894, rule5895, rule5896, rule5897, rule5898, rule5899, rule5900, rule5901, rule5902, rule5903, rule5904, rule5905, rule5906, rule5907, rule5908, rule5909, rule5910, rule5911, rule5912, rule5913, rule5914, rule5915, rule5916, rule5917, rule5918, rule5919, rule5920, rule5921, rule5922, rule5923, rule5924, rule5925, rule5926, rule5927, rule5928, rule5929, rule5930, rule5931, rule5932, rule5933, rule5934, rule5935, rule5936, rule5937, rule5938, rule5939, rule5940, rule5941, rule5942, rule5943, rule5944, rule5945, rule5946, rule5947, rule5948, rule5949, rule5950, rule5951, rule5952, rule5953, rule5954, rule5955, rule5956, rule5957, rule5958, rule5959, rule5960, rule5961, rule5962, rule5963, rule5964, rule5965, rule5966, rule5967, rule5968, rule5969, rule5970, rule5971, rule5972, rule5973, rule5974, rule5975, rule5976, rule5977, rule5978, rule5979, rule5980, rule5981, rule5982, rule5983, rule5984, rule5985, rule5986, rule5987, rule5988, rule5989, rule5990, rule5991, rule5992, rule5993, rule5994, rule5995, rule5996, rule5997, rule5998, rule5999, rule6000, rule6001, rule6002, rule6003, rule6004, rule6005, rule6006, rule6007, rule6008, rule6009, rule6010, rule6011, rule6012, rule6013, rule6014, rule6015, rule6016, rule6017, rule6018, rule6019, rule6020, rule6021, rule6022, rule6023, rule6024, rule6025, rule6026, rule6027, rule6028, rule6029, rule6030, rule6031, rule6032, rule6033, rule6034, rule6035, rule6036, rule6037, rule6038, rule6039, rule6040, rule6041, rule6042, rule6043, rule6044, rule6045, rule6046, rule6047, rule6048, rule6049, rule6050, rule6051, rule6052, rule6053, rule6054, rule6055, rule6056, rule6057, rule6058, rule6059, rule6060, rule6061, rule6062, rule6063, rule6064, rule6065, rule6066, rule6067, rule6068, rule6069, rule6070, rule6071, rule6072, rule6073, rule6074, rule6075, rule6076, rule6077, rule6078, rule6079, rule6080, rule6081, rule6082, rule6083, rule6084, rule6085, rule6086, ] def replacement5646(c, d, e, f, m, x): return -Dist(d*m/f, Int((c + d*x)**(m + S(-1))*cosh(e + f*x), x), x) + Simp((c + d*x)**m*cosh(e + f*x)/f, x) def replacement5647(c, d, e, f, m, x): return -Dist(d*m/f, Int((c + d*x)**(m + S(-1))*sinh(e + f*x), x), x) + Simp((c + d*x)**m*sinh(e + f*x)/f, x) def replacement5648(c, d, e, f, m, x): return -Dist(f/(d*(m + S(1))), Int((c + d*x)**(m + S(1))*cosh(e + f*x), x), x) + Simp((c + d*x)**(m + S(1))*sinh(e + f*x)/(d*(m + S(1))), x) def replacement5649(c, d, e, f, m, x): return -Dist(f/(d*(m + S(1))), Int((c + d*x)**(m + S(1))*sinh(e + f*x), x), x) + Simp((c + d*x)**(m + S(1))*cosh(e + f*x)/(d*(m + S(1))), x) def replacement5650(c, d, e, f, x): return Simp(SinhIntegral(e + f*x)/d, x) def replacement5651(c, d, e, f, x): return Simp(CoshIntegral(e + f*x)/d, x) def replacement5652(c, d, e, f, x): return Dist(sinh((-c*f + d*e)/d), Int(cosh(c*f/d + f*x)/(c + d*x), x), x) + Dist(cosh((-c*f + d*e)/d), Int(sinh(c*f/d + f*x)/(c + d*x), x), x) def replacement5653(c, d, e, f, x): return Dist(sinh((-c*f + d*e)/d), Int(sinh(c*f/d + f*x)/(c + d*x), x), x) + Dist(cosh((-c*f + d*e)/d), Int(cosh(c*f/d + f*x)/(c + d*x), x), x) def replacement5654(c, d, e, f, m, x): return -Dist(S(1)/2, Int((c + d*x)**m*exp(-e - f*x), x), x) + Dist(S(1)/2, Int((c + d*x)**m*exp(e + f*x), x), x) def replacement5655(c, d, e, f, m, x): return Dist(S(1)/2, Int((c + d*x)**m*exp(-e - f*x), x), x) + Dist(S(1)/2, Int((c + d*x)**m*exp(e + f*x), x), x) def replacement5656(b, c, d, e, f, n, x): return -Dist(b**S(2)*(n + S(-1))/n, Int((b*sinh(e + f*x))**(n + S(-2))*(c + d*x), x), x) - Simp(d*(b*sinh(e + f*x))**n/(f**S(2)*n**S(2)), x) + Simp(b*(b*sinh(e + f*x))**(n + S(-1))*(c + d*x)*cosh(e + f*x)/(f*n), x) def replacement5657(b, c, d, e, f, n, x): return Dist(b**S(2)*(n + S(-1))/n, Int((b*cosh(e + f*x))**(n + S(-2))*(c + d*x), x), x) - Simp(d*(b*cosh(e + f*x))**n/(f**S(2)*n**S(2)), x) + Simp(b*(b*cosh(e + f*x))**(n + S(-1))*(c + d*x)*sinh(e + f*x)/(f*n), x) def replacement5658(b, c, d, e, f, m, n, x): return -Dist(b**S(2)*(n + S(-1))/n, Int((b*sinh(e + f*x))**(n + S(-2))*(c + d*x)**m, x), x) + Dist(d**S(2)*m*(m + S(-1))/(f**S(2)*n**S(2)), Int((b*sinh(e + f*x))**n*(c + d*x)**(m + S(-2)), x), x) + Simp(b*(b*sinh(e + f*x))**(n + S(-1))*(c + d*x)**m*cosh(e + f*x)/(f*n), x) - Simp(d*m*(b*sinh(e + f*x))**n*(c + d*x)**(m + S(-1))/(f**S(2)*n**S(2)), x) def replacement5659(b, c, d, e, f, m, n, x): return Dist(b**S(2)*(n + S(-1))/n, Int((b*cosh(e + f*x))**(n + S(-2))*(c + d*x)**m, x), x) + Dist(d**S(2)*m*(m + S(-1))/(f**S(2)*n**S(2)), Int((b*cosh(e + f*x))**n*(c + d*x)**(m + S(-2)), x), x) + Simp(b*(b*cosh(e + f*x))**(n + S(-1))*(c + d*x)**m*sinh(e + f*x)/(f*n), x) - Simp(d*m*(b*cosh(e + f*x))**n*(c + d*x)**(m + S(-1))/(f**S(2)*n**S(2)), x) def replacement5660(c, d, e, f, m, n, x): return Int(ExpandTrigReduce((c + d*x)**m, sinh(e + f*x)**n, x), x) def replacement5661(c, d, e, f, m, n, x): return Int(ExpandTrigReduce((c + d*x)**m, cosh(e + f*x)**n, x), x) def replacement5662(c, d, e, f, m, n, x): return -Dist(f*n/(d*(m + S(1))), Int(ExpandTrigReduce((c + d*x)**(m + S(1)), sinh(e + f*x)**(n + S(-1))*cosh(e + f*x), x), x), x) + Simp((c + d*x)**(m + S(1))*sinh(e + f*x)**n/(d*(m + S(1))), x) def replacement5663(c, d, e, f, m, n, x): return -Dist(f*n/(d*(m + S(1))), Int(ExpandTrigReduce((c + d*x)**(m + S(1)), sinh(e + f*x)*cosh(e + f*x)**(n + S(-1)), x), x), x) + Simp((c + d*x)**(m + S(1))*cosh(e + f*x)**n/(d*(m + S(1))), x) def replacement5664(b, c, d, e, f, m, n, x): return Dist(f**S(2)*n**S(2)/(d**S(2)*(m + S(1))*(m + S(2))), Int((b*sinh(e + f*x))**n*(c + d*x)**(m + S(2)), x), x) + Dist(b**S(2)*f**S(2)*n*(n + S(-1))/(d**S(2)*(m + S(1))*(m + S(2))), Int((b*sinh(e + f*x))**(n + S(-2))*(c + d*x)**(m + S(2)), x), x) + Simp((b*sinh(e + f*x))**n*(c + d*x)**(m + S(1))/(d*(m + S(1))), x) - Simp(b*f*n*(b*sinh(e + f*x))**(n + S(-1))*(c + d*x)**(m + S(2))*cosh(e + f*x)/(d**S(2)*(m + S(1))*(m + S(2))), x) def replacement5665(b, c, d, e, f, m, n, x): return Dist(f**S(2)*n**S(2)/(d**S(2)*(m + S(1))*(m + S(2))), Int((b*cosh(e + f*x))**n*(c + d*x)**(m + S(2)), x), x) - Dist(b**S(2)*f**S(2)*n*(n + S(-1))/(d**S(2)*(m + S(1))*(m + S(2))), Int((b*cosh(e + f*x))**(n + S(-2))*(c + d*x)**(m + S(2)), x), x) + Simp((b*cosh(e + f*x))**n*(c + d*x)**(m + S(1))/(d*(m + S(1))), x) - Simp(b*f*n*(b*cosh(e + f*x))**(n + S(-1))*(c + d*x)**(m + S(2))*sinh(e + f*x)/(d**S(2)*(m + S(1))*(m + S(2))), x) def replacement5666(b, c, d, e, f, n, x): return -Dist((n + S(2))/(b**S(2)*(n + S(1))), Int((b*sinh(e + f*x))**(n + S(2))*(c + d*x), x), x) - Simp(d*(b*sinh(e + f*x))**(n + S(2))/(b**S(2)*f**S(2)*(n + S(1))*(n + S(2))), x) + Simp((b*sinh(e + f*x))**(n + S(1))*(c + d*x)*cosh(e + f*x)/(b*f*(n + S(1))), x) def replacement5667(b, c, d, e, f, n, x): return Dist((n + S(2))/(b**S(2)*(n + S(1))), Int((b*cosh(e + f*x))**(n + S(2))*(c + d*x), x), x) + Simp(d*(b*cosh(e + f*x))**(n + S(2))/(b**S(2)*f**S(2)*(n + S(1))*(n + S(2))), x) - Simp((b*cosh(e + f*x))**(n + S(1))*(c + d*x)*sinh(e + f*x)/(b*f*(n + S(1))), x) def replacement5668(b, c, d, e, f, m, n, x): return -Dist((n + S(2))/(b**S(2)*(n + S(1))), Int((b*sinh(e + f*x))**(n + S(2))*(c + d*x)**m, x), x) + Dist(d**S(2)*m*(m + S(-1))/(b**S(2)*f**S(2)*(n + S(1))*(n + S(2))), Int((b*sinh(e + f*x))**(n + S(2))*(c + d*x)**(m + S(-2)), x), x) + Simp((b*sinh(e + f*x))**(n + S(1))*(c + d*x)**m*cosh(e + f*x)/(b*f*(n + S(1))), x) - Simp(d*m*(b*sinh(e + f*x))**(n + S(2))*(c + d*x)**(m + S(-1))/(b**S(2)*f**S(2)*(n + S(1))*(n + S(2))), x) def replacement5669(b, c, d, e, f, m, n, x): return Dist((n + S(2))/(b**S(2)*(n + S(1))), Int((b*cosh(e + f*x))**(n + S(2))*(c + d*x)**m, x), x) - Dist(d**S(2)*m*(m + S(-1))/(b**S(2)*f**S(2)*(n + S(1))*(n + S(2))), Int((b*cosh(e + f*x))**(n + S(2))*(c + d*x)**(m + S(-2)), x), x) - Simp((b*cosh(e + f*x))**(n + S(1))*(c + d*x)**m*sinh(e + f*x)/(b*f*(n + S(1))), x) + Simp(d*m*(b*cosh(e + f*x))**(n + S(2))*(c + d*x)**(m + S(-1))/(b**S(2)*f**S(2)*(n + S(1))*(n + S(2))), x) def replacement5670(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (a + b*sinh(e + f*x))**n, x), x) def replacement5671(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (a + b*cosh(e + f*x))**n, x), x) def replacement5672(a, b, c, d, e, f, m, n, x): return Dist((S(2)*a)**n, Int((c + d*x)**m*cosh(-Pi*a/(S(4)*b) + e/S(2) + f*x/S(2))**(S(2)*n), x), x) def replacement5673(a, b, c, d, e, f, m, n, x): return Dist((S(2)*a)**IntPart(n)*(a + b*sinh(e + f*x))**FracPart(n)*cosh(-Pi*a/(S(4)*b) + e/S(2) + f*x/S(2))**(-S(2)*FracPart(n)), Int((c + d*x)**m*cosh(-Pi*a/(S(4)*b) + e/S(2) + f*x/S(2))**(S(2)*n), x), x) def replacement5674(a, b, c, d, e, f, m, n, x): return Dist((S(2)*a)**n, Int((c + d*x)**m*cosh(e/S(2) + f*x/S(2))**(S(2)*n), x), x) def replacement5675(a, b, c, d, e, f, m, n, x): return Dist((-S(2)*a)**n, Int((c + d*x)**m*sinh(e/S(2) + f*x/S(2))**(S(2)*n), x), x) def replacement5676(a, b, c, d, e, f, m, n, x): return Dist((S(2)*a)**IntPart(n)*(a + b*cosh(e + f*x))**FracPart(n)*cosh(e/S(2) + f*x/S(2))**(-S(2)*FracPart(n)), Int((c + d*x)**m*cosh(e/S(2) + f*x/S(2))**(S(2)*n), x), x) def replacement5677(a, b, c, d, e, f, m, n, x): return Dist((-S(2)*a)**IntPart(n)*(a + b*cosh(e + f*x))**FracPart(n)*sinh(e/S(2) + f*x/S(2))**(-S(2)*FracPart(n)), Int((c + d*x)**m*sinh(e/S(2) + f*x/S(2))**(S(2)*n), x), x) def replacement5678(a, b, c, d, e, f, m, x): return Dist(S(-2), Int((c + d*x)**m*exp(e + f*x)/(-S(2)*a*exp(e + f*x) - b*exp(S(2)*e + S(2)*f*x) + b), x), x) def replacement5679(a, b, c, d, e, f, m, x): return Dist(S(2), Int((c + d*x)**m*exp(e + f*x)/(S(2)*a*exp(e + f*x) + b*exp(S(2)*e + S(2)*f*x) + b), x), x) def replacement5680(a, b, c, d, e, f, m, x): return Dist(a/(a**S(2) + b**S(2)), Int((c + d*x)**m/(a + b*sinh(e + f*x)), x), x) + Dist(b*d*m/(f*(a**S(2) + b**S(2))), Int((c + d*x)**(m + S(-1))*cosh(e + f*x)/(a + b*sinh(e + f*x)), x), x) - Simp(b*(c + d*x)**m*cosh(e + f*x)/(f*(a + b*sinh(e + f*x))*(a**S(2) + b**S(2))), x) def replacement5681(a, b, c, d, e, f, m, x): return Dist(a/(a**S(2) - b**S(2)), Int((c + d*x)**m/(a + b*cosh(e + f*x)), x), x) + Dist(b*d*m/(f*(a**S(2) - b**S(2))), Int((c + d*x)**(m + S(-1))*sinh(e + f*x)/(a + b*cosh(e + f*x)), x), x) - Simp(b*(c + d*x)**m*sinh(e + f*x)/(f*(a + b*cosh(e + f*x))*(a**S(2) - b**S(2))), x) def replacement5682(a, b, c, d, e, f, m, n, x): return Dist(a/(a**S(2) + b**S(2)), Int((a + b*sinh(e + f*x))**(n + S(1))*(c + d*x)**m, x), x) - Dist(b*(n + S(2))/((a**S(2) + b**S(2))*(n + S(1))), Int((a + b*sinh(e + f*x))**(n + S(1))*(c + d*x)**m*sinh(e + f*x), x), x) - Dist(b*d*m/(f*(a**S(2) + b**S(2))*(n + S(1))), Int((a + b*sinh(e + f*x))**(n + S(1))*(c + d*x)**(m + S(-1))*cosh(e + f*x), x), x) + Simp(b*(a + b*sinh(e + f*x))**(n + S(1))*(c + d*x)**m*cosh(e + f*x)/(f*(a**S(2) + b**S(2))*(n + S(1))), x) def replacement5683(a, b, c, d, e, f, m, n, x): return Dist(a/(a**S(2) - b**S(2)), Int((a + b*cosh(e + f*x))**(n + S(1))*(c + d*x)**m, x), x) - Dist(b*(n + S(2))/((a**S(2) - b**S(2))*(n + S(1))), Int((a + b*cosh(e + f*x))**(n + S(1))*(c + d*x)**m*cosh(e + f*x), x), x) - Dist(b*d*m/(f*(a**S(2) - b**S(2))*(n + S(1))), Int((a + b*cosh(e + f*x))**(n + S(1))*(c + d*x)**(m + S(-1))*sinh(e + f*x), x), x) + Simp(b*(a + b*cosh(e + f*x))**(n + S(1))*(c + d*x)**m*sinh(e + f*x)/(f*(a**S(2) - b**S(2))*(n + S(1))), x) def replacement5684(a, b, m, n, u, v, x): return Int((a + b*sinh(ExpandToSum(v, x)))**n*ExpandToSum(u, x)**m, x) def replacement5685(a, b, m, n, u, v, x): return Int((a + b*cosh(ExpandToSum(v, x)))**n*ExpandToSum(u, x)**m, x) def replacement5686(a, b, c, d, e, f, m, n, x): return Int((a + b*sinh(e + f*x))**n*(c + d*x)**m, x) def replacement5687(a, b, c, d, e, f, m, n, x): return Int((a + b*cosh(e + f*x))**n*(c + d*x)**m, x) def replacement5688(a, b, c, d, n, p, x): return Int(ExpandIntegrand(sinh(c + d*x), (a + b*x**n)**p, x), x) def replacement5689(a, b, c, d, n, p, x): return Int(ExpandIntegrand(cosh(c + d*x), (a + b*x**n)**p, x), x) def replacement5690(a, b, c, d, n, p, x): return -Dist(d/(b*n*(p + S(1))), Int(x**(S(1) - n)*(a + b*x**n)**(p + S(1))*cosh(c + d*x), x), x) - Dist((S(1) - n)/(b*n*(p + S(1))), Int(x**(-n)*(a + b*x**n)**(p + S(1))*sinh(c + d*x), x), x) + Simp(x**(S(1) - n)*(a + b*x**n)**(p + S(1))*sinh(c + d*x)/(b*n*(p + S(1))), x) def replacement5691(a, b, c, d, n, p, x): return -Dist(d/(b*n*(p + S(1))), Int(x**(S(1) - n)*(a + b*x**n)**(p + S(1))*sinh(c + d*x), x), x) - Dist((S(1) - n)/(b*n*(p + S(1))), Int(x**(-n)*(a + b*x**n)**(p + S(1))*cosh(c + d*x), x), x) + Simp(x**(S(1) - n)*(a + b*x**n)**(p + S(1))*cosh(c + d*x)/(b*n*(p + S(1))), x) def replacement5692(a, b, c, d, n, p, x): return Int(ExpandIntegrand(sinh(c + d*x), (a + b*x**n)**p, x), x) def replacement5693(a, b, c, d, n, p, x): return Int(ExpandIntegrand(cosh(c + d*x), (a + b*x**n)**p, x), x) def replacement5694(a, b, c, d, n, p, x): return Int(x**(n*p)*(a*x**(-n) + b)**p*sinh(c + d*x), x) def replacement5695(a, b, c, d, n, p, x): return Int(x**(n*p)*(a*x**(-n) + b)**p*cosh(c + d*x), x) def replacement5696(a, b, c, d, n, p, x): return Int((a + b*x**n)**p*sinh(c + d*x), x) def replacement5697(a, b, c, d, n, p, x): return Int((a + b*x**n)**p*cosh(c + d*x), x) def replacement5698(a, b, c, d, e, m, n, p, x): return Int(ExpandIntegrand(sinh(c + d*x), (e*x)**m*(a + b*x**n)**p, x), x) def replacement5699(a, b, c, d, e, m, n, p, x): return Int(ExpandIntegrand(cosh(c + d*x), (e*x)**m*(a + b*x**n)**p, x), x) def replacement5700(a, b, c, d, e, m, n, p, x): return -Dist(d*e**m/(b*n*(p + S(1))), Int((a + b*x**n)**(p + S(1))*cosh(c + d*x), x), x) + Simp(e**m*(a + b*x**n)**(p + S(1))*sinh(c + d*x)/(b*n*(p + S(1))), x) def replacement5701(a, b, c, d, e, m, n, p, x): return -Dist(d*e**m/(b*n*(p + S(1))), Int((a + b*x**n)**(p + S(1))*sinh(c + d*x), x), x) + Simp(e**m*(a + b*x**n)**(p + S(1))*cosh(c + d*x)/(b*n*(p + S(1))), x) def replacement5702(a, b, c, d, m, n, p, x): return -Dist(d/(b*n*(p + S(1))), Int(x**(m - n + S(1))*(a + b*x**n)**(p + S(1))*cosh(c + d*x), x), x) - Dist((m - n + S(1))/(b*n*(p + S(1))), Int(x**(m - n)*(a + b*x**n)**(p + S(1))*sinh(c + d*x), x), x) + Simp(x**(m - n + S(1))*(a + b*x**n)**(p + S(1))*sinh(c + d*x)/(b*n*(p + S(1))), x) def replacement5703(a, b, c, d, m, n, p, x): return -Dist(d/(b*n*(p + S(1))), Int(x**(m - n + S(1))*(a + b*x**n)**(p + S(1))*sinh(c + d*x), x), x) - Dist((m - n + S(1))/(b*n*(p + S(1))), Int(x**(m - n)*(a + b*x**n)**(p + S(1))*cosh(c + d*x), x), x) + Simp(x**(m - n + S(1))*(a + b*x**n)**(p + S(1))*cosh(c + d*x)/(b*n*(p + S(1))), x) def replacement5704(a, b, c, d, m, n, p, x): return Int(ExpandIntegrand(sinh(c + d*x), x**m*(a + b*x**n)**p, x), x) def replacement5705(a, b, c, d, m, n, p, x): return Int(ExpandIntegrand(cosh(c + d*x), x**m*(a + b*x**n)**p, x), x) def replacement5706(a, b, c, d, m, n, p, x): return Int(x**(m + n*p)*(a*x**(-n) + b)**p*sinh(c + d*x), x) def replacement5707(a, b, c, d, m, n, p, x): return Int(x**(m + n*p)*(a*x**(-n) + b)**p*cosh(c + d*x), x) def replacement5708(a, b, c, d, e, m, n, p, x): return Int((e*x)**m*(a + b*x**n)**p*sinh(c + d*x), x) def replacement5709(a, b, c, d, e, m, n, p, x): return Int((e*x)**m*(a + b*x**n)**p*cosh(c + d*x), x) def replacement5710(c, d, n, x): return -Dist(S(1)/2, Int(exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int(exp(c + d*x**n), x), x) def replacement5711(c, d, n, x): return Dist(S(1)/2, Int(exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int(exp(c + d*x**n), x), x) def replacement5712(a, b, c, d, n, p, x): return Int(ExpandTrigReduce((a + b*sinh(c + d*x**n))**p, x), x) def replacement5713(a, b, c, d, n, p, x): return Int(ExpandTrigReduce((a + b*cosh(c + d*x**n))**p, x), x) def replacement5714(a, b, c, d, n, p, x): return -Subst(Int((a + b*sinh(c + d*x**(-n)))**p/x**S(2), x), x, S(1)/x) def replacement5715(a, b, c, d, n, p, x): return -Subst(Int((a + b*cosh(c + d*x**(-n)))**p/x**S(2), x), x, S(1)/x) def With5716(a, b, c, d, n, p, x): k = Denominator(n) return Dist(k, Subst(Int(x**(k + S(-1))*(a + b*sinh(c + d*x**(k*n)))**p, x), x, x**(S(1)/k)), x) def With5717(a, b, c, d, n, p, x): k = Denominator(n) return Dist(k, Subst(Int(x**(k + S(-1))*(a + b*cosh(c + d*x**(k*n)))**p, x), x, x**(S(1)/k)), x) def replacement5718(c, d, n, x): return -Dist(S(1)/2, Int(exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int(exp(c + d*x**n), x), x) def replacement5719(c, d, n, x): return Dist(S(1)/2, Int(exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int(exp(c + d*x**n), x), x) def replacement5720(a, b, c, d, n, p, x): return Int(ExpandTrigReduce((a + b*sinh(c + d*x**n))**p, x), x) def replacement5721(a, b, c, d, n, p, x): return Int(ExpandTrigReduce((a + b*cosh(c + d*x**n))**p, x), x) def replacement5722(a, b, c, d, n, p, u, x): return Dist(S(1)/Coefficient(u, x, S(1)), Subst(Int((a + b*sinh(c + d*x**n))**p, x), x, u), x) def replacement5723(a, b, c, d, n, p, u, x): return Dist(S(1)/Coefficient(u, x, S(1)), Subst(Int((a + b*cosh(c + d*x**n))**p, x), x, u), x) def replacement5724(a, b, c, d, n, p, u, x): return Int((a + b*sinh(c + d*u**n))**p, x) def replacement5725(a, b, c, d, n, p, u, x): return Int((a + b*cosh(c + d*u**n))**p, x) def replacement5726(a, b, p, u, x): return Int((a + b*sinh(ExpandToSum(u, x)))**p, x) def replacement5727(a, b, p, u, x): return Int((a + b*cosh(ExpandToSum(u, x)))**p, x) def replacement5728(d, n, x): return Simp(SinhIntegral(d*x**n)/n, x) def replacement5729(d, n, x): return Simp(CoshIntegral(d*x**n)/n, x) def replacement5730(c, d, n, x): return Dist(sinh(c), Int(cosh(d*x**n)/x, x), x) + Dist(cosh(c), Int(sinh(d*x**n)/x, x), x) def replacement5731(c, d, n, x): return Dist(sinh(c), Int(sinh(d*x**n)/x, x), x) + Dist(cosh(c), Int(cosh(d*x**n)/x, x), x) def With5732(a, b, c, d, m, n, p, x): if isinstance(x, (int, Integer, float, Float)): return False mn = (m + S(1))/n if And(IntegerQ(mn), Or(Equal(p, S(1)), Greater(mn, S(0)))): return True return False def replacement5732(a, b, c, d, m, n, p, x): mn = (m + S(1))/n return Dist(S(1)/n, Subst(Int(x**(mn + S(-1))*(a + b*sinh(c + d*x))**p, x), x, x**n), x) def With5733(a, b, c, d, m, n, p, x): if isinstance(x, (int, Integer, float, Float)): return False mn = (m + S(1))/n if And(IntegerQ(mn), Or(Equal(p, S(1)), Greater(mn, S(0)))): return True return False def replacement5733(a, b, c, d, m, n, p, x): mn = (m + S(1))/n return Dist(S(1)/n, Subst(Int(x**(mn + S(-1))*(a + b*cosh(c + d*x))**p, x), x, x**n), x) def With5734(a, b, c, d, e, m, n, p, x): if isinstance(x, (int, Integer, float, Float)): return False mn = (m + S(1))/n if And(IntegerQ(mn), Or(Equal(p, S(1)), Greater(mn, S(0)))): return True return False def replacement5734(a, b, c, d, e, m, n, p, x): mn = (m + S(1))/n return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*sinh(c + d*x**n))**p, x), x) def With5735(a, b, c, d, e, m, n, p, x): if isinstance(x, (int, Integer, float, Float)): return False mn = (m + S(1))/n if And(IntegerQ(mn), Or(Equal(p, S(1)), Greater(mn, S(0)))): return True return False def replacement5735(a, b, c, d, e, m, n, p, x): mn = (m + S(1))/n return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*cosh(c + d*x**n))**p, x), x) def replacement5736(c, d, e, m, n, x): return -Dist(e**n*(m - n + S(1))/(d*n), Int((e*x)**(m - n)*cosh(c + d*x**n), x), x) + Simp(e**(n + S(-1))*(e*x)**(m - n + S(1))*cosh(c + d*x**n)/(d*n), x) def replacement5737(c, d, e, m, n, x): return -Dist(e**n*(m - n + S(1))/(d*n), Int((e*x)**(m - n)*sinh(c + d*x**n), x), x) + Simp(e**(n + S(-1))*(e*x)**(m - n + S(1))*sinh(c + d*x**n)/(d*n), x) def replacement5738(c, d, e, m, n, x): return -Dist(d*e**(-n)*n/(m + S(1)), Int((e*x)**(m + n)*cosh(c + d*x**n), x), x) + Simp((e*x)**(m + S(1))*sinh(c + d*x**n)/(e*(m + S(1))), x) def replacement5739(c, d, e, m, n, x): return -Dist(d*e**(-n)*n/(m + S(1)), Int((e*x)**(m + n)*sinh(c + d*x**n), x), x) + Simp((e*x)**(m + S(1))*cosh(c + d*x**n)/(e*(m + S(1))), x) def replacement5740(c, d, e, m, n, x): return -Dist(S(1)/2, Int((e*x)**m*exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int((e*x)**m*exp(c + d*x**n), x), x) def replacement5741(c, d, e, m, n, x): return Dist(S(1)/2, Int((e*x)**m*exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int((e*x)**m*exp(c + d*x**n), x), x) def replacement5742(a, b, m, n, p, x): return Dist(b*n*p/(n + S(-1)), Int(sinh(a + b*x**n)**(p + S(-1))*cosh(a + b*x**n), x), x) - Simp(x**(S(1) - n)*sinh(a + b*x**n)**p/(n + S(-1)), x) def replacement5743(a, b, m, n, p, x): return Dist(b*n*p/(n + S(-1)), Int(sinh(a + b*x**n)*cosh(a + b*x**n)**(p + S(-1)), x), x) - Simp(x**(S(1) - n)*cosh(a + b*x**n)**p/(n + S(-1)), x) def replacement5744(a, b, m, n, p, x): return -Dist((p + S(-1))/p, Int(x**m*sinh(a + b*x**n)**(p + S(-2)), x), x) - Simp(sinh(a + b*x**n)**p/(b**S(2)*n*p**S(2)), x) + Simp(x**n*sinh(a + b*x**n)**(p + S(-1))*cosh(a + b*x**n)/(b*n*p), x) def replacement5745(a, b, m, n, p, x): return Dist((p + S(-1))/p, Int(x**m*cosh(a + b*x**n)**(p + S(-2)), x), x) - Simp(cosh(a + b*x**n)**p/(b**S(2)*n*p**S(2)), x) + Simp(x**n*sinh(a + b*x**n)*cosh(a + b*x**n)**(p + S(-1))/(b*n*p), x) def replacement5746(a, b, m, n, p, x): return -Dist((p + S(-1))/p, Int(x**m*sinh(a + b*x**n)**(p + S(-2)), x), x) + Dist((m - S(2)*n + S(1))*(m - n + S(1))/(b**S(2)*n**S(2)*p**S(2)), Int(x**(m - S(2)*n)*sinh(a + b*x**n)**p, x), x) - Simp(x**(m - S(2)*n + S(1))*(m - n + S(1))*sinh(a + b*x**n)**p/(b**S(2)*n**S(2)*p**S(2)), x) + Simp(x**(m - n + S(1))*sinh(a + b*x**n)**(p + S(-1))*cosh(a + b*x**n)/(b*n*p), x) def replacement5747(a, b, m, n, p, x): return Dist((p + S(-1))/p, Int(x**m*cosh(a + b*x**n)**(p + S(-2)), x), x) + Dist((m - S(2)*n + S(1))*(m - n + S(1))/(b**S(2)*n**S(2)*p**S(2)), Int(x**(m - S(2)*n)*cosh(a + b*x**n)**p, x), x) - Simp(x**(m - S(2)*n + S(1))*(m - n + S(1))*cosh(a + b*x**n)**p/(b**S(2)*n**S(2)*p**S(2)), x) + Simp(x**(m - n + S(1))*sinh(a + b*x**n)*cosh(a + b*x**n)**(p + S(-1))/(b*n*p), x) def replacement5748(a, b, m, n, p, x): return Dist(b**S(2)*n**S(2)*p**S(2)/((m + S(1))*(m + n + S(1))), Int(x**(m + S(2)*n)*sinh(a + b*x**n)**p, x), x) + Dist(b**S(2)*n**S(2)*p*(p + S(-1))/((m + S(1))*(m + n + S(1))), Int(x**(m + S(2)*n)*sinh(a + b*x**n)**(p + S(-2)), x), x) + Simp(x**(m + S(1))*sinh(a + b*x**n)**p/(m + S(1)), x) - Simp(b*n*p*x**(m + n + S(1))*sinh(a + b*x**n)**(p + S(-1))*cosh(a + b*x**n)/((m + S(1))*(m + n + S(1))), x) def replacement5749(a, b, m, n, p, x): return Dist(b**S(2)*n**S(2)*p**S(2)/((m + S(1))*(m + n + S(1))), Int(x**(m + S(2)*n)*cosh(a + b*x**n)**p, x), x) - Dist(b**S(2)*n**S(2)*p*(p + S(-1))/((m + S(1))*(m + n + S(1))), Int(x**(m + S(2)*n)*cosh(a + b*x**n)**(p + S(-2)), x), x) + Simp(x**(m + S(1))*cosh(a + b*x**n)**p/(m + S(1)), x) - Simp(b*n*p*x**(m + n + S(1))*sinh(a + b*x**n)*cosh(a + b*x**n)**(p + S(-1))/((m + S(1))*(m + n + S(1))), x) def With5750(a, b, c, d, e, m, n, p, x): k = Denominator(m) return Dist(k/e, Subst(Int(x**(k*(m + S(1)) + S(-1))*(a + b*sinh(c + d*e**(-n)*x**(k*n)))**p, x), x, (e*x)**(S(1)/k)), x) def With5751(a, b, c, d, e, m, n, p, x): k = Denominator(m) return Dist(k/e, Subst(Int(x**(k*(m + S(1)) + S(-1))*(a + b*cosh(c + d*e**(-n)*x**(k*n)))**p, x), x, (e*x)**(S(1)/k)), x) def replacement5752(a, b, c, d, e, m, n, p, x): return Int(ExpandTrigReduce((e*x)**m, (a + b*sinh(c + d*x**n))**p, x), x) def replacement5753(a, b, c, d, e, m, n, p, x): return Int(ExpandTrigReduce((e*x)**m, (a + b*cosh(c + d*x**n))**p, x), x) def replacement5754(a, b, m, n, p, x): return -Dist((p + S(2))/(p + S(1)), Int(x**m*sinh(a + b*x**n)**(p + S(2)), x), x) - Simp(sinh(a + b*x**n)**(p + S(2))/(b**S(2)*n*(p + S(1))*(p + S(2))), x) + Simp(x**n*sinh(a + b*x**n)**(p + S(1))*cosh(a + b*x**n)/(b*n*(p + S(1))), x) def replacement5755(a, b, m, n, p, x): return Dist((p + S(2))/(p + S(1)), Int(x**m*cosh(a + b*x**n)**(p + S(2)), x), x) + Simp(cosh(a + b*x**n)**(p + S(2))/(b**S(2)*n*(p + S(1))*(p + S(2))), x) - Simp(x**n*sinh(a + b*x**n)*cosh(a + b*x**n)**(p + S(1))/(b*n*(p + S(1))), x) def replacement5756(a, b, m, n, p, x): return -Dist((p + S(2))/(p + S(1)), Int(x**m*sinh(a + b*x**n)**(p + S(2)), x), x) + Dist((m - S(2)*n + S(1))*(m - n + S(1))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), Int(x**(m - S(2)*n)*sinh(a + b*x**n)**(p + S(2)), x), x) + Simp(x**(m - n + S(1))*sinh(a + b*x**n)**(p + S(1))*cosh(a + b*x**n)/(b*n*(p + S(1))), x) - Simp(x**(m - S(2)*n + S(1))*(m - n + S(1))*sinh(a + b*x**n)**(p + S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), x) def replacement5757(a, b, m, n, p, x): return Dist((p + S(2))/(p + S(1)), Int(x**m*cosh(a + b*x**n)**(p + S(2)), x), x) - Dist((m - S(2)*n + S(1))*(m - n + S(1))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), Int(x**(m - S(2)*n)*cosh(a + b*x**n)**(p + S(2)), x), x) - Simp(x**(m - n + S(1))*sinh(a + b*x**n)*cosh(a + b*x**n)**(p + S(1))/(b*n*(p + S(1))), x) + Simp(x**(m - S(2)*n + S(1))*(m - n + S(1))*cosh(a + b*x**n)**(p + S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), x) def replacement5758(a, b, c, d, m, n, p, x): return -Subst(Int(x**(-m + S(-2))*(a + b*sinh(c + d*x**(-n)))**p, x), x, S(1)/x) def replacement5759(a, b, c, d, m, n, p, x): return -Subst(Int(x**(-m + S(-2))*(a + b*cosh(c + d*x**(-n)))**p, x), x, S(1)/x) def With5760(a, b, c, d, e, m, n, p, x): k = Denominator(m) return -Dist(k/e, Subst(Int(x**(-k*(m + S(1)) + S(-1))*(a + b*sinh(c + d*e**(-n)*x**(-k*n)))**p, x), x, (e*x)**(-S(1)/k)), x) def With5761(a, b, c, d, e, m, n, p, x): k = Denominator(m) return -Dist(k/e, Subst(Int(x**(-k*(m + S(1)) + S(-1))*(a + b*cosh(c + d*e**(-n)*x**(-k*n)))**p, x), x, (e*x)**(-S(1)/k)), x) def replacement5762(a, b, c, d, e, m, n, p, x): return -Dist((e*x)**m*(S(1)/x)**m, Subst(Int(x**(-m + S(-2))*(a + b*sinh(c + d*x**(-n)))**p, x), x, S(1)/x), x) def replacement5763(a, b, c, d, e, m, n, p, x): return -Dist((e*x)**m*(S(1)/x)**m, Subst(Int(x**(-m + S(-2))*(a + b*cosh(c + d*x**(-n)))**p, x), x, S(1)/x), x) def With5764(a, b, c, d, m, n, p, x): k = Denominator(n) return Dist(k, Subst(Int(x**(k*(m + S(1)) + S(-1))*(a + b*sinh(c + d*x**(k*n)))**p, x), x, x**(S(1)/k)), x) def With5765(a, b, c, d, m, n, p, x): k = Denominator(n) return Dist(k, Subst(Int(x**(k*(m + S(1)) + S(-1))*(a + b*cosh(c + d*x**(k*n)))**p, x), x, x**(S(1)/k)), x) def replacement5766(a, b, c, d, e, m, n, p, x): return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*sinh(c + d*x**n))**p, x), x) def replacement5767(a, b, c, d, e, m, n, p, x): return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*cosh(c + d*x**n))**p, x), x) def replacement5768(a, b, c, d, m, n, p, x): return Dist(S(1)/(m + S(1)), Subst(Int((a + b*sinh(c + d*x**(n/(m + S(1)))))**p, x), x, x**(m + S(1))), x) def replacement5769(a, b, c, d, m, n, p, x): return Dist(S(1)/(m + S(1)), Subst(Int((a + b*cosh(c + d*x**(n/(m + S(1)))))**p, x), x, x**(m + S(1))), x) def replacement5770(a, b, c, d, e, m, n, p, x): return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*sinh(c + d*x**n))**p, x), x) def replacement5771(a, b, c, d, e, m, n, p, x): return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*cosh(c + d*x**n))**p, x), x) def replacement5772(c, d, e, m, n, x): return -Dist(S(1)/2, Int((e*x)**m*exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int((e*x)**m*exp(c + d*x**n), x), x) def replacement5773(c, d, e, m, n, x): return Dist(S(1)/2, Int((e*x)**m*exp(-c - d*x**n), x), x) + Dist(S(1)/2, Int((e*x)**m*exp(c + d*x**n), x), x) def replacement5774(a, b, c, d, e, m, n, p, x): return Int(ExpandTrigReduce((e*x)**m, (a + b*sinh(c + d*x**n))**p, x), x) def replacement5775(a, b, c, d, e, m, n, p, x): return Int(ExpandTrigReduce((e*x)**m, (a + b*cosh(c + d*x**n))**p, x), x) def replacement5776(a, b, c, d, m, n, p, u, x): return Dist(Coefficient(u, x, S(1))**(-m + S(-1)), Subst(Int((a + b*sinh(c + d*x**n))**p*(x - Coefficient(u, x, S(0)))**m, x), x, u), x) def replacement5777(a, b, c, d, m, n, p, u, x): return Dist(Coefficient(u, x, S(1))**(-m + S(-1)), Subst(Int((a + b*cosh(c + d*x**n))**p*(x - Coefficient(u, x, S(0)))**m, x), x, u), x) def replacement5778(a, b, c, d, e, m, n, p, u, x): return Int((e*x)**m*(a + b*sinh(c + d*u**n))**p, x) def replacement5779(a, b, c, d, e, m, n, p, u, x): return Int((e*x)**m*(a + b*cosh(c + d*u**n))**p, x) def replacement5780(a, b, e, m, p, u, x): return Int((e*x)**m*(a + b*sinh(ExpandToSum(u, x)))**p, x) def replacement5781(a, b, e, m, p, u, x): return Int((e*x)**m*(a + b*cosh(ExpandToSum(u, x)))**p, x) def replacement5782(a, b, m, n, p, x): return Simp(sinh(a + b*x**n)**(p + S(1))/(b*n*(p + S(1))), x) def replacement5783(a, b, m, n, p, x): return Simp(cosh(a + b*x**n)**(p + S(1))/(b*n*(p + S(1))), x) def replacement5784(a, b, m, n, p, x): return -Dist((m - n + S(1))/(b*n*(p + S(1))), Int(x**(m - n)*sinh(a + b*x**n)**(p + S(1)), x), x) + Simp(x**(m - n + S(1))*sinh(a + b*x**n)**(p + S(1))/(b*n*(p + S(1))), x) def replacement5785(a, b, m, n, p, x): return -Dist((m - n + S(1))/(b*n*(p + S(1))), Int(x**(m - n)*cosh(a + b*x**n)**(p + S(1)), x), x) + Simp(x**(m - n + S(1))*cosh(a + b*x**n)**(p + S(1))/(b*n*(p + S(1))), x) def replacement5786(a, b, c, x): return -Dist(S(1)/2, Int(exp(-a - b*x - c*x**S(2)), x), x) + Dist(S(1)/2, Int(exp(a + b*x + c*x**S(2)), x), x) def replacement5787(a, b, c, x): return Dist(S(1)/2, Int(exp(-a - b*x - c*x**S(2)), x), x) + Dist(S(1)/2, Int(exp(a + b*x + c*x**S(2)), x), x) def replacement5788(a, b, c, n, x): return Int(ExpandTrigReduce(sinh(a + b*x + c*x**S(2))**n, x), x) def replacement5789(a, b, c, n, x): return Int(ExpandTrigReduce(cosh(a + b*x + c*x**S(2))**n, x), x) def replacement5790(n, v, x): return Int(sinh(ExpandToSum(v, x))**n, x) def replacement5791(n, v, x): return Int(cosh(ExpandToSum(v, x))**n, x) def replacement5792(a, b, c, d, e, x): return Simp(e*cosh(a + b*x + c*x**S(2))/(S(2)*c), x) def replacement5793(a, b, c, d, e, x): return Simp(e*sinh(a + b*x + c*x**S(2))/(S(2)*c), x) def replacement5794(a, b, c, d, e, x): return -Dist((b*e - S(2)*c*d)/(S(2)*c), Int(sinh(a + b*x + c*x**S(2)), x), x) + Simp(e*cosh(a + b*x + c*x**S(2))/(S(2)*c), x) def replacement5795(a, b, c, d, e, x): return -Dist((b*e - S(2)*c*d)/(S(2)*c), Int(cosh(a + b*x + c*x**S(2)), x), x) + Simp(e*sinh(a + b*x + c*x**S(2))/(S(2)*c), x) def replacement5796(a, b, c, d, e, m, x): return -Dist(e**S(2)*(m + S(-1))/(S(2)*c), Int((d + e*x)**(m + S(-2))*cosh(a + b*x + c*x**S(2)), x), x) + Simp(e*(d + e*x)**(m + S(-1))*cosh(a + b*x + c*x**S(2))/(S(2)*c), x) def replacement5797(a, b, c, d, e, m, x): return -Dist(e**S(2)*(m + S(-1))/(S(2)*c), Int((d + e*x)**(m + S(-2))*sinh(a + b*x + c*x**S(2)), x), x) + Simp(e*(d + e*x)**(m + S(-1))*sinh(a + b*x + c*x**S(2))/(S(2)*c), x) def replacement5798(a, b, c, d, e, m, x): return -Dist((b*e - S(2)*c*d)/(S(2)*c), Int((d + e*x)**(m + S(-1))*sinh(a + b*x + c*x**S(2)), x), x) - Dist(e**S(2)*(m + S(-1))/(S(2)*c), Int((d + e*x)**(m + S(-2))*cosh(a + b*x + c*x**S(2)), x), x) + Simp(e*(d + e*x)**(m + S(-1))*cosh(a + b*x + c*x**S(2))/(S(2)*c), x) def replacement5799(a, b, c, d, e, m, x): return -Dist((b*e - S(2)*c*d)/(S(2)*c), Int((d + e*x)**(m + S(-1))*cosh(a + b*x + c*x**S(2)), x), x) - Dist(e**S(2)*(m + S(-1))/(S(2)*c), Int((d + e*x)**(m + S(-2))*sinh(a + b*x + c*x**S(2)), x), x) + Simp(e*(d + e*x)**(m + S(-1))*sinh(a + b*x + c*x**S(2))/(S(2)*c), x) def replacement5800(a, b, c, d, e, m, x): return -Dist(S(2)*c/(e**S(2)*(m + S(1))), Int((d + e*x)**(m + S(2))*cosh(a + b*x + c*x**S(2)), x), x) + Simp((d + e*x)**(m + S(1))*sinh(a + b*x + c*x**S(2))/(e*(m + S(1))), x) def replacement5801(a, b, c, d, e, m, x): return -Dist(S(2)*c/(e**S(2)*(m + S(1))), Int((d + e*x)**(m + S(2))*sinh(a + b*x + c*x**S(2)), x), x) + Simp((d + e*x)**(m + S(1))*cosh(a + b*x + c*x**S(2))/(e*(m + S(1))), x) def replacement5802(a, b, c, d, e, m, x): return -Dist(S(2)*c/(e**S(2)*(m + S(1))), Int((d + e*x)**(m + S(2))*cosh(a + b*x + c*x**S(2)), x), x) - Dist((b*e - S(2)*c*d)/(e**S(2)*(m + S(1))), Int((d + e*x)**(m + S(1))*cosh(a + b*x + c*x**S(2)), x), x) + Simp((d + e*x)**(m + S(1))*sinh(a + b*x + c*x**S(2))/(e*(m + S(1))), x) def replacement5803(a, b, c, d, e, m, x): return -Dist(S(2)*c/(e**S(2)*(m + S(1))), Int((d + e*x)**(m + S(2))*sinh(a + b*x + c*x**S(2)), x), x) - Dist((b*e - S(2)*c*d)/(e**S(2)*(m + S(1))), Int((d + e*x)**(m + S(1))*sinh(a + b*x + c*x**S(2)), x), x) + Simp((d + e*x)**(m + S(1))*cosh(a + b*x + c*x**S(2))/(e*(m + S(1))), x) def replacement5804(a, b, c, d, e, m, x): return Int((d + e*x)**m*sinh(a + b*x + c*x**S(2)), x) def replacement5805(a, b, c, d, e, m, x): return Int((d + e*x)**m*cosh(a + b*x + c*x**S(2)), x) def replacement5806(a, b, c, d, e, m, n, x): return Int(ExpandTrigReduce((d + e*x)**m, sinh(a + b*x + c*x**S(2))**n, x), x) def replacement5807(a, b, c, d, e, m, n, x): return Int(ExpandTrigReduce((d + e*x)**m, cosh(a + b*x + c*x**S(2))**n, x), x) def replacement5808(m, n, u, v, x): return Int(ExpandToSum(u, x)**m*sinh(ExpandToSum(v, x))**n, x) def replacement5809(m, n, u, v, x): return Int(ExpandToSum(u, x)**m*cosh(ExpandToSum(v, x))**n, x) def replacement5810(a, b, e, f, m, x): return Dist(S(2), Int((a + b*x)**m*exp(S(2)*e + S(2)*f*x)/(exp(S(2)*e + S(2)*f*x) + S(1)), x), x) - Simp((a + b*x)**(m + S(1))/(b*(m + S(1))), x) def replacement5811(a, b, e, f, m, x): return -Dist(S(2), Int((a + b*x)**m*exp(S(2)*e + S(2)*f*x)/(S(1) - exp(S(2)*e + S(2)*f*x)), x), x) - Simp((a + b*x)**(m + S(1))/(b*(m + S(1))), x) def replacement5812(a, b, c, e, f, m, n, x): return Dist(c**S(2), Int((c*tanh(e + f*x))**(n + S(-2))*(a + b*x)**m, x), x) + Dist(b*c*m/(f*(n + S(-1))), Int((c*tanh(e + f*x))**(n + S(-1))*(a + b*x)**(m + S(-1)), x), x) - Simp(c*(c*tanh(e + f*x))**(n + S(-1))*(a + b*x)**m/(f*(n + S(-1))), x) def replacement5813(a, b, c, e, f, m, n, x): return Dist(c**S(2), Int((c/tanh(e + f*x))**(n + S(-2))*(a + b*x)**m, x), x) + Dist(b*c*m/(f*(n + S(-1))), Int((c/tanh(e + f*x))**(n + S(-1))*(a + b*x)**(m + S(-1)), x), x) - Simp(c*(c/tanh(e + f*x))**(n + S(-1))*(a + b*x)**m/(f*(n + S(-1))), x) def replacement5814(a, b, c, e, f, m, n, x): return Dist(c**(S(-2)), Int((c*tanh(e + f*x))**(n + S(2))*(a + b*x)**m, x), x) - Dist(b*m/(c*f*(n + S(1))), Int((c*tanh(e + f*x))**(n + S(1))*(a + b*x)**(m + S(-1)), x), x) + Simp((c*tanh(e + f*x))**(n + S(1))*(a + b*x)**m/(c*f*(n + S(1))), x) def replacement5815(a, b, c, e, f, m, n, x): return Dist(c**(S(-2)), Int((c/tanh(e + f*x))**(n + S(2))*(a + b*x)**m, x), x) - Dist(b*m/(c*f*(n + S(1))), Int((c/tanh(e + f*x))**(n + S(1))*(a + b*x)**(m + S(-1)), x), x) + Simp((c/tanh(e + f*x))**(n + S(1))*(a + b*x)**m/(c*f*(n + S(1))), x) def replacement5816(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (a + b*tanh(e + f*x))**n, x), x) def replacement5817(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (a + b/tanh(e + f*x))**n, x), x) def replacement5818(a, b, c, d, e, f, m, x): return Dist(a*d*m/(S(2)*b*f), Int((c + d*x)**(m + S(-1))/(a + b*tanh(e + f*x)), x), x) + Simp((c + d*x)**(m + S(1))/(S(2)*a*d*(m + S(1))), x) - Simp(a*(c + d*x)**m/(S(2)*b*f*(a + b*tanh(e + f*x))), x) def replacement5819(a, b, c, d, e, f, m, x): return Dist(a*d*m/(S(2)*b*f), Int((c + d*x)**(m + S(-1))/(a + b/tanh(e + f*x)), x), x) + Simp((c + d*x)**(m + S(1))/(S(2)*a*d*(m + S(1))), x) - Simp(a*(c + d*x)**m/(S(2)*b*f*(a + b/tanh(e + f*x))), x) def replacement5820(a, b, c, d, e, f, x): return Dist(f/(a*d), Int(sinh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) - Dist(f/(b*d), Int(cosh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) - Simp(S(1)/(d*(a + b*tanh(e + f*x))*(c + d*x)), x) def replacement5821(a, b, c, d, e, f, x): return -Dist(f/(a*d), Int(sinh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) + Dist(f/(b*d), Int(cosh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) - Simp(S(1)/(d*(a + b/tanh(e + f*x))*(c + d*x)), x) def replacement5822(a, b, c, d, e, f, m, x): return Dist(S(2)*b*f/(a*d*(m + S(1))), Int((c + d*x)**(m + S(1))/(a + b*tanh(e + f*x)), x), x) + Simp((c + d*x)**(m + S(1))/(d*(a + b*tanh(e + f*x))*(m + S(1))), x) - Simp(f*(c + d*x)**(m + S(2))/(b*d**S(2)*(m + S(1))*(m + S(2))), x) def replacement5823(a, b, c, d, e, f, m, x): return Dist(S(2)*b*f/(a*d*(m + S(1))), Int((c + d*x)**(m + S(1))/(a + b/tanh(e + f*x)), x), x) + Simp((c + d*x)**(m + S(1))/(d*(a + b/tanh(e + f*x))*(m + S(1))), x) - Simp(f*(c + d*x)**(m + S(2))/(b*d**S(2)*(m + S(1))*(m + S(2))), x) def replacement5824(a, b, c, d, e, f, x): return Dist(S(1)/(S(2)*a), Int(cosh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) - Dist(S(1)/(S(2)*b), Int(sinh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) + Simp(log(c + d*x)/(S(2)*a*d), x) def replacement5825(a, b, c, d, e, f, x): return -Dist(S(1)/(S(2)*a), Int(cosh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) + Dist(S(1)/(S(2)*b), Int(sinh(S(2)*e + S(2)*f*x)/(c + d*x), x), x) + Simp(log(c + d*x)/(S(2)*a*d), x) def replacement5826(a, b, c, d, e, f, m, x): return Dist(S(1)/(S(2)*a), Int((c + d*x)**m*exp(-S(2)*a*(e + f*x)/b), x), x) + Simp((c + d*x)**(m + S(1))/(S(2)*a*d*(m + S(1))), x) def replacement5827(a, b, c, d, e, f, m, x): return -Dist(S(1)/(S(2)*a), Int((c + d*x)**m*exp(-S(2)*a*(e + f*x)/b), x), x) + Simp((c + d*x)**(m + S(1))/(S(2)*a*d*(m + S(1))), x) def replacement5828(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (-sinh(S(2)*e + S(2)*f*x)/(S(2)*b) + cosh(S(2)*e + S(2)*f*x)/(S(2)*a) + S(1)/(S(2)*a))**(-n), x), x) def replacement5829(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (sinh(S(2)*e + S(2)*f*x)/(S(2)*b) - cosh(S(2)*e + S(2)*f*x)/(S(2)*a) + S(1)/(S(2)*a))**(-n), x), x) def replacement5830(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (S(1)/(S(2)*a) + exp(-S(2)*a*(e + f*x)/b)/(S(2)*a))**(-n), x), x) def replacement5831(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (S(1)/(S(2)*a) - exp(-S(2)*a*(e + f*x)/b)/(S(2)*a))**(-n), x), x) def With5832(a, b, c, d, e, f, m, n, x): u = IntHide((a + b*tanh(e + f*x))**n, x) return -Dist(d*m, Int(Dist((c + d*x)**(m + S(-1)), u, x), x), x) + Dist((c + d*x)**m, u, x) def With5833(a, b, c, d, e, f, m, n, x): u = IntHide((a + b/tanh(e + f*x))**n, x) return -Dist(d*m, Int(Dist((c + d*x)**(m + S(-1)), u, x), x), x) + Dist((c + d*x)**m, u, x) def replacement5834(a, b, c, d, e, f, m, x): return -Dist(S(2)*b, Int((c + d*x)**m/(a**S(2) - b**S(2) + (a - b)**S(2)*exp(-S(2)*e - S(2)*f*x)), x), x) + Simp((c + d*x)**(m + S(1))/(d*(a - b)*(m + S(1))), x) def replacement5835(a, b, c, d, e, f, m, x): return Dist(S(2)*b, Int((c + d*x)**m/(a**S(2) - b**S(2) - (a + b)**S(2)*exp(S(2)*e + S(2)*f*x)), x), x) + Simp((c + d*x)**(m + S(1))/(d*(a + b)*(m + S(1))), x) def replacement5836(a, b, c, d, e, f, x): return -Dist(S(1)/(f*(a**S(2) - b**S(2))), Int((-S(2)*a*c*f - S(2)*a*d*f*x + b*d)/(a + b*tanh(e + f*x)), x), x) - Simp((c + d*x)**S(2)/(S(2)*d*(a**S(2) - b**S(2))), x) + Simp(b*(c + d*x)/(f*(a + b*tanh(e + f*x))*(a**S(2) - b**S(2))), x) def replacement5837(a, b, c, d, e, f, x): return -Dist(S(1)/(f*(a**S(2) - b**S(2))), Int((-S(2)*a*c*f - S(2)*a*d*f*x + b*d)/(a + b/tanh(e + f*x)), x), x) - Simp((c + d*x)**S(2)/(S(2)*d*(a**S(2) - b**S(2))), x) + Simp(b*(c + d*x)/(f*(a + b/tanh(e + f*x))*(a**S(2) - b**S(2))), x) def replacement5838(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (-S(2)*b/(a**S(2) - b**S(2) + (a - b)**S(2)*exp(-S(2)*e - S(2)*f*x)) + S(1)/(a - b))**(-n), x), x) def replacement5839(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (S(2)*b/(a**S(2) - b**S(2) - (a + b)**S(2)*exp(S(2)*e + S(2)*f*x)) + S(1)/(a + b))**(-n), x), x) def replacement5840(a, b, m, n, u, v, x): return Int((a + b*tanh(ExpandToSum(v, x)))**n*ExpandToSum(u, x)**m, x) def replacement5841(a, b, m, n, u, v, x): return Int((a + b/tanh(ExpandToSum(v, x)))**n*ExpandToSum(u, x)**m, x) def replacement5842(a, b, c, d, e, f, m, n, x): return Int((a + b*tanh(e + f*x))**n*(c + d*x)**m, x) def replacement5843(a, b, c, d, e, f, m, n, x): return Int((a + b/tanh(e + f*x))**n*(c + d*x)**m, x) def replacement5844(a, b, c, d, n, p, x): return Dist(S(1)/n, Subst(Int(x**(S(-1) + S(1)/n)*(a + b*tanh(c + d*x))**p, x), x, x**n), x) def replacement5845(a, b, c, d, n, p, x): return Dist(S(1)/n, Subst(Int(x**(S(-1) + S(1)/n)*(a + b/tanh(c + d*x))**p, x), x, x**n), x) def replacement5846(a, b, c, d, n, p, x): return Int((a + b*tanh(c + d*x**n))**p, x) def replacement5847(a, b, c, d, n, p, x): return Int((a + b/tanh(c + d*x**n))**p, x) def replacement5848(a, b, c, d, n, p, u, x): return Dist(S(1)/Coefficient(u, x, S(1)), Subst(Int((a + b*tanh(c + d*x**n))**p, x), x, u), x) def replacement5849(a, b, c, d, n, p, u, x): return Dist(S(1)/Coefficient(u, x, S(1)), Subst(Int((a + b/tanh(c + d*x**n))**p, x), x, u), x) def replacement5850(a, b, p, u, x): return Int((a + b*tanh(ExpandToSum(u, x)))**p, x) def replacement5851(a, b, p, u, x): return Int((a + b/tanh(ExpandToSum(u, x)))**p, x) def replacement5852(a, b, c, d, m, n, p, x): return Dist(S(1)/n, Subst(Int(x**(S(-1) + (m + S(1))/n)*(a + b*tanh(c + d*x))**p, x), x, x**n), x) def replacement5853(a, b, c, d, m, n, p, x): return Dist(S(1)/n, Subst(Int(x**(S(-1) + (m + S(1))/n)*(a + b/tanh(c + d*x))**p, x), x, x**n), x) def replacement5854(c, d, m, n, x): return Dist((m - n + S(1))/(d*n), Int(x**(m - n)*tanh(c + d*x**n), x), x) + Int(x**m, x) - Simp(x**(m - n + S(1))*tanh(c + d*x**n)/(d*n), x) def replacement5855(c, d, m, n, x): return Dist((m - n + S(1))/(d*n), Int(x**(m - n)/tanh(c + d*x**n), x), x) + Int(x**m, x) - Simp(x**(m - n + S(1))/(d*n*tanh(c + d*x**n)), x) def replacement5856(a, b, c, d, m, n, p, x): return Int(x**m*(a + b*tanh(c + d*x**n))**p, x) def replacement5857(a, b, c, d, m, n, p, x): return Int(x**m*(a + b/tanh(c + d*x**n))**p, x) def replacement5858(a, b, c, d, e, m, n, p, x): return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b*tanh(c + d*x**n))**p, x), x) def replacement5859(a, b, c, d, e, m, n, p, x): return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b/tanh(c + d*x**n))**p, x), x) def replacement5860(a, b, e, m, p, u, x): return Int((e*x)**m*(a + b*tanh(ExpandToSum(u, x)))**p, x) def replacement5861(a, b, e, m, p, u, x): return Int((e*x)**m*(a + b/tanh(ExpandToSum(u, x)))**p, x) def replacement5862(a, b, m, n, p, q, x): return Dist((m - n + S(1))/(b*n*p), Int(x**(m - n)*(S(1)/cosh(a + b*x**n))**p, x), x) - Simp(x**(m - n + S(1))*(S(1)/cosh(a + b*x**n))**p/(b*n*p), x) def replacement5863(a, b, m, n, p, q, x): return Dist((m - n + S(1))/(b*n*p), Int(x**(m - n)*(S(1)/sinh(a + b*x**n))**p, x), x) - Simp(x**(m - n + S(1))*(S(1)/sinh(a + b*x**n))**p/(b*n*p), x) def replacement5864(a, b, c, n, x): return Int(tanh(a + b*x + c*x**S(2))**n, x) def replacement5865(a, b, c, n, x): return Int((S(1)/tanh(a + b*x + c*x**S(2)))**n, x) def replacement5866(a, b, c, d, e, x): return Dist((-b*e + S(2)*c*d)/(S(2)*c), Int(tanh(a + b*x + c*x**S(2)), x), x) + Simp(e*log(cosh(a + b*x + c*x**S(2)))/(S(2)*c), x) def replacement5867(a, b, c, d, e, x): return Dist((-b*e + S(2)*c*d)/(S(2)*c), Int(S(1)/tanh(a + b*x + c*x**S(2)), x), x) + Simp(e*log(sinh(a + b*x + c*x**S(2)))/(S(2)*c), x) def replacement5868(a, b, c, d, e, m, n, x): return Int((d + e*x)**m*tanh(a + b*x + c*x**S(2))**n, x) def replacement5869(a, b, c, d, e, m, n, x): return Int((d + e*x)**m*(S(1)/tanh(a + b*x + c*x**S(2)))**n, x) def replacement5870(a, b, c, d, m, x): return -Dist(I*d*m/b, Int((c + d*x)**(m + S(-1))*log(-I*exp(a + b*x) + S(1)), x), x) + Dist(I*d*m/b, Int((c + d*x)**(m + S(-1))*log(I*exp(a + b*x) + S(1)), x), x) + Simp(S(2)*(c + d*x)**m*ArcTan(exp(a + b*x))/b, x) def replacement5871(a, b, c, d, m, x): return -Dist(d*m/b, Int((c + d*x)**(m + S(-1))*log(S(1) - exp(a + b*x)), x), x) + Dist(d*m/b, Int((c + d*x)**(m + S(-1))*log(exp(a + b*x) + S(1)), x), x) + Simp(-S(2)*(c + d*x)**m*atanh(exp(a + b*x))/b, x) def replacement5872(a, b, c, d, m, x): return -Dist(d*m/b, Int((c + d*x)**(m + S(-1))*tanh(a + b*x), x), x) + Simp((c + d*x)**m*tanh(a + b*x)/b, x) def replacement5873(a, b, c, d, m, x): return Dist(d*m/b, Int((c + d*x)**(m + S(-1))/tanh(a + b*x), x), x) - Simp((c + d*x)**m/(b*tanh(a + b*x)), x) def replacement5874(a, b, c, d, n, x): return Dist((n + S(-2))/(n + S(-1)), Int((c + d*x)*(S(1)/cosh(a + b*x))**(n + S(-2)), x), x) + Simp(d*(S(1)/cosh(a + b*x))**(n + S(-2))/(b**S(2)*(n + S(-2))*(n + S(-1))), x) + Simp((c + d*x)*(S(1)/cosh(a + b*x))**(n + S(-2))*tanh(a + b*x)/(b*(n + S(-1))), x) def replacement5875(a, b, c, d, n, x): return -Dist((n + S(-2))/(n + S(-1)), Int((c + d*x)*(S(1)/sinh(a + b*x))**(n + S(-2)), x), x) - Simp(d*(S(1)/sinh(a + b*x))**(n + S(-2))/(b**S(2)*(n + S(-2))*(n + S(-1))), x) - Simp((c + d*x)*(S(1)/sinh(a + b*x))**(n + S(-2))/(b*(n + S(-1))*tanh(a + b*x)), x) def replacement5876(a, b, c, d, m, n, x): return Dist((n + S(-2))/(n + S(-1)), Int((c + d*x)**m*(S(1)/cosh(a + b*x))**(n + S(-2)), x), x) - Dist(d**S(2)*m*(m + S(-1))/(b**S(2)*(n + S(-2))*(n + S(-1))), Int((c + d*x)**(m + S(-2))*(S(1)/cosh(a + b*x))**(n + S(-2)), x), x) + Simp((c + d*x)**m*(S(1)/cosh(a + b*x))**(n + S(-2))*tanh(a + b*x)/(b*(n + S(-1))), x) + Simp(d*m*(c + d*x)**(m + S(-1))*(S(1)/cosh(a + b*x))**(n + S(-2))/(b**S(2)*(n + S(-2))*(n + S(-1))), x) def replacement5877(a, b, c, d, m, n, x): return -Dist((n + S(-2))/(n + S(-1)), Int((c + d*x)**m*(S(1)/sinh(a + b*x))**(n + S(-2)), x), x) + Dist(d**S(2)*m*(m + S(-1))/(b**S(2)*(n + S(-2))*(n + S(-1))), Int((c + d*x)**(m + S(-2))*(S(1)/sinh(a + b*x))**(n + S(-2)), x), x) - Simp((c + d*x)**m*(S(1)/sinh(a + b*x))**(n + S(-2))/(b*(n + S(-1))*tanh(a + b*x)), x) - Simp(d*m*(c + d*x)**(m + S(-1))*(S(1)/sinh(a + b*x))**(n + S(-2))/(b**S(2)*(n + S(-2))*(n + S(-1))), x) def replacement5878(a, b, c, d, n, x): return Dist((n + S(1))/n, Int((c + d*x)*(S(1)/cosh(a + b*x))**(n + S(2)), x), x) - Simp(d*(S(1)/cosh(a + b*x))**n/(b**S(2)*n**S(2)), x) - Simp((c + d*x)*(S(1)/cosh(a + b*x))**(n + S(1))*sinh(a + b*x)/(b*n), x) def replacement5879(a, b, c, d, n, x): return -Dist((n + S(1))/n, Int((c + d*x)*(S(1)/sinh(a + b*x))**(n + S(2)), x), x) - Simp(d*(S(1)/sinh(a + b*x))**n/(b**S(2)*n**S(2)), x) - Simp((c + d*x)*(S(1)/sinh(a + b*x))**(n + S(1))*cosh(a + b*x)/(b*n), x) def replacement5880(a, b, c, d, m, n, x): return Dist((n + S(1))/n, Int((c + d*x)**m*(S(1)/cosh(a + b*x))**(n + S(2)), x), x) + Dist(d**S(2)*m*(m + S(-1))/(b**S(2)*n**S(2)), Int((c + d*x)**(m + S(-2))*(S(1)/cosh(a + b*x))**n, x), x) - Simp((c + d*x)**m*(S(1)/cosh(a + b*x))**(n + S(1))*sinh(a + b*x)/(b*n), x) - Simp(d*m*(c + d*x)**(m + S(-1))*(S(1)/cosh(a + b*x))**n/(b**S(2)*n**S(2)), x) def replacement5881(a, b, c, d, m, n, x): return -Dist((n + S(1))/n, Int((c + d*x)**m*(S(1)/sinh(a + b*x))**(n + S(2)), x), x) + Dist(d**S(2)*m*(m + S(-1))/(b**S(2)*n**S(2)), Int((c + d*x)**(m + S(-2))*(S(1)/sinh(a + b*x))**n, x), x) - Simp((c + d*x)**m*(S(1)/sinh(a + b*x))**(n + S(1))*cosh(a + b*x)/(b*n), x) - Simp(d*m*(c + d*x)**(m + S(-1))*(S(1)/sinh(a + b*x))**n/(b**S(2)*n**S(2)), x) def replacement5882(a, b, c, d, m, n, x): return Dist((S(1)/cosh(a + b*x))**n*cosh(a + b*x)**n, Int((c + d*x)**m*cosh(a + b*x)**(-n), x), x) def replacement5883(a, b, c, d, m, n, x): return Dist((S(1)/sinh(a + b*x))**n*sinh(a + b*x)**n, Int((c + d*x)**m*sinh(a + b*x)**(-n), x), x) def replacement5884(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (a + b/cosh(e + f*x))**n, x), x) def replacement5885(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (a + b/sinh(e + f*x))**n, x), x) def replacement5886(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (a*cosh(e + f*x) + b)**n*cosh(e + f*x)**(-n), x), x) def replacement5887(a, b, c, d, e, f, m, n, x): return Int(ExpandIntegrand((c + d*x)**m, (a*sinh(e + f*x) + b)**n*sinh(e + f*x)**(-n), x), x) def replacement5888(m, n, u, v, x): return Int((S(1)/cosh(ExpandToSum(v, x)))**n*ExpandToSum(u, x)**m, x) def replacement5889(m, n, u, v, x): return Int((S(1)/sinh(ExpandToSum(v, x)))**n*ExpandToSum(u, x)**m, x) def replacement5890(a, b, c, d, m, n, x): return Int((c + d*x)**m*(S(1)/cosh(a + b*x))**n, x) def replacement5891(a, b, c, d, m, n, x): return Int((c + d*x)**m*(S(1)/sinh(a + b*x))**n, x) def replacement5892(a, b, c, d, n, p, x): return Dist(S(1)/n, Subst(Int(x**(S(-1) + S(1)/n)*(a + b/cosh(c + d*x))**p, x), x, x**n), x) def replacement5893(a, b, c, d, n, p, x): return Dist(S(1)/n, Subst(Int(x**(S(-1) + S(1)/n)*(a + b/sinh(c + d*x))**p, x), x, x**n), x) def replacement5894(a, b, c, d, n, p, x): return Int((a + b/cosh(c + d*x**n))**p, x) def replacement5895(a, b, c, d, n, p, x): return Int((a + b/sinh(c + d*x**n))**p, x) def replacement5896(a, b, c, d, n, p, u, x): return Dist(S(1)/Coefficient(u, x, S(1)), Subst(Int((a + b/cosh(c + d*x**n))**p, x), x, u), x) def replacement5897(a, b, c, d, n, p, u, x): return Dist(S(1)/Coefficient(u, x, S(1)), Subst(Int((a + b/sinh(c + d*x**n))**p, x), x, u), x) def replacement5898(a, b, p, u, x): return Int((a + b/cosh(ExpandToSum(u, x)))**p, x) def replacement5899(a, b, p, u, x): return Int((a + b/sinh(ExpandToSum(u, x)))**p, x) def replacement5900(a, b, c, d, m, n, p, x): return Dist(S(1)/n, Subst(Int(x**(S(-1) + (m + S(1))/n)*(a + b/cosh(c + d*x))**p, x), x, x**n), x) def replacement5901(a, b, c, d, m, n, p, x): return Dist(S(1)/n, Subst(Int(x**(S(-1) + (m + S(1))/n)*(a + b/sinh(c + d*x))**p, x), x, x**n), x) def replacement5902(a, b, c, d, m, n, p, x): return Int(x**m*(a + b/cosh(c + d*x**n))**p, x) def replacement5903(a, b, c, d, m, n, p, x): return Int(x**m*(a + b/sinh(c + d*x**n))**p, x) def replacement5904(a, b, c, d, e, m, n, p, x): return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b/cosh(c + d*x**n))**p, x), x) def replacement5905(a, b, c, d, e, m, n, p, x): return Dist(e**IntPart(m)*x**(-FracPart(m))*(e*x)**FracPart(m), Int(x**m*(a + b/sinh(c + d*x**n))**p, x), x) def replacement5906(a, b, e, m, p, u, x): return Int((e*x)**m*(a + b/cosh(ExpandToSum(u, x)))**p, x) def replacement5907(a, b, e, m, p, u, x): return Int((e*x)**m*(a + b/sinh(ExpandToSum(u, x)))**p, x) def replacement5908(a, b, m, n, p, x): return Dist((m - n + S(1))/(b*n*(p + S(-1))), Int(x**(m - n)*(S(1)/cosh(a + b*x**n))**(p + S(-1)), x), x) - Simp(x**(m - n + S(1))*(S(1)/cosh(a + b*x**n))**(p + S(-1))/(b*n*(p + S(-1))), x) def replacement5909(a, b, m, n, p, x): return Dist((m - n + S(1))/(b*n*(p + S(-1))), Int(x**(m - n)*(S(1)/sinh(a + b*x**n))**(p + S(-1)), x), x) - Simp(x**(m - n + S(1))*(S(1)/sinh(a + b*x**n))**(p + S(-1))/(b*n*(p + S(-1))), x) def replacement5910(a, b, c, d, m, n, x): return -Dist(d*m/(b*(n + S(1))), Int((c + d*x)**(m + S(-1))*sinh(a + b*x)**(n + S(1)), x), x) + Simp((c + d*x)**m*sinh(a + b*x)**(n + S(1))/(b*(n + S(1))), x) def replacement5911(a, b, c, d, m, n, x): return -Dist(d*m/(b*(n + S(1))), Int((c + d*x)**(m + S(-1))*cosh(a + b*x)**(n + S(1)), x), x) + Simp((c + d*x)**m*cosh(a + b*x)**(n + S(1))/(b*(n + S(1))), x) def replacement5912(a, b, c, d, m, n, p, x): return Int(ExpandTrigReduce((c + d*x)**m, sinh(a + b*x)**n*cosh(a + b*x)**p, x), x) def replacement5913(a, b, c, d, m, n, p, x): return Int((c + d*x)**m*sinh(a + b*x)**n*tanh(a + b*x)**(p + S(-2)), x) - Int((c + d*x)**m*sinh(a + b*x)**(n + S(-2))*tanh(a + b*x)**p, x) def replacement5914(a, b, c, d, m, n, p, x): return Int((c + d*x)**m*(S(1)/tanh(a + b*x))**p*cosh(a + b*x)**(n + S(-2)), x) + Int((c + d*x)**m*(S(1)/tanh(a + b*x))**(p + S(-2))*cosh(a + b*x)**n, x) def replacement5915(a, b, c, d, m, n, p, x): return Dist(d*m/(b*n), Int((c + d*x)**(m + S(-1))*(S(1)/cosh(a + b*x))**n, x), x) - Simp((c + d*x)**m*(S(1)/cosh(a + b*x))**n/(b*n), x) def replacement5916(a, b, c, d, m, n, p, x): return Dist(d*m/(b*n), Int((c + d*x)**(m + S(-1))*(S(1)/sinh(a + b*x))**n, x), x) - Simp((c + d*x)**m*(S(1)/sinh(a + b*x))**n/(b*n), x) def replacement5917(a, b, c, d, m, n, x): return -Dist(d*m/(b*(n + S(1))), Int((c + d*x)**(m + S(-1))*tanh(a + b*x)**(n + S(1)), x), x) + Simp((c + d*x)**m*tanh(a + b*x)**(n + S(1))/(b*(n + S(1))), x) def replacement5918(a, b, c, d, m, n, x): return Dist(d*m/(b*(n + S(1))), Int((c + d*x)**(m + S(-1))*(S(1)/tanh(a + b*x))**(n + S(1)), x), x) - Simp((c + d*x)**m*(S(1)/tanh(a + b*x))**(n + S(1))/(b*(n + S(1))), x) def replacement5919(a, b, c, d, m, p, x): return -Int((c + d*x)**m*tanh(a + b*x)**(p + S(-2))/cosh(a + b*x)**S(3), x) + Int((c + d*x)**m*tanh(a + b*x)**(p + S(-2))/cosh(a + b*x), x) def replacement5920(a, b, c, d, m, n, p, x): return Int((c + d*x)**m*(S(1)/cosh(a + b*x))**n*tanh(a + b*x)**(p + S(-2)), x) - Int((c + d*x)**m*(S(1)/cosh(a + b*x))**(n + S(2))*tanh(a + b*x)**(p + S(-2)), x) def replacement5921(a, b, c, d, m, p, x): return Int((c + d*x)**m*(S(1)/tanh(a + b*x))**(p + S(-2))/sinh(a + b*x)**S(3), x) + Int((c + d*x)**m*(S(1)/tanh(a + b*x))**(p + S(-2))/sinh(a + b*x), x) def replacement5922(a, b, c, d, m, n, p, x): return Int((c + d*x)**m*(S(1)/sinh(a + b*x))**n*(S(1)/tanh(a + b*x))**(p + S(-2)), x) + Int((c + d*x)**m*(S(1)/sinh(a + b*x))**(n + S(2))*(S(1)/tanh(a + b*x))**(p + S(-2)), x) def With5923(a, b, c, d, m, n, p, x): u = IntHide((S(1)/cosh(a + b*x))**n*tanh(a + b*x)**p, x) return -Dist(d*m, Int(u*(c + d*x)**(m + S(-1)), x), x) + Dist((c + d*x)**m, u, x) def With5924(a, b, c, d, m, n, p, x): u = IntHide((S(1)/sinh(a + b*x))**n*(S(1)/tanh(a + b*x))**p, x) return -Dist(d*m, Int(u*(c + d*x)**(m + S(-1)), x), x) + Dist((c + d*x)**m, u, x) def replacement5925(a, b, c, d, m, n, x): return Dist(S(2)**n, Int((c + d*x)**m*(S(1)/sinh(S(2)*a + S(2)*b*x))**n, x), x) def With5926(a, b, c, d, m, n, p, x): u = IntHide((S(1)/sinh(a + b*x))**n*(S(1)/cosh(a + b*x))**p, x) return -Dist(d*m, Int(u*(c + d*x)**(m + S(-1)), x), x) + Dist((c + d*x)**m, u, x) def replacement5927(F, G, m, n, p, u, v, w, x): return Int(ExpandToSum(u, x)**m*F(ExpandToSum(v, x))**n*G(ExpandToSum(v, x))**p, x) def replacement5928(a, b, c, d, e, f, m, n, x): return -Dist(f*m/(b*d*(n + S(1))), Int((a + b*sinh(c + d*x))**(n + S(1))*(e + f*x)**(m + S(-1)), x), x) + Simp((a + b*sinh(c + d*x))**(n + S(1))*(e + f*x)**m/(b*d*(n + S(1))), x) def replacement5929(a, b, c, d, e, f, m, n, x): return -Dist(f*m/(b*d*(n + S(1))), Int((a + b*cosh(c + d*x))**(n + S(1))*(e + f*x)**(m + S(-1)), x), x) + Simp((a + b*cosh(c + d*x))**(n + S(1))*(e + f*x)**m/(b*d*(n + S(1))), x) def replacement5930(a, b, c, d, e, f, m, n, x): return -Dist(f*m/(b*d*(n + S(1))), Int((a + b*tanh(c + d*x))**(n + S(1))*(e + f*x)**(m + S(-1)), x), x) + Simp((a + b*tanh(c + d*x))**(n + S(1))*(e + f*x)**m/(b*d*(n + S(1))), x) def replacement5931(a, b, c, d, e, f, m, n, x): return Dist(f*m/(b*d*(n + S(1))), Int((a + b/tanh(c + d*x))**(n + S(1))*(e + f*x)**(m + S(-1)), x), x) - Simp((a + b/tanh(c + d*x))**(n + S(1))*(e + f*x)**m/(b*d*(n + S(1))), x) def replacement5932(a, b, c, d, e, f, m, n, x): return Dist(f*m/(b*d*(n + S(1))), Int((a + b/cosh(c + d*x))**(n + S(1))*(e + f*x)**(m + S(-1)), x), x) - Simp((a + b/cosh(c + d*x))**(n + S(1))*(e + f*x)**m/(b*d*(n + S(1))), x) def replacement5933(a, b, c, d, e, f, m, n, x): return Dist(f*m/(b*d*(n + S(1))), Int((a + b/sinh(c + d*x))**(n + S(1))*(e + f*x)**(m + S(-1)), x), x) - Simp((a + b/sinh(c + d*x))**(n + S(1))*(e + f*x)**m/(b*d*(n + S(1))), x) def replacement5934(a, b, c, d, e, f, m, p, q, x): return Int(ExpandTrigReduce((e + f*x)**m, sinh(a + b*x)**p*sinh(c + d*x)**q, x), x) def replacement5935(a, b, c, d, e, f, m, p, q, x): return Int(ExpandTrigReduce((e + f*x)**m, cosh(a + b*x)**p*cosh(c + d*x)**q, x), x) def replacement5936(a, b, c, d, e, f, m, p, q, x): return Int(ExpandTrigReduce((e + f*x)**m, sinh(a + b*x)**p*cosh(c + d*x)**q, x), x) def replacement5937(F, G, a, b, c, d, e, f, m, p, q, x): return Int(ExpandTrigExpand((e + f*x)**m*G(c + d*x)**q, F, c + d*x, p, b/d, x), x) def replacement5938(F, a, b, c, d, e, x): return Simp(F**(c*(a + b*x))*e*cosh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)), x) - Simp(F**(c*(a + b*x))*b*c*log(F)*sinh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)), x) def replacement5939(F, a, b, c, d, e, x): return Simp(F**(c*(a + b*x))*e*sinh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)), x) - Simp(F**(c*(a + b*x))*b*c*log(F)*cosh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)), x) def replacement5940(F, a, b, c, d, e, n, x): return -Dist(e**S(2)*n*(n + S(-1))/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), Int(F**(c*(a + b*x))*sinh(d + e*x)**(n + S(-2)), x), x) - Simp(F**(c*(a + b*x))*b*c*log(F)*sinh(d + e*x)**n/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x) + Simp(F**(c*(a + b*x))*e*n*sinh(d + e*x)**(n + S(-1))*cosh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x) def replacement5941(F, a, b, c, d, e, n, x): return Dist(e**S(2)*n*(n + S(-1))/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), Int(F**(c*(a + b*x))*cosh(d + e*x)**(n + S(-2)), x), x) - Simp(F**(c*(a + b*x))*b*c*log(F)*cosh(d + e*x)**n/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x) + Simp(F**(c*(a + b*x))*e*n*sinh(d + e*x)*cosh(d + e*x)**(n + S(-1))/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x) def replacement5942(F, a, b, c, d, e, n, x): return Simp(F**(c*(a + b*x))*sinh(d + e*x)**(n + S(1))*cosh(d + e*x)/(e*(n + S(1))), x) - Simp(F**(c*(a + b*x))*b*c*log(F)*sinh(d + e*x)**(n + S(2))/(e**S(2)*(n + S(1))*(n + S(2))), x) def replacement5943(F, a, b, c, d, e, n, x): return -Simp(F**(c*(a + b*x))*sinh(d + e*x)*cosh(d + e*x)**(n + S(1))/(e*(n + S(1))), x) + Simp(F**(c*(a + b*x))*b*c*log(F)*cosh(d + e*x)**(n + S(2))/(e**S(2)*(n + S(1))*(n + S(2))), x) def replacement5944(F, a, b, c, d, e, n, x): return -Dist((-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*(n + S(2))**S(2))/(e**S(2)*(n + S(1))*(n + S(2))), Int(F**(c*(a + b*x))*sinh(d + e*x)**(n + S(2)), x), x) + Simp(F**(c*(a + b*x))*sinh(d + e*x)**(n + S(1))*cosh(d + e*x)/(e*(n + S(1))), x) - Simp(F**(c*(a + b*x))*b*c*log(F)*sinh(d + e*x)**(n + S(2))/(e**S(2)*(n + S(1))*(n + S(2))), x) def replacement5945(F, a, b, c, d, e, n, x): return Dist((-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*(n + S(2))**S(2))/(e**S(2)*(n + S(1))*(n + S(2))), Int(F**(c*(a + b*x))*cosh(d + e*x)**(n + S(2)), x), x) - Simp(F**(c*(a + b*x))*sinh(d + e*x)*cosh(d + e*x)**(n + S(1))/(e*(n + S(1))), x) + Simp(F**(c*(a + b*x))*b*c*log(F)*cosh(d + e*x)**(n + S(2))/(e**S(2)*(n + S(1))*(n + S(2))), x) def replacement5946(F, a, b, c, d, e, n, x): return Dist((exp(S(2)*d + S(2)*e*x) + S(-1))**(-n)*exp(n*(d + e*x))*sinh(d + e*x)**n, Int(F**(c*(a + b*x))*(exp(S(2)*d + S(2)*e*x) + S(-1))**n*exp(-n*(d + e*x)), x), x) def replacement5947(F, a, b, c, d, e, n, x): return Dist((exp(S(2)*d + S(2)*e*x) + S(1))**(-n)*exp(n*(d + e*x))*cosh(d + e*x)**n, Int(F**(c*(a + b*x))*(exp(S(2)*d + S(2)*e*x) + S(1))**n*exp(-n*(d + e*x)), x), x) def replacement5948(F, a, b, c, d, e, n, x): return Int(ExpandIntegrand(F**(c*(a + b*x))*(exp(S(2)*d + S(2)*e*x) + S(-1))**n*(exp(S(2)*d + S(2)*e*x) + S(1))**(-n), x), x) def replacement5949(F, a, b, c, d, e, n, x): return Int(ExpandIntegrand(F**(c*(a + b*x))*(exp(S(2)*d + S(2)*e*x) + S(-1))**(-n)*(exp(S(2)*d + S(2)*e*x) + S(1))**n, x), x) def replacement5950(F, a, b, c, d, e, n, x): return Dist(e**S(2)*n*(n + S(1))/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), Int(F**(c*(a + b*x))*(S(1)/cosh(d + e*x))**(n + S(2)), x), x) - Simp(F**(c*(a + b*x))*b*c*(S(1)/cosh(d + e*x))**n*log(F)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x) - Simp(F**(c*(a + b*x))*e*n*(S(1)/cosh(d + e*x))**(n + S(1))*sinh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x) def replacement5951(F, a, b, c, d, e, n, x): return -Dist(e**S(2)*n*(n + S(1))/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), Int(F**(c*(a + b*x))*(S(1)/sinh(d + e*x))**(n + S(2)), x), x) - Simp(F**(c*(a + b*x))*b*c*(S(1)/sinh(d + e*x))**n*log(F)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x) - Simp(F**(c*(a + b*x))*e*n*(S(1)/sinh(d + e*x))**(n + S(1))*cosh(d + e*x)/(-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*n**S(2)), x) def replacement5952(F, a, b, c, d, e, n, x): return Simp(F**(c*(a + b*x))*(S(1)/cosh(d + e*x))**(n + S(-1))*sinh(d + e*x)/(e*(n + S(-1))), x) + Simp(F**(c*(a + b*x))*b*c*(S(1)/cosh(d + e*x))**(n + S(-2))*log(F)/(e**S(2)*(n + S(-2))*(n + S(-1))), x) def replacement5953(F, a, b, c, d, e, n, x): return -Simp(F**(c*(a + b*x))*(S(1)/sinh(d + e*x))**(n + S(-1))*cosh(d + e*x)/(e*(n + S(-1))), x) - Simp(F**(c*(a + b*x))*b*c*(S(1)/sinh(d + e*x))**(n + S(-2))*log(F)/(e**S(2)*(n + S(-2))*(n + S(-1))), x) def replacement5954(F, a, b, c, d, e, n, x): return Dist((-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*(n + S(-2))**S(2))/(e**S(2)*(n + S(-2))*(n + S(-1))), Int(F**(c*(a + b*x))*(S(1)/cosh(d + e*x))**(n + S(-2)), x), x) + Simp(F**(c*(a + b*x))*(S(1)/cosh(d + e*x))**(n + S(-1))*sinh(d + e*x)/(e*(n + S(-1))), x) + Simp(F**(c*(a + b*x))*b*c*(S(1)/cosh(d + e*x))**(n + S(-2))*log(F)/(e**S(2)*(n + S(-2))*(n + S(-1))), x) def replacement5955(F, a, b, c, d, e, n, x): return -Dist((-b**S(2)*c**S(2)*log(F)**S(2) + e**S(2)*(n + S(-2))**S(2))/(e**S(2)*(n + S(-2))*(n + S(-1))), Int(F**(c*(a + b*x))*(S(1)/sinh(d + e*x))**(n + S(-2)), x), x) - Simp(F**(c*(a + b*x))*(S(1)/sinh(d + e*x))**(n + S(-1))*cosh(d + e*x)/(e*(n + S(-1))), x) - Simp(F**(c*(a + b*x))*b*c*(S(1)/sinh(d + e*x))**(n + S(-2))*log(F)/(e**S(2)*(n + S(-2))*(n + S(-1))), x) def replacement5956(F, a, b, c, d, e, n, x): return Simp(S(2)**n*F**(c*(a + b*x))*Hypergeometric2F1(n, b*c*log(F)/(S(2)*e) + n/S(2), b*c*log(F)/(S(2)*e) + n/S(2) + S(1), -exp(S(2)*d + S(2)*e*x))*exp(n*(d + e*x))/(b*c*log(F) + e*n), x) def replacement5957(F, a, b, c, d, e, n, x): return Simp((S(-2))**n*F**(c*(a + b*x))*Hypergeometric2F1(n, b*c*log(F)/(S(2)*e) + n/S(2), b*c*log(F)/(S(2)*e) + n/S(2) + S(1), exp(S(2)*d + S(2)*e*x))*exp(n*(d + e*x))/(b*c*log(F) + e*n), x) def replacement5958(F, a, b, c, d, e, n, x): return Dist((exp(S(2)*d + S(2)*e*x) + S(1))**n*(S(1)/cosh(d + e*x))**n*exp(-n*(d + e*x)), Int(SimplifyIntegrand(F**(c*(a + b*x))*(exp(S(2)*d + S(2)*e*x) + S(1))**(-n)*exp(n*(d + e*x)), x), x), x) def replacement5959(F, a, b, c, d, e, n, x): return Dist((S(1) - exp(-S(2)*d - S(2)*e*x))**n*(S(1)/sinh(d + e*x))**n*exp(n*(d + e*x)), Int(SimplifyIntegrand(F**(c*(a + b*x))*(S(1) - exp(-S(2)*d - S(2)*e*x))**(-n)*exp(-n*(d + e*x)), x), x), x) def replacement5960(F, a, b, c, d, e, f, g, n, x): return Dist(S(2)**n*f**n, Int(F**(c*(a + b*x))*cosh(-Pi*f/(S(4)*g) + d/S(2) + e*x/S(2))**(S(2)*n), x), x) def replacement5961(F, a, b, c, d, e, f, g, n, x): return Dist(S(2)**n*g**n, Int(F**(c*(a + b*x))*cosh(d/S(2) + e*x/S(2))**(S(2)*n), x), x) def replacement5962(F, a, b, c, d, e, f, g, n, x): return Dist(S(2)**n*g**n, Int(F**(c*(a + b*x))*sinh(d/S(2) + e*x/S(2))**(S(2)*n), x), x) def replacement5963(F, a, b, c, d, e, f, g, m, n, x): return Dist(g**n, Int(F**(c*(a + b*x))*tanh(-Pi*f/(S(4)*g) + d/S(2) + e*x/S(2))**m, x), x) def replacement5964(F, a, b, c, d, e, f, g, m, n, x): return Dist(g**n, Int(F**(c*(a + b*x))*tanh(d/S(2) + e*x/S(2))**m, x), x) def replacement5965(F, a, b, c, d, e, f, g, m, n, x): return Dist(g**n, Int(F**(c*(a + b*x))*(S(1)/tanh(d/S(2) + e*x/S(2)))**m, x), x) def replacement5966(F, a, b, c, d, e, f, g, h, i, x): return Dist(S(2)*i, Int(F**(c*(a + b*x))*cosh(d + e*x)/(f + g*sinh(d + e*x)), x), x) + Int(F**(c*(a + b*x))*(h - i*cosh(d + e*x))/(f + g*sinh(d + e*x)), x) def replacement5967(F, a, b, c, d, e, f, g, h, i, x): return Dist(S(2)*i, Int(F**(c*(a + b*x))*sinh(d + e*x)/(f + g*cosh(d + e*x)), x), x) + Int(F**(c*(a + b*x))*(h - i*sinh(d + e*x))/(f + g*cosh(d + e*x)), x) def replacement5968(F, G, c, n, u, v, x): return Int(F**(c*ExpandToSum(u, x))*G(ExpandToSum(v, x))**n, x) def With5969(F, a, b, c, d, e, m, n, x): u = IntHide(F**(c*(a + b*x))*sinh(d + e*x)**n, x) return -Dist(m, Int(u*x**(m + S(-1)), x), x) + Simp(u*x**m, x) def With5970(F, a, b, c, d, e, m, n, x): u = IntHide(F**(c*(a + b*x))*cosh(d + e*x)**n, x) return -Dist(m, Int(u*x**(m + S(-1)), x), x) + Simp(u*x**m, x) def replacement5971(F, a, b, c, d, e, f, g, m, n, x): return Int(ExpandTrigReduce(F**(c*(a + b*x)), sinh(d + e*x)**m*cosh(f + g*x)**n, x), x) def replacement5972(F, a, b, c, d, e, f, g, m, n, p, x): return Int(ExpandTrigReduce(F**(c*(a + b*x))*x**p, sinh(d + e*x)**m*cosh(f + g*x)**n, x), x) def replacement5973(F, G, H, a, b, c, d, e, m, n, x): return Int(ExpandTrigToExp(F**(c*(a + b*x)), G(d + e*x)**m*H(d + e*x)**n, x), x) def replacement5974(F, n, u, v, x): return Int(ExpandTrigToExp(F**u, sinh(v)**n, x), x) def replacement5975(F, n, u, v, x): return Int(ExpandTrigToExp(F**u, cosh(v)**n, x), x) def replacement5976(F, m, n, u, v, x): return Int(ExpandTrigToExp(F**u, sinh(v)**m*cosh(v)**n, x), x) def replacement5977(b, c, n, p, x): return Int(((c*x**n)**b/S(2) - (c*x**n)**(-b)/S(2))**p, x) def replacement5978(b, c, n, p, x): return Int(((c*x**n)**b/S(2) + (c*x**n)**(-b)/S(2))**p, x) def replacement5979(a, b, c, n, p, x): return -Simp(x*(p + S(2))*sinh(a + b*log(c*x**n))**(p + S(2))/(p + S(1)), x) + Simp(x*sinh(a + b*log(c*x**n))**(p + S(2))/(b*n*(p + S(1))*tanh(a + b*log(c*x**n))), x) def replacement5980(a, b, c, n, p, x): return Simp(x*(p + S(2))*cosh(a + b*log(c*x**n))**(p + S(2))/(p + S(1)), x) - Simp(x*cosh(a + b*log(c*x**n))**(p + S(2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(1))), x) def replacement5981(a, b, c, n, x): return Dist(x*sqrt(sinh(a + b*log(c*x**n)))/sqrt((c*x**n)**(S(4)/n)*exp(S(2)*a) + S(-1)), Int(sqrt((c*x**n)**(S(4)/n)*exp(S(2)*a) + S(-1))/x, x), x) def replacement5982(a, b, c, n, x): return Dist(x*sqrt(cosh(a + b*log(c*x**n)))/sqrt((c*x**n)**(S(4)/n)*exp(S(2)*a) + S(1)), Int(sqrt((c*x**n)**(S(4)/n)*exp(S(2)*a) + S(1))/x, x), x) def replacement5983(a, b, c, n, p, x): return Int(ExpandIntegrand(((c*x**n)**(S(1)/(n*p))*exp(a*b*n*p)/(S(2)*b*n*p) - (c*x**n)**(-S(1)/(n*p))*exp(-a*b*n*p)/(S(2)*b*n*p))**p, x), x) def replacement5984(a, b, c, n, p, x): return Int(ExpandIntegrand(((c*x**n)**(S(1)/(n*p))*exp(a*b*n*p)/S(2) + (c*x**n)**(-S(1)/(n*p))*exp(-a*b*n*p)/S(2))**p, x), x) def replacement5985(a, b, c, n, x): return -Simp(x*sinh(a + b*log(c*x**n))/(b**S(2)*n**S(2) + S(-1)), x) + Simp(b*n*x*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2) + S(-1)), x) def replacement5986(a, b, c, n, x): return -Simp(x*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2) + S(-1)), x) + Simp(b*n*x*sinh(a + b*log(c*x**n))/(b**S(2)*n**S(2) + S(-1)), x) def replacement5987(a, b, c, n, p, x): return -Dist(b**S(2)*n**S(2)*p*(p + S(-1))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), Int(sinh(a + b*log(c*x**n))**(p + S(-2)), x), x) - Simp(x*sinh(a + b*log(c*x**n))**p/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x) + Simp(b*n*p*x*sinh(a + b*log(c*x**n))**(p + S(-1))*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x) def replacement5988(a, b, c, n, p, x): return Dist(b**S(2)*n**S(2)*p*(p + S(-1))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), Int(cosh(a + b*log(c*x**n))**(p + S(-2)), x), x) - Simp(x*cosh(a + b*log(c*x**n))**p/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x) + Simp(b*n*p*x*sinh(a + b*log(c*x**n))*cosh(a + b*log(c*x**n))**(p + S(-1))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x) def replacement5989(a, b, c, n, p, x): return -Dist((b**S(2)*n**S(2)*(p + S(2))**S(2) + S(-1))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), Int(sinh(a + b*log(c*x**n))**(p + S(2)), x), x) - Simp(x*sinh(a + b*log(c*x**n))**(p + S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), x) + Simp(x*sinh(a + b*log(c*x**n))**(p + S(2))/(b*n*(p + S(1))*tanh(a + b*log(c*x**n))), x) def replacement5990(a, b, c, n, p, x): return Dist((b**S(2)*n**S(2)*(p + S(2))**S(2) + S(-1))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), Int(cosh(a + b*log(c*x**n))**(p + S(2)), x), x) + Simp(x*cosh(a + b*log(c*x**n))**(p + S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), x) - Simp(x*cosh(a + b*log(c*x**n))**(p + S(2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(1))), x) def replacement5991(a, b, c, n, p, x): return Simp(x*(S(2) - S(2)*(c*x**n)**(-S(2)*b)*exp(-S(2)*a))**(-p)*((c*x**n)**b*exp(a) - (c*x**n)**(-b)*exp(-a))**p*Hypergeometric2F1(-p, -(b*n*p + S(1))/(S(2)*b*n), S(1) - (b*n*p + S(1))/(S(2)*b*n), (c*x**n)**(-S(2)*b)*exp(-S(2)*a))/(b*n*p + S(1)), x) def replacement5992(a, b, c, n, p, x): return Simp(x*(S(2) + S(2)*(c*x**n)**(-S(2)*b)*exp(-S(2)*a))**(-p)*((c*x**n)**b*exp(a) + (c*x**n)**(-b)*exp(-a))**p*Hypergeometric2F1(-p, -(b*n*p + S(1))/(S(2)*b*n), S(1) - (b*n*p + S(1))/(S(2)*b*n), -(c*x**n)**(-S(2)*b)*exp(-S(2)*a))/(b*n*p + S(1)), x) def replacement5993(a, b, c, m, n, p, x): return -Simp(x**(m + S(1))*(p + S(2))*sinh(a + b*log(c*x**n))**(p + S(2))/((m + S(1))*(p + S(1))), x) + Simp(x**(m + S(1))*sinh(a + b*log(c*x**n))**(p + S(2))/(b*n*(p + S(1))*tanh(a + b*log(c*x**n))), x) def replacement5994(a, b, c, m, n, p, x): return Simp(x**(m + S(1))*(p + S(2))*cosh(a + b*log(c*x**n))**(p + S(2))/((m + S(1))*(p + S(1))), x) - Simp(x**(m + S(1))*cosh(a + b*log(c*x**n))**(p + S(2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(1))), x) def replacement5995(a, b, c, m, n, p, x): return Dist(S(2)**(-p), Int(ExpandIntegrand(x**m*((c*x**n)**((m + S(1))/(n*p))*(m + S(1))*exp(a*b*n*p/(m + S(1)))/(b*n*p) - (c*x**n)**(-(m + S(1))/(n*p))*(m + S(1))*exp(-a*b*n*p/(m + S(1)))/(b*n*p))**p, x), x), x) def replacement5996(a, b, c, m, n, p, x): return Dist(S(2)**(-p), Int(ExpandIntegrand(x**m*((c*x**n)**((m + S(1))/(n*p))*exp(a*b*n*p/(m + S(1))) + (c*x**n)**(-(m + S(1))/(n*p))*exp(-a*b*n*p/(m + S(1))))**p, x), x), x) def replacement5997(a, b, c, m, n, x): return -Simp(x**(m + S(1))*(m + S(1))*sinh(a + b*log(c*x**n))/(b**S(2)*n**S(2) - (m + S(1))**S(2)), x) + Simp(b*n*x**(m + S(1))*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2) - (m + S(1))**S(2)), x) def replacement5998(a, b, c, m, n, x): return -Simp(x**(m + S(1))*(m + S(1))*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2) - (m + S(1))**S(2)), x) + Simp(b*n*x**(m + S(1))*sinh(a + b*log(c*x**n))/(b**S(2)*n**S(2) - (m + S(1))**S(2)), x) def replacement5999(a, b, c, m, n, p, x): return -Dist(b**S(2)*n**S(2)*p*(p + S(-1))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), Int(x**m*sinh(a + b*log(c*x**n))**(p + S(-2)), x), x) - Simp(x**(m + S(1))*(m + S(1))*sinh(a + b*log(c*x**n))**p/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x) + Simp(b*n*p*x**(m + S(1))*sinh(a + b*log(c*x**n))**(p + S(-1))*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x) def replacement6000(a, b, c, m, n, p, x): return Dist(b**S(2)*n**S(2)*p*(p + S(-1))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), Int(x**m*cosh(a + b*log(c*x**n))**(p + S(-2)), x), x) - Simp(x**(m + S(1))*(m + S(1))*cosh(a + b*log(c*x**n))**p/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x) + Simp(b*n*p*x**(m + S(1))*sinh(a + b*log(c*x**n))*cosh(a + b*log(c*x**n))**(p + S(-1))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x) def replacement6001(a, b, c, m, n, p, x): return -Dist((b**S(2)*n**S(2)*(p + S(2))**S(2) - (m + S(1))**S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), Int(x**m*sinh(a + b*log(c*x**n))**(p + S(2)), x), x) + Simp(x**(m + S(1))*sinh(a + b*log(c*x**n))**(p + S(2))/(b*n*(p + S(1))*tanh(a + b*log(c*x**n))), x) - Simp(x**(m + S(1))*(m + S(1))*sinh(a + b*log(c*x**n))**(p + S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), x) def replacement6002(a, b, c, m, n, p, x): return Dist((b**S(2)*n**S(2)*(p + S(2))**S(2) - (m + S(1))**S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), Int(x**m*cosh(a + b*log(c*x**n))**(p + S(2)), x), x) - Simp(x**(m + S(1))*cosh(a + b*log(c*x**n))**(p + S(2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(1))), x) + Simp(x**(m + S(1))*(m + S(1))*cosh(a + b*log(c*x**n))**(p + S(2))/(b**S(2)*n**S(2)*(p + S(1))*(p + S(2))), x) def replacement6003(a, b, c, m, n, p, x): return Simp(x**(m + S(1))*(S(2) - S(2)*(c*x**n)**(-S(2)*b)*exp(-S(2)*a))**(-p)*((c*x**n)**b*exp(a) - (c*x**n)**(-b)*exp(-a))**p*Hypergeometric2F1(-p, -(b*n*p + m + S(1))/(S(2)*b*n), S(1) - (b*n*p + m + S(1))/(S(2)*b*n), (c*x**n)**(-S(2)*b)*exp(-S(2)*a))/(b*n*p + m + S(1)), x) def replacement6004(a, b, c, m, n, p, x): return Simp(x**(m + S(1))*(S(2) + S(2)*(c*x**n)**(-S(2)*b)*exp(-S(2)*a))**(-p)*((c*x**n)**b*exp(a) + (c*x**n)**(-b)*exp(-a))**p*Hypergeometric2F1(-p, -(b*n*p + m + S(1))/(S(2)*b*n), S(1) - (b*n*p + m + S(1))/(S(2)*b*n), -(c*x**n)**(-S(2)*b)*exp(-S(2)*a))/(b*n*p + m + S(1)), x) def replacement6005(b, c, n, p, x): return Dist(S(2)**p, Int(((c*x**n)**b/((c*x**n)**(S(2)*b) + S(1)))**p, x), x) def replacement6006(b, c, n, p, x): return Dist(S(2)**p, Int(((c*x**n)**b/((c*x**n)**(S(2)*b) + S(-1)))**p, x), x) def replacement6007(a, b, c, n, x): return Dist(S(2)*exp(-a*b*n), Int((c*x**n)**(S(1)/n)/((c*x**n)**(S(2)/n) + exp(-S(2)*a*b*n)), x), x) def replacement6008(a, b, c, n, x): return Dist(-S(2)*b*n*exp(-a*b*n), Int((c*x**n)**(S(1)/n)/(-(c*x**n)**(S(2)/n) + exp(-S(2)*a*b*n)), x), x) def replacement6009(a, b, c, n, p, x): return Simp(x*(p + S(-2))*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))/(p + S(-1)), x) + Simp(x*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(-1))), x) def replacement6010(a, b, c, n, p, x): return -Simp(x*(p + S(-2))*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(p + S(-1)), x) - Simp(x*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(b*n*(p + S(-1))*tanh(a + b*log(c*x**n))), x) def replacement6011(a, b, c, n, p, x): return Dist((b**S(2)*n**S(2)*(p + S(-2))**S(2) + S(-1))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), Int((S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2)), x), x) + Simp(x*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), x) + Simp(x*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(-1))), x) def replacement6012(a, b, c, n, p, x): return -Dist((b**S(2)*n**S(2)*(p + S(-2))**S(2) + S(-1))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), Int((S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2)), x), x) - Simp(x*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), x) - Simp(x*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(b*n*(p + S(-1))*tanh(a + b*log(c*x**n))), x) def replacement6013(a, b, c, n, p, x): return Dist(b**S(2)*n**S(2)*p*(p + S(1))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), Int((S(1)/cosh(a + b*log(c*x**n)))**(p + S(2)), x), x) - Simp(x*(S(1)/cosh(a + b*log(c*x**n)))**p/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x) - Simp(b*n*p*x*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(1))*sinh(a + b*log(c*x**n))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x) def replacement6014(a, b, c, n, p, x): return -Dist(b**S(2)*n**S(2)*p*(p + S(1))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), Int((S(1)/sinh(a + b*log(c*x**n)))**(p + S(2)), x), x) - Simp(x*(S(1)/sinh(a + b*log(c*x**n)))**p/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x) - Simp(b*n*p*x*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(1))*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2)*p**S(2) + S(-1)), x) def replacement6015(a, b, c, n, p, x): return Simp(S(2)**p*x*((c*x**n)**b*exp(a)/((c*x**n)**(S(2)*b)*exp(S(2)*a) + S(1)))**p*((c*x**n)**(S(2)*b)*exp(S(2)*a) + S(1))**p*Hypergeometric2F1(p, (b*n*p + S(1))/(S(2)*b*n), S(1) + (b*n*p + S(1))/(S(2)*b*n), -(c*x**n)**(S(2)*b)*exp(S(2)*a))/(b*n*p + S(1)), x) def replacement6016(a, b, c, n, p, x): return Simp(x*((c*x**n)**b*exp(a)/((c*x**n)**(S(2)*b)*exp(S(2)*a) + S(-1)))**p*(-S(2)*(c*x**n)**(S(2)*b)*exp(S(2)*a) + S(2))**p*Hypergeometric2F1(p, (b*n*p + S(1))/(S(2)*b*n), S(1) + (b*n*p + S(1))/(S(2)*b*n), (c*x**n)**(S(2)*b)*exp(S(2)*a))/(b*n*p + S(1)), x) def replacement6017(b, c, m, n, p, x): return Dist(S(2)**p, Int(x**m*((c*x**n)**b/((c*x**n)**(S(2)*b) + S(1)))**p, x), x) def replacement6018(b, c, m, n, p, x): return Dist(S(2)**p, Int(x**m*((c*x**n)**b/((c*x**n)**(S(2)*b) + S(-1)))**p, x), x) def replacement6019(a, b, c, m, n, x): return Dist(S(2)*exp(-a*b*n/(m + S(1))), Int(x**m*(c*x**n)**((m + S(1))/n)/((c*x**n)**(S(2)*(m + S(1))/n) + exp(-S(2)*a*b*n/(m + S(1)))), x), x) def replacement6020(a, b, c, m, n, x): return Dist(-S(2)*b*n*exp(-a*b*n/(m + S(1)))/(m + S(1)), Int(x**m*(c*x**n)**((m + S(1))/n)/(-(c*x**n)**(S(2)*(m + S(1))/n) + exp(-S(2)*a*b*n/(m + S(1)))), x), x) def replacement6021(a, b, c, m, n, p, x): return Simp(x**(m + S(1))*(p + S(-2))*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))/((m + S(1))*(p + S(-1))), x) + Simp(x**(m + S(1))*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(-1))), x) def replacement6022(a, b, c, m, n, p, x): return -Simp(x**(m + S(1))*(p + S(-2))*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/((m + S(1))*(p + S(-1))), x) - Simp(x**(m + S(1))*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(b*n*(p + S(-1))*tanh(a + b*log(c*x**n))), x) def replacement6023(a, b, c, m, n, p, x): return Dist((b**S(2)*n**S(2)*(p + S(-2))**S(2) - (m + S(1))**S(2))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), Int(x**m*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2)), x), x) + Simp(x**(m + S(1))*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))*tanh(a + b*log(c*x**n))/(b*n*(p + S(-1))), x) + Simp(x**(m + S(1))*(m + S(1))*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(-2))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), x) def replacement6024(a, b, c, m, n, p, x): return -Dist((b**S(2)*n**S(2)*(p + S(-2))**S(2) - (m + S(1))**S(2))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), Int(x**m*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2)), x), x) - Simp(x**(m + S(1))*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(b*n*(p + S(-1))*tanh(a + b*log(c*x**n))), x) - Simp(x**(m + S(1))*(m + S(1))*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(-2))/(b**S(2)*n**S(2)*(p + S(-2))*(p + S(-1))), x) def replacement6025(a, b, c, m, n, p, x): return Dist(b**S(2)*n**S(2)*p*(p + S(1))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), Int(x**m*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(2)), x), x) - Simp(x**(m + S(1))*(m + S(1))*(S(1)/cosh(a + b*log(c*x**n)))**p/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x) - Simp(b*n*p*x**(m + S(1))*(S(1)/cosh(a + b*log(c*x**n)))**(p + S(1))*sinh(a + b*log(c*x**n))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x) def replacement6026(a, b, c, m, n, p, x): return -Dist(b**S(2)*n**S(2)*p*(p + S(1))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), Int(x**m*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(2)), x), x) - Simp(x**(m + S(1))*(m + S(1))*(S(1)/sinh(a + b*log(c*x**n)))**p/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x) - Simp(b*n*p*x**(m + S(1))*(S(1)/sinh(a + b*log(c*x**n)))**(p + S(1))*cosh(a + b*log(c*x**n))/(b**S(2)*n**S(2)*p**S(2) - (m + S(1))**S(2)), x) def replacement6027(a, b, c, m, n, p, x): return Simp(S(2)**p*x**(m + S(1))*((c*x**n)**b*exp(a)/((c*x**n)**(S(2)*b)*exp(S(2)*a) + S(1)))**p*((c*x**n)**(S(2)*b)*exp(S(2)*a) + S(1))**p*Hypergeometric2F1(p, (b*n*p + m + S(1))/(S(2)*b*n), S(1) + (b*n*p + m + S(1))/(S(2)*b*n), -(c*x**n)**(S(2)*b)*exp(S(2)*a))/(b*n*p + m + S(1)), x) def replacement6028(a, b, c, m, n, p, x): return Simp(S(2)**p*x**(m + S(1))*((c*x**n)**b*exp(a)/((c*x**n)**(S(2)*b)*exp(S(2)*a) + S(-1)))**p*(-(c*x**n)**(S(2)*b)*exp(S(2)*a) + S(1))**p*Hypergeometric2F1(p, (b*n*p + m + S(1))/(S(2)*b*n), S(1) + (b*n*p + m + S(1))/(S(2)*b*n), (c*x**n)**(S(2)*b)*exp(S(2)*a))/(b*n*p + m + S(1)), x) def replacement6029(a, b, p, x): return -Dist(p, Int(log(b*x)**(p + S(-1))*sinh(a*x*log(b*x)**p), x), x) + Simp(cosh(a*x*log(b*x)**p)/a, x) def replacement6030(a, b, p, x): return -Dist(p, Int(log(b*x)**(p + S(-1))*cosh(a*x*log(b*x)**p), x), x) + Simp(sinh(a*x*log(b*x)**p)/a, x) def replacement6031(a, b, n, p, x): return -Dist(p/n, Int(log(b*x)**(p + S(-1))*sinh(a*x**n*log(b*x)**p), x), x) + Dist((n + S(-1))/(a*n), Int(x**(-n)*cosh(a*x**n*log(b*x)**p), x), x) + Simp(x**(S(1) - n)*cosh(a*x**n*log(b*x)**p)/(a*n), x) def replacement6032(a, b, n, p, x): return -Dist(p/n, Int(log(b*x)**(p + S(-1))*cosh(a*x**n*log(b*x)**p), x), x) + Dist((n + S(-1))/(a*n), Int(x**(-n)*sinh(a*x**n*log(b*x)**p), x), x) + Simp(x**(S(1) - n)*sinh(a*x**n*log(b*x)**p)/(a*n), x) def replacement6033(a, b, m, n, p, x): return -Dist(p/n, Int(x**(n + S(-1))*log(b*x)**(p + S(-1))*sinh(a*x**n*log(b*x)**p), x), x) - Simp(cosh(a*x**n*log(b*x)**p)/(a*n), x) def replacement6034(a, b, m, n, p, x): return -Dist(p/n, Int(x**(n + S(-1))*log(b*x)**(p + S(-1))*cosh(a*x**n*log(b*x)**p), x), x) + Simp(sinh(a*x**n*log(b*x)**p)/(a*n), x) def replacement6035(a, b, m, n, p, x): return -Dist(p/n, Int(x**m*log(b*x)**(p + S(-1))*sinh(a*x**n*log(b*x)**p), x), x) - Dist((m - n + S(1))/(a*n), Int(x**(m - n)*cosh(a*x**n*log(b*x)**p), x), x) + Simp(x**(m - n + S(1))*cosh(a*x**n*log(b*x)**p)/(a*n), x) def replacement6036(a, b, m, n, p, x): return -Dist(p/n, Int(x**m*log(b*x)**(p + S(-1))*cosh(a*x**n*log(b*x)**p), x), x) - Dist((m - n + S(1))/(a*n), Int(x**(m - n)*sinh(a*x**n*log(b*x)**p), x), x) + Simp(x**(m - n + S(1))*sinh(a*x**n*log(b*x)**p)/(a*n), x) def replacement6037(a, c, d, n, x): return -Dist(S(1)/d, Subst(Int(sinh(a*x)**n/x**S(2), x), x, S(1)/(c + d*x)), x) def replacement6038(a, c, d, n, x): return -Dist(S(1)/d, Subst(Int(cosh(a*x)**n/x**S(2), x), x, S(1)/(c + d*x)), x) def replacement6039(a, b, c, d, e, n, x): return -Dist(S(1)/d, Subst(Int(sinh(b*e/d - e*x*(-a*d + b*c)/d)**n/x**S(2), x), x, S(1)/(c + d*x)), x) def replacement6040(a, b, c, d, e, n, x): return -Dist(S(1)/d, Subst(Int(cosh(b*e/d - e*x*(-a*d + b*c)/d)**n/x**S(2), x), x, S(1)/(c + d*x)), x) def With6041(n, u, x): lst = QuotientOfLinearsParts(u, x) return Int(sinh((x*Part(lst, S(2)) + Part(lst, S(1)))/(x*Part(lst, S(4)) + Part(lst, S(3))))**n, x) def With6042(n, u, x): lst = QuotientOfLinearsParts(u, x) return Int(cosh((x*Part(lst, S(2)) + Part(lst, S(1)))/(x*Part(lst, S(4)) + Part(lst, S(3))))**n, x) def replacement6043(p, q, u, v, w, x): return Int(u*sinh(v)**(p + q), x) def replacement6044(p, q, u, v, w, x): return Int(u*cosh(v)**(p + q), x) def replacement6045(p, q, v, w, x): return Int(ExpandTrigReduce(sinh(v)**p*sinh(w)**q, x), x) def replacement6046(p, q, v, w, x): return Int(ExpandTrigReduce(cosh(v)**p*cosh(w)**q, x), x) def replacement6047(m, p, q, v, w, x): return Int(ExpandTrigReduce(x**m, sinh(v)**p*sinh(w)**q, x), x) def replacement6048(m, p, q, v, w, x): return Int(ExpandTrigReduce(x**m, cosh(v)**p*cosh(w)**q, x), x) def replacement6049(p, u, v, w, x): return Dist(S(2)**(-p), Int(u*sinh(S(2)*v)**p, x), x) def replacement6050(p, q, v, w, x): return Int(ExpandTrigReduce(sinh(v)**p*cosh(w)**q, x), x) def replacement6051(m, p, q, v, w, x): return Int(ExpandTrigReduce(x**m, sinh(v)**p*cosh(w)**q, x), x) def replacement6052(n, v, w, x): return -Dist(cosh(v - w), Int(tanh(w)**(n + S(-1))/cosh(w), x), x) + Int(cosh(v)*tanh(w)**(n + S(-1)), x) def replacement6053(n, v, w, x): return Dist(cosh(v - w), Int((S(1)/tanh(w))**(n + S(-1))/sinh(w), x), x) + Int((S(1)/tanh(w))**(n + S(-1))*sinh(v), x) def replacement6054(n, v, w, x): return Dist(sinh(v - w), Int((S(1)/tanh(w))**(n + S(-1))/sinh(w), x), x) + Int((S(1)/tanh(w))**(n + S(-1))*cosh(v), x) def replacement6055(n, v, w, x): return -Dist(sinh(v - w), Int(tanh(w)**(n + S(-1))/cosh(w), x), x) + Int(sinh(v)*tanh(w)**(n + S(-1)), x) def replacement6056(n, v, w, x): return Dist(sinh(v - w), Int((S(1)/cosh(w))**(n + S(-1)), x), x) + Dist(cosh(v - w), Int((S(1)/cosh(w))**(n + S(-1))*tanh(w), x), x) def replacement6057(n, v, w, x): return Dist(sinh(v - w), Int((S(1)/sinh(w))**(n + S(-1)), x), x) + Dist(cosh(v - w), Int((S(1)/sinh(w))**(n + S(-1))/tanh(w), x), x) def replacement6058(n, v, w, x): return Dist(sinh(v - w), Int((S(1)/sinh(w))**(n + S(-1))/tanh(w), x), x) + Dist(cosh(v - w), Int((S(1)/sinh(w))**(n + S(-1)), x), x) def replacement6059(n, v, w, x): return Dist(sinh(v - w), Int((S(1)/cosh(w))**(n + S(-1))*tanh(w), x), x) + Dist(cosh(v - w), Int((S(1)/cosh(w))**(n + S(-1)), x), x) def replacement6060(a, b, c, d, e, f, m, n, x): return Int((a + b*sinh(S(2)*c + S(2)*d*x)/S(2))**n*(e + f*x)**m, x) def replacement6061(a, b, c, d, m, n, x): return Dist(S(2)**(-n), Int(x**m*(S(2)*a + b*cosh(S(2)*c + S(2)*d*x) - b)**n, x), x) def replacement6062(a, b, c, d, m, n, x): return Dist(S(2)**(-n), Int(x**m*(S(2)*a + b*cosh(S(2)*c + S(2)*d*x) + b)**n, x), x) def replacement6063(a, b, c, d, e, f, m, n, p, x): return Dist(d**(-m + S(-1)), Subst(Int((-c*f + d*e + f*x)**m*sinh(a + b*x**n)**p, x), x, c + d*x), x) def replacement6064(a, b, c, d, e, f, m, n, p, x): return Dist(d**(-m + S(-1)), Subst(Int((-c*f + d*e + f*x)**m*cosh(a + b*x**n)**p, x), x, c + d*x), x) def replacement6065(a, b, c, d, e, f, g, m, x): return Dist(S(2), Int((f + g*x)**m/(S(2)*a + b - c + (b + c)*cosh(S(2)*d + S(2)*e*x)), x), x) def replacement6066(b, c, d, e, f, g, m, x): return Dist(S(2), Int((f + g*x)**m/(b - c + (b + c)*cosh(S(2)*d + S(2)*e*x)), x), x) def replacement6067(a, b, c, d, e, f, g, m, x): return Dist(S(2), Int((f + g*x)**m/(S(2)*a + b - c + (b + c)*cosh(S(2)*d + S(2)*e*x)), x), x) def replacement6068(b, c, d, e, f, g, m, x): return Dist(S(2), Int((f + g*x)**m/(b - c + (b + c)*cosh(S(2)*d + S(2)*e*x)), x), x) def replacement6069(a, b, c, d, e, f, g, m, x): return Dist(S(2), Int((f + g*x)**m/(S(2)*a + b - c + (b + c)*cosh(S(2)*d + S(2)*e*x)), x), x) def replacement6070(a, b, c, d, e, f, m, x): return Int((e + f*x)**m*exp(c + d*x)/(a + b*exp(c + d*x) - Rt(a**S(2) + b**S(2), S(2))), x) + Int((e + f*x)**m*exp(c + d*x)/(a + b*exp(c + d*x) + Rt(a**S(2) + b**S(2), S(2))), x) - Simp((e + f*x)**(m + S(1))/(b*f*(m + S(1))), x) def replacement6071(a, b, c, d, e, f, m, x): return Int((e + f*x)**m*exp(c + d*x)/(a + b*exp(c + d*x) - Rt(a**S(2) - b**S(2), S(2))), x) + Int((e + f*x)**m*exp(c + d*x)/(a + b*exp(c + d*x) + Rt(a**S(2) - b**S(2), S(2))), x) - Simp((e + f*x)**(m + S(1))/(b*f*(m + S(1))), x) def replacement6072(a, b, c, d, e, f, m, n, x): return Dist(S(1)/a, Int((e + f*x)**m*cosh(c + d*x)**(n + S(-2)), x), x) + Dist(S(1)/b, Int((e + f*x)**m*sinh(c + d*x)*cosh(c + d*x)**(n + S(-2)), x), x) def replacement6073(a, b, c, d, e, f, m, n, x): return Dist(S(1)/a, Int((e + f*x)**m*sinh(c + d*x)**(n + S(-2)), x), x) + Dist(S(1)/b, Int((e + f*x)**m*sinh(c + d*x)**(n + S(-2))*cosh(c + d*x), x), x) def replacement6074(a, b, c, d, e, f, m, n, x): return Dist(S(1)/b, Int((e + f*x)**m*sinh(c + d*x)*cosh(c + d*x)**(n + S(-2)), x), x) - Dist(a/b**S(2), Int((e + f*x)**m*cosh(c + d*x)**(n + S(-2)), x), x) + Dist((a**S(2) + b**S(2))/b**S(2), Int((e + f*x)**m*cosh(c + d*x)**(n + S(-2))/(a + b*sinh(c + d*x)), x), x) def replacement6075(a, b, c, d, e, f, m, n, x): return Dist(S(1)/b, Int((e + f*x)**m*sinh(c + d*x)**(n + S(-2))*cosh(c + d*x), x), x) - Dist(a/b**S(2), Int((e + f*x)**m*sinh(c + d*x)**(n + S(-2)), x), x) + Dist((a**S(2) - b**S(2))/b**S(2), Int((e + f*x)**m*sinh(c + d*x)**(n + S(-2))/(a + b*cosh(c + d*x)), x), x) def replacement6076(A, B, a, b, c, d, e, f, x): return -Dist(B*f/(a*d), Int(cosh(c + d*x)/(a + b*sinh(c + d*x)), x), x) + Simp(B*(e + f*x)*cosh(c + d*x)/(a*d*(a + b*sinh(c + d*x))), x) def replacement6077(A, B, a, b, c, d, e, f, x): return -Dist(B*f/(a*d), Int(sinh(c + d*x)/(a + b*cosh(c + d*x)), x), x) + Simp(B*(e + f*x)*sinh(c + d*x)/(a*d*(a + b*cosh(c + d*x))), x) def replacement6078(a, b, m, n, v, x): return Int((a*cosh(v) + b*sinh(v))**n, x) def replacement6079(a, b, m, n, v, x): return Int((a*sinh(v) + b*cosh(v))**n, x) def replacement6080(a, b, c, d, m, n, u, x): return Int(ExpandTrigReduce(u, sinh(a + b*x)**m*sinh(c + d*x)**n, x), x) def replacement6081(a, b, c, d, m, n, u, x): return Int(ExpandTrigReduce(u, cosh(a + b*x)**m*cosh(c + d*x)**n, x), x) def replacement6082(a, b, c, d, x): return Dist(S(1)/sinh((-a*d + b*c)/b), Int(tanh(c + d*x), x), x) - Dist(S(1)/sinh((-a*d + b*c)/d), Int(tanh(a + b*x), x), x) def replacement6083(a, b, c, d, x): return Dist(S(1)/sinh((-a*d + b*c)/b), Int(S(1)/tanh(a + b*x), x), x) - Dist(S(1)/sinh((-a*d + b*c)/d), Int(S(1)/tanh(c + d*x), x), x) def replacement6084(a, b, c, d, x): return -Dist(b*cosh((-a*d + b*c)/d)/d, Int(S(1)/(cosh(a + b*x)*cosh(c + d*x)), x), x) + Simp(b*x/d, x) def replacement6085(a, b, c, d, x): return Dist(cosh((-a*d + b*c)/d), Int(S(1)/(sinh(a + b*x)*sinh(c + d*x)), x), x) + Simp(b*x/d, x) def replacement6086(a, b, n, u, v, x): return Int(u*(a*exp(a*v/b))**n, x)