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This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
    )import_modulematchpy)PatternReplacementRuleCustomConstraintis_match(  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SubstForrG  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Factorr  CosIntegralSinIntegralLogIntegralSinhIntegralCoshIntegralRuleErf	PolyGammaExpIntegralEiExpIntegralELogGammaUtilityOperator	FactorialZeta
ProductLogDerivativeDividesHypergeometricPFQIntHideOneQNullrubi_exprubi_logDiscriminantNegativeQuotient)IntegralSsqrtAndOrIntegerFloatModIAbssimplifyMulAddPowsign
EulerGammaWC)symbolsSymbol)sincostancotcscsecr  erf)acoshasinhatanhacothacschasechcoshsinhtanhcothsechcsch)atanacscasinacotacosasecatan2)pic                 C      g | ]}t |qS  r  .0ir  r  G/usr/lib/python3/dist-packages/sympy/integrals/rubi/rules/logarithms.py
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|||||||||||||}t|t}ttttdtd tdtd tdtd tttdtd tdtd tdtd tdtd  t||||||||||}t|t}ttttdtd tdtd t tttdtd tdtd tdtd tdtd  t||||||||||}t|t}ttttdtd tdtd tdtd td
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td    t|	|
|||||||||||}t|t}ttttdtd tdtd tdtd ttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td    t|	|
||||||||||||}t|t}ttttdtd tdtd tdtd ttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td    t|	|
||||||||||||}t|t}ttttdtd tdtd tdtd td
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   t  t|	|
|||||||||||||}t|t}ttttdtd tdtd tdtd td
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   tdtd  t|	|
|||||||||||}t|t}tttttdtd tdtd td	td ttdtd tdtd  t||||||}t|t}tttd
tdtdtdtttdtd tdtd td	td   ttdtd tdtd  t|	|
|||||||
}t|t}tttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   tdtd ttdtd tdtd  t|	|
||||||||| |!}t|t}ttttdtd tdtd tdtd td
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td    t|	|
|||||||||| |}t|t}tttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   t ttdtd tdtd td  t|	|
||||||||| ||}t|t}ttttdtd tdtd tdtd td
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   t  t|	|
|||||||||| ||||"|#}t|t}ttttdtd tdtd tdtd td
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td    t|	|
||||||||| |$}t|t}ttttdtd tdtd tdtd td
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   t  t|	|
||||||||| |%||&}t|t}ttttdtd tdtd tdtd td
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   t  t|	|
|||||||||| |$}t|t}ttttdtd td
tdtdtdttt tdtd tdtd td	td   tdtd  t|	|
|||||||'|(}t|t}ttttdtd tdtd tdtd td
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   tdtd  t|	|
|||||||||||)}t|t}ttttd	tdttdtd tdtd  ttdtd tdtd ttdtd tdtd   t||||||+|,||*
}t|t}ttttdtdttd	tdttdtd tdtd    ttdtd tdtd ttdtd tdtd   t|	|
||||||+|,||*}t|tÃ}ttttdtd tdtd tdtd td
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td    ttdtd tdtd  t|	|
|||||||+|,||||-}t|tă}ttttdtd tdtd tdtd td
tdtdtdtttdtd tdtd td	td   tdtd  ttdtd tdtd  t|	|
||||||+|,|||$|.}t|tŃ}ttttdtd tdtd tdtd td
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   tdtd  ttdtd tdtd  t|	|
|||||||+|,|||/|!ttǃ}t|tȃ}ttttdtd tdtd tdtd td
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   tdtd  ttdtd tdtd  t|	|
|||||||+|,|||||0}t|tɃ}ttttd	tdttdtd tdtd  tttd tdtd   t||||||1|2}t|t˃}tttd
tdtdtdttd	tdttdtd tdtd    tttd tdtd   t||||||1|3|4	}t|t̃}tttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   ttd tdtd ttdtd  tdtd  t|	|
|||||||+|||5}t|t̓}tttd
tdtdtdttttdtd  tdtd tdtd tdtd td	td   tttd tdtd   t|	|
||||||+|||6}t|tσ}tttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   ttttd tdtd   t|	|
|||||||||7}t|tЃ}tttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   ttttdtd  ttttdtd    t|	|
|||||;|<|=|>|||8|9|:}t|tӃ}tttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   ttttd tdtd   t|	|
|||||||||?}t|tԃ}tttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   ttttdtd  ttttdtd    t|	|
|||||;|<|=|>|||8}t|tՃ}tttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   tdtd tttdtd tdtd tdtd  ttdtd tdtd  t|	|
|||||||+|,|A|||||@}t|tփ}tttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   tdtd tttdtd tdtd tdtd tdtd td  ttdtd tdtd  t|	|
|||||||+|,|A||||||B}t|t׃}tttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   tdtd ttttdtd tdtd tdtd tdtd  ttdtd tdtd  t|	|
|||||||+|,|A||||C|||B}t|tڃ}tttttdtd tdtd  td
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td    tdtd t|	|
|||||||||D|$|E}t|t܃}tttd
tdtdtdtttt tdtd  tdtd tdtd tdtd td	td   tdtd t t|	|
|||||||||!}t|t݃}tttd
tdtdtdttt tttdtd tdtd   tdtd tdtd tdtd td	td   tdtd t t|	|
|||||||||F|!}t|t߃}ttttdtd td
tdtdtdttt tdtd tdtd tdtd tdtd tdtd td	td   tdtd  t|	|
||||||||C|G}t|t}ttttdtd tt tdtd tdtd tdtd  td
tdtdtdttt tdtd tdtd tdtd tdtd tdtd td	td   tdtd  t|	|
|||||||||||C|G}t|t}tttd
tdtdtdtttdtd td	td   tttd tdtd   t|	|
|||||H}t|t}ttttt tdtd td
td td	td ttttdtd tdtd    t|	|
|||||I|J	}t|t}ttttt ttdtd td
td tdtd  td	td ttttdtd tdtd    t|	|
|||||I|J	} t| t}ttttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   tdtd  t|	|
||||||||D}t|t}ttttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   tdtd  t|	|
|||||||K|!tt}t|t}ttttd
tdtdtdtttdtd tdtd tdtd tdtd tdtd td	td   tdtd  t|	|
|||||||K|!tt}t|t}tttd
tdtdtdtttd tdtd ttdtd  tdtd tdtd tdtd tdtd td	td   tdtd tdtd t|	|
||||||||L|M}t|t}	tttd
tdtdtdtttdtd tdtd tdtd td	td   tdtd tdtd t|	|
||||||N|O
}
t|
t}tttttdtd td	td t tdtd t td
td tdtd t|	|
|||||C|P	}t|t}ttttdtd tttdtd td	td t tdtd t td
td tdtd  t|	|
||||||C||Q}t|t}tttdtdtttdtd td
td tdtd ttdtd td	td  tdtd tdtd tdtd  t|	|
||||||S|R
}t|t}tttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd t|	|
|||||S|W|T|U|V}t|t}tttttdtd td
td tdtd ttdtd td	td  ttdtd tdtd  t|	|
||||||U|X|Y}t|t}tttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd ttdtd tdtd  t|	|
|||||||S|W|T|U|X|V}t|t}tttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd ttdtd tdtd  t|	|
|||||||S|W|T|U|Z|V}t|t}tttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd ttdtd tdtd  t|	|
|||||||S|W|T|U|[}t|t}tttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd t ttdtd tdtd  t|	|
|||||||S|W|T|U|[|M|\}t|t}tttdttdtd tdtd td tttdtd td
td tdtd ttdtd td	td    t|	|
||||||U|X
}t|t}tttdttdtd tdtd td tttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd   t|	|
|||||||S|W|T|U|X} t| t}!tttdttdtd tdtd td tttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd   t|	|
|||||||S|W|T|U|Z}"t|"t}#tttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd ttdtd tdtd td  t|	|
|||||||S|W|T|U|]|V}$t|$t}%tttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd ttdtd tdtd td  t|	|
|||||||S|W|T|U|[|V}&t|&t}'tttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd t ttdtd tdtd td  t|	|
||||||||S|W|T|U|]|X}(t|(t })tttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd t ttdtd tdtd td  t|	|
||||||||S|W|T|U|[|Z}*t|*t}+ttttdtd tdtd tdtd tttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd  t|	|
|||||||S|W|T|U|V|/|},t|,t}-ttttdtd td
td tdtd ttdtd td	td tdtd  ttt tdtd tdtd  t|	|
|||||a|^|U||_|`}.t|.t}/ttttdtd td
td tdtd ttdtd td	td tdtd  tttdtd  t|	|
|||a|^|U||_|`}0t|0t}1ttttdtd td
td tdtd ttdtd td	td tdtd  ttt tdtd  t|	|
|||||a|^|U|}2t|2t}3ttttdtd td
td tdtd ttdtd td	td tdtd  tt t|	|
|||a|^|U|	}4t|4t}5ttttdtd td
td tdtd ttdtd td	td tdtd  ttt tdtd tdtd  t|	|
|||||a|^|U||_|b}6t|6t}7ttttdtd td
td tdtd ttdtd td	td tdtd  tttdtd  t|	|
|||a|^|U||_|b}8t|8t}9tttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd ttdtd td	td ttdtd tdtd   t|	|
|||||||S|W|T|U|]|X}:t|:t	};tttttdtd td
td tdtd ttdtd td	td  ttdtd td	td ttdtd tdtd   t|	|
||||||U|]|[|c}<t|<t
}=tttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd ttdtd td	td ttdtd tdtd   t|	|
|||||||S|W|T|U|]|[|V}>t|>t}?tttttdtd td
td tdtd ttdtd td	td  tttd tdtd   t|	|
||||||d|e
}@t|@t}Atttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd ttd tdtd ttdtd  tdtd  t|	|
|||||||||S|W|T|U|f}Bt|Bt}Ctttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd ttd tdtd tdtd  t|	|
||||||||S|W|T|U|g}Dt|Dt}Etttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd ttdtd td	td ttdtd tdtd   t|	|
||||||||S|W|T|U|[|Z}Ft|Ft}Gttttttt tdtd tdtd  ttdtd td
td ttdtd td	td   t|	|
|||||h|a|U|_|`}Ht|Ht}Itttttdtd tt ttdtd td
td ttdtd td	td   t|	|
|||h|a|U|_|`
}Jt|Jt}Kttttttt tdtd t  ttdtd td
td ttdtd td	td   t|	|
|||||h|a|U|_|b}Lt|Lt}Mttttt tt ttdtd td
td ttdtd td	td   t|	|
|||h|a|U|_|b
}Nt|Nt}Ottttttt tdtd tdtd  ttdtd td
td ttdtd td	td   t|	|
|||||i|a|U|_|`}Pt|Pt}Qtttttdtd tt ttdtd td
td ttdtd td	td   t|	|
|||i|a|U|_|`
}Rt|Rt}Sttttttt tdtd t  ttdtd td
td ttdtd td	td   t|	|
|||||i|a|U|_|b}Tt|Tt}Uttttt tt ttdtd td
td ttdtd td	td   t|	|
|||i|a|U|_|b
}Vt|Vt}Wtttttttt tdtd t  ttdtd td
td ttdtd td	td   t|	|
||||||j|a|U|_|\}Xt|Xt}Ytttttttt  ttdtd td
td ttdtd td	td   t|	|
||||j|a|U|_|\}Zt|Zt}[tttttttt tdtd t  ttdtd td
td ttdtd td	td   t|	|
||||||j|a|U|_|b}\t|\t}]tttttttt  ttdtd td
td ttdtd td	td   t|	|
||||j|a|U|_|b}^t|^t}_tttttttt tdtd t  ttdtd td
td ttdtd td	td   t|	|
||||||k|a|U|_|\}`t|`t}atttttttt  ttdtd td
td ttdtd td	td   t|	|
||||k|a|U|_|\}bt|bt}ctttttttt tdtd t  ttdtd td
td ttdtd td	td   t|	|
||||||k|a|U|_|b}dt|dt}etttttttt  ttdtd td
td ttdtd td	td   t|	|
||||k|a|U|_|b}ft|ft}gtttdtdtttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd  ttd tdtd ttdtd  tdtd  t|	|
|||||||||S|W|T|U|l|m}ht|ht }itttdtdtttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd  ttd tdtd tdtd  t|	|
||||||||S|W|T|U|l|n}jt|jt!}ktttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tttd tdtd  ttdtd   t|	|
||||S|||||W|T}lt|lt"}mtttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tttd tdtd   t|	|
||||S||||W|T}nt|nt#}ottttttdtd td
td tdtd ttdtd td	td t  tdtd tdtd tdtd tdtd  t|	|
|||||S|W|T|K|VtƐt$}pt|pt%}qtttdtdtttdtd  t||o|ptƐt&}rt|rt'}sttttt tdtd td
td tdtd td	td t|	|
||||q}tt|tt(}utttttdtd td	td t|||r|s}vt|vt)}wtttd
tdtdtdttt tdtd tdtd tdtd td	td   ttdtd tdtd  t|	|
||||||||t}xt|xt*}yttttdtd tdtd tdtd td
tdtdtdttt tdtd tdtd tdtd td	td    t|	|
|||||||||}zt|zt+}{ttttdtd td
tdtdtdtttdtd td	td    t|	|
||||u|r|v	}|t||t,}}tttd
tdtdtdttt tdtd tdtd tdtd td	td   t-ttdtd tdtd tdtd  t|	|
||||||||$}~t|~t.}tttd
tdtdtdtttd tdtd tdtd tdtd td	td   ttd tdtd tdtd  t|	|
|||||||w
}t|t/}tttd
tdtdtdttttd tdtd  tdtd td	td   t t|	|
|||||!}t|t0}ttttdtd td
tdtdtdttttd tdtd  tdtd td	td   t  t|	|
|||||!|x	}t|t1}ttttdtd td
tdtdtdttttd tdtd  tdtd td	td   t  t|	|
||||||!|y
}t|t2}ttttt ttƐt3}t|t4}ttt5td
tdtdtdtt   tt t|	|
|ztƐt6}t|t7}ttttttdtd tdtd t tdtd  tdtd td	td t|	|
||||||{	}t|t8}ttttttdtd tdtd tdtd tdtd  tdtd td	td t|	|
|||||||	}t|t9}tttd
tdtdtdtttdtdttdtd tdtd   tdtd td	td   tdtd t|	|
|||||||!
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tdtdtdtttdtd td	td   tdtd t|	|
|||K|!}t|t;}tttd
tdtdtdtttdtd td	td   tdtd ttdtd tdtd  t|	|
|||||K|!	}t|t<}ttttdtd tdtd tdtd td
tdtdtdtttdtd td	td   tdtd  t|	|
||||||K|!|}|}t|t=}tttttdtd td	td tttd tdtd   t|||||K|~}t|t>}tttttdtd td	td t? t||||}t|t@}tttAtd
tdtdtdtttdtd td	td   tdtd  t|	|
|||K||!tƐtB	}t|tC}tttAtd
tdtdtdtttdtd td	td   tdtd  t|	|
|||K||!tƐtD	}t|tE}ttttd
tdtdtdtt   t|	|
|KtƐtF}t|tG}ttttdtd tdtd tdtd ttttdtd td
td td	td  tdtd tdtd td  t||	|
|||||||&}t|tH}ttttdtd tdtd tdtd tttttdtd td
td td	td  tdtd tdtd   t||	|
||||||||&|}t|tI}tttttdtd tttd td	td ttdtd  td
td tdtd  tdtd t|	|
|||||}t|tJ}tttttdtd tttd td	td td
td tdtd  tdtd t|	|||||}t|tK}ttttdtd tdtd tttdtd tttd td	td ttdtd  td
td tdtd  tdtd  t|	|
|||||||||}t|tL}ttttdtd tdtd tttdtd tttd td	td td
td tdtd  tdtd  t|	|||||||||}t|tM}tttdtdttttdtd ttdtd  tdtd  t||||||}t|tN}ttttt|z}t|tO}ttttttdtd td
td  t|	|
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td tdtd tt t|	|
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td  tt t|	|z}t|tS}ttttt t|ztƐtT}t|tU}tttttt5 t||}t|tV}ttttt tt5 t||tƐtW}t|tX}ttttd
tdtttdtd tdtd tdtd  t|	|
|||}t|tY}ttttd
tdtttdtd tdtd tdtd  t t|	|
|||}t|tZ}ttttdtd ttd
tdtttdtd tdtd tdtd   t|	|
||||}t|Đt[}tttdtdtd tdtttdtd td	td   tttdtdtttdtd td	td    t|	|
|||||}t|Ɛt\}ttttd
tdtt  t|	||}t|Ȑt]}tttt|tƐt^}t|ʐt_}tttdtdtt`t t}t|̐ta}ttt5td
td t5tdtd tttdtd   tdtd tdtd t|	|
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sympy.integrals.rubi.constraintsr#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  logx_r  r  r   replacement2009n_replacement2010replacement2011replacement2012r  replacement2013replacement2014replacement2015replacement2016replacement2017replacement2018replacement2019replacement2020m_replacement2021replacement2022replacement2023replacement2024replacement2025replacement2026replacement2027replacement2028replacement2029replacement2030replacement2031replacement2032replacement2033replacement2034replacement2035u_v_p_replacement2036replacement2037replacement2038a_replacement2039With2040replacement2041r   With2042replacement2042replacement2043g_replacement2044replacement2045replacement2046e_replacement2047With2048g1_g2_With2049replacement2050replacement2051replacement2052replacement2053r  r_replacement2054F_With2055replacement2056f_replacement2057replacement2058replacement2059d_With2060mn_replacement2061replacement2062Px_replacement2063RFx_With2064replacement2064With2065replacement2065replacement2066replacement2067q_replacement2068replacement2069replacement2070n2_replacement2071replacement2072replacement2073replacement2074replacement2075replacement2076replacement2077replacement2078replacement2079replacement2080replacement2081replacement2082replacement2083replacement2084replacement2085replacement2086replacement2087replacement2088replacement2089replacement2090replacement2091replacement2092replacement2093replacement2094replacement2095replacement2096replacement2097replacement2098replacement2099With2100With2101replacement2102replacement2103With2104With2105replacement2106replacement2107replacement2108replacement2109replacement2110replacement2111replacement2112replacement2113replacement2114replacement2115With2116With2117With2118replacement2118With2119replacement2119replacement2120replacement2121replacement2122replacement2123replacement2124r	  With2125With2126replacement2127replacement2128replacement2129With2130replacement2130w_With2131replacement2131replacement2132replacement2133replacement2134replacement2135replacement2136replacement2137With2138Qx_With2139RGx_With2140replacement2140With2141replacement2141With2142replacement2142replacement2143replacement2144replacement2145replacement2146replacement2147replacement2148replacement2149replacement2150replacement2151replacement2152With2153replacement2154With2155replacement2155replacement2156With2157replacement2157replacement2158replacement2159replacement2160replacement2161replacement2162With2163replacement2163r  replacement2164replacement2165replacement2166(  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zpattern2009Zrule2009Zpattern2010Zrule2010Zpattern2011Zrule2011Zpattern2012Zrule2012Zpattern2013Zrule2013Zpattern2014Zrule2014Zpattern2015Zrule2015Zpattern2016Zrule2016Zpattern2017Zrule2017Zpattern2018Zrule2018Zpattern2019Zrule2019Zpattern2020Zrule2020Zpattern2021Zrule2021Zpattern2022Zrule2022Zpattern2023Zrule2023Zpattern2024Zrule2024Zpattern2025Zrule2025Zpattern2026Zrule2026Zpattern2027Zrule2027Zpattern2028Zrule2028Zpattern2029Zrule2029Zpattern2030Zrule2030Zpattern2031Zrule2031Zpattern2032Zrule2032Zpattern2033Zrule2033Zpattern2034Zrule2034Zpattern2035Zrule2035Zpattern2036Zrule2036Zpattern2037Zrule2037Zpattern2038Zrule2038Zpattern2039Zrule2039Zpattern2040Zrule2040Zpattern2041Zrule2041Zpattern2042Zrule2042Zpattern2043Zrule2043Zpattern2044Zrule2044Zpattern2045Zrule2045Zpattern2046Zrule2046Zpattern2047Zrule2047Zpattern2048Zrule20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S r  )r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    r  r  c              	   C   sV   t | |t|||||  |	  |
    |td  || |	 |
 |td   |S r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r       Vr  c                 C   s   t ||	 |
 | |td  t| |t|||||  |
  |    |	td  |||  |  || t| |t|||||  |
  |    |	 |||  |td   ||td   | S Nr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r       r  c                 C   s>   t || |td  t| |||  |   | | |  |S r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r       >r  c              	   C   sj   t |||  td|  |||  |td   t|||  |td  t| |||  |   ||S r  r  r  r   r  r  r  r  r  r       jr  c                 C   s   t |||||  |	  |
  |td  |	|
   |||  |td   t| |t|||||  |	  |
    |td  ||	 |
   t|  |td  ||	 |
   || |	 |
  |S r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    r  r  c                 C   s   t tt|||||  |	  |
  |td  |	|
    |||  |td   tt| |t|||||  |	  |
    t|td ||	 |
  td  t|  |td  ||	 |
   || |	 |
 t|td ||	 |
  td  |S r  r  r  r  r  r  r    s   r  c                 C   s  t tt|||||  |	  |
  |td  |	|
    |||  |td   tt| |t|||||  |	  |
    t|td  ||	 |
  td  t|  |td  ||	 |
   || |	 |
 t|td  ||	 |
  td  |S r  r  r  r  r  r  r    s    r  c                 C   s   t |td ||
 | |	td   t| |t|||||  |
  |    |	td  |||  |  || t| |t|||||  |
  |    |	td  |||  |td   || |
 | |	td   | S r  r  r  r  r  r  r       r  c                 C   sF  t |||||  |
  |  |td  |
|   | |t|||||  |
  |     |td  ||
 |  |	   | |t|||||  |
  |    |	  |||  |td   t|	td | |t|||||  |
  |     |td  ||
 |   t|  |td  ||
 |   ||td   |S r  r  r  r  r  r  r    s   H r  c                 C   s4   t ttd|||   t| | |  | | S Nr  r  r  r  r   r  r  r  r  r  r  r  r  r  r       4r  c              	   C   s|   t |tt| |||   | | ||   |||   ||t| |t|||| |     t|||   | | S r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r    s   |r  c                 C   s   t || | |	 |
 | t| |t|||||  |	  |
    |td  t||||   | | ||    |||   || t| |t|||||  |	  |
    | t||||   | | ||    | | S r  r  r  r  r  r  r       r  c              
   C   s   t || |	 |
 ||td   t|||  |td  |||   || t| |t|||||  |	  |
    |||  |td   ||td   | S r  r  r  r   r  r  r  r  r  r  r       r  c                 C   s   t || | |	 |
 | | ||   t| |t|||||  |	  |
    |td  |||   || t| |t|||||  |	  |
    | |||   |||  | | ||    | S r  r  r  r  r  r  r    r  r  c                 C   s   t || |	 |
 | ||td   t| |t|||||  |
  |    |	td  |||  |td   |||   || t| |t|||||  |
  |    |	 |||  |td   ||td   | S r  r  r  r  r  r  r    r  r  c                 C   sD   t t|||  | | |t|||||  |	  |
     ||S r  r   r   r  r  r  r  r  r       Dr  c                 C   sn  t |td ||
 | |	td   t| |t|||||  |
  |    |	td  |||  |  || t || | ||   || |
 | |	td   t| |t|||||  |
  |    |	td  |||  |td   || t| |t|||||  |
  |    |	td  |||   |||  |  || |
 | |	td   | S r  r  r  r  r  r  r    s   p r  c              
   C   sH   t t| |t|||||  |
  |    |	 |||  |  ||S r  r  r  r  r  r  r    r  r  c              	   C   s>   t | |t||t|	|
|  |    | t||
|  |
S r  r   r  r2  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    r  r  c              	   C   sB   t | |t|||||  |
  |    |	 |||  |  |S r  r   r  r  r  r  r  r    s   Br  c              	   C   sJ   t |ttd||||   ||||     || | ||    |S r  r  r  r  )r  r  r  r  r  r  r  r  r  r  r  r       Jr  c
           
   	   C   sh   t | ttd|||	  |||	    |	|	t |tt||||	   |||	  |||	    |	|	 S r  )r  r   r  r  )
r  r  r  r  r  r  r  r  r  r  r  r  r  r       hr  c              
   C   s   t ||	|  |
 |||   |}t|| | | tt||||   ||| t| |t|||||  |  |    || S r  r  r  r   r-  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    s   "br  c              
   C   st   t ||	  ||	   | tt| ||  |
 | | | || |  |t|  |	  ||t||||   |S r  )r  r+   r   r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r       tr  c              	   C   sr   t |ttttfrdS t| |t|||||  |  |    | ||	|  |
 |||   |}t|r7dS dS NFT
isinstanceintr  floatr  r   r  r)   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    s   Lr  c              	   C   sV   t | |t|||||  |  |    | ||	|  |
 |||   |}t||S r  r   r  r   r  r  r  r  r    s   L
r  c              	   C   sN   t | |t|||||  |  |    | ||	|  |
  |||   |S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r       Nr  c                 C   s@   t |ttd| ||  |||    td| |  | S r  r  r  r  r  r  r     s   @r   c              
   C   s   t |tttd| |||   |||td    ||t | |t|td|    ttd|||td    || S Nr  r  r  r   r  r  r  r  r  r  r  	  s   r  c                 C   sZ   t || t| |t|||||  |	  |
    |||  || | ||    ||S r  r  r   r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r       Zr  c                 C   sZ   t || t| |t|||||
  |  |	    |||
  || |
 ||    |
|
S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    r  r  c                 C   s   t tdt|||
td    |
}t|| | |	 tt||||
   |
|
|
 t|| |t|||||
  |  |	     |
 S r  r  r  r  r  r   r-  r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    s   &dr  c                 C   s   t tdt|| ||	 |td    |}t|| |
 | tt||||   ||| t|| |t|||||  |
  |     | S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    s   .dr  c                 C   s   t ttd||
td  |  t|||
td    t| |t|||||
  |  |	    ttd||
td  |   |
|
S r  r  r  r  r   r  r  r  r  r  r	    s   r	  c                 C   s   t ttd||	 |td  ||   t|||  t||	|    t| |t|||||  |
  |    ttd||	 |td  ||    ||S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r
  #  s   r
  c                 C   s   t || | | | | t| |t|||||  |  |    |td  ttdt| |	|
|   td  |||   ||t| |t|||||  |  |    | ttdt| |	|
|   td  | | S )Nr  r  r  )r  r   r  r  r  r   r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  '  s   r  c                 C   s   t || | | | ||  t| |t|||||  |  |    |td  ttd| |	|
|  |   |||   ||t| |t|||||  |  |    | ttd| |	|
|  |   ||  | S Nr  r  r  r   r  r  r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  +     r  c                 C   s   t || | | | ||  t| |t|||||  |  |    |td  t|td ||	|
|  |   |||   || t| |t|||||  |  |    | t|td ||	|
|  |   ||  | S Nr  r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  /  r  r  c              
   C   s   t || ||	|  |
  |}t|| | | tt||||   ||| t||t|||||  |  |    || S r  r  )Fr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  3  s   br  c                 C   sR   t td| tt| |t|||||
  |  |	    | |
 |
|
|
| |
S r  r  r  r+   r   r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  8     Rr  c                 C   sR   t td| tt| |t|||||  |  |	    | | |||| |S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  <  r  r  c                 C   sN   t td|	 tt| |t|||||  |  |    | ||||	 |S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  @  r  r  c                 C   s^   t td| tt| |t|||||  |
  |    |	 |||  |  |||| |S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  D     ^r  c                 C   s^   t td|||td    |}t|| t|| || t| |t|||    || S r  )r  r  r  r   r  )r  r  r  r  r  r  r  r  r  r  r  r  H  s   "<r  c              	   C   D   t ttdt|| ||   ||||    |  ||  |S r  r  r  r  r  r  r  r   r  r  r  r  r  r  M  r  r  c              	   C   r  r  r  r  r  r  r  r  Q  r  r  c                 C   s<   t t| ||t|||||
  |  |	    |  |
|
S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  U     <r  c              	   C   sZ   t |
ttttfrdS t||t|||||
  |  |	    | | |
}t|r+dS dS r  r  r!  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Y  s   4r  c              	   C   s>   t ||t|||||
  |  |	    | | |
}t||
S r  r  r  r  r  r  r  b  s   4
r  c              
   C   s\   t |
ttttfrdS t| ||t|||||
  |  |	    |  |
}t|r,dS dS r  r  r  r  r  r  r   h  s   6r   c              
   C   s@   t | ||t|||||
  |  |	    |  |
}t||
S r  r  r  r  r  r  r!  q  s   6
r!  c              
   C   s^   t |
| |t|td|  | ||   |td| |  td|   |	    |  |S )N   r  )r   r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r"  w  r  r"  c
           
   
   C   s4   t || |t||t||	|  |    |  |	S r  r  )
r  r  r  r  r  r  r  r  r  r  r  r  r  r#  {  r  r#  c                 C   sJ   t tt||| |  | |||| |  | ||||  |  |  S r  r+   r   r  )r  r  r  r  r  r  r  r  r  r  r  r%    r  r%  c	           	      C   sR   t t|| t||| |  |  |||| |  | ||||  |  |  S r  r  )	r  r  r  r  r  r  r  r  r  r  r  r  r&    r  r&  c
           
      C   s*   t t||| | |  | t||	|	S r  )r  r  r   )
r  r  r  r  r  r  r  r  r  r  r  r  r  r'       *r'  c              	   C   s   t || |	 |  | ||   | tt||| ||
  |  |||
  |   |  |	td  |||
   |
|
 t| ||
  t||| ||
  |  |||
  |   |  |	  | |
 S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r)    s   r)  c                 C   s2   t ttdt|  | | |||   | |S r  r  r  r  r  r  r  r  r  r  r  r  r  r*       2r*  c              
   C   s  t ||	 | |  | ||   | tt||| ||  |	  |||  |	   |  |td  t|  | ||  ||||     | ||  |||    ||tt||| ||  |	  |||  |	   |  | t|  | ||  ||||     | | S r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r+    s    r+  c              
   C   s  t ||	 | |  | ||   | tt||| ||  |	  |||  |	   |  |td  t|  | ||   || ||     | ||  |||    ||tt||| ||  |	  |||  |	   |  | t|  | ||   || ||     | | S r  r  r  r  r  r  r,    s    r,  c                 C   s   t ||	 |  | ||   | tt|||  | ||  |||    || tt||| ||  |	  |||  |	   |  t|||   | | S r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r-    r  r-  c              
   C   s   t || tt||| ||  |	  |||  |	   |  | |||   ||t | | ||  | tt||| ||  |	  |||  |	   |  | |||  |||    || S r  r  r  r  r  r  r.    r  r.  c                 C   sT   t |td t|| ||   |||    ||td  |  | ||    |S r  r  r  r  r  r  r/    s   Tr/  c              	   C   s   t |td ||| ||  |	  |||  |
  |  td ||	    | ||   tt||| ||  |	  |||  |	   |  ||	   |td | |	 |||   |  | ||    |S r  r  r  r  r  r  r  r  r  r0       r0  c              	   C   s   t |td ||| ||  |	  |||  |
  |  td||	    |||   tt||| ||  |	  |||  |	   |   ||	   |td | |	 | ||   |  | ||    |S r  r  r  r  r  r  r1    r  r1  c              	   C   s   t ||	 | |  | ||   |  | ||   tt||| ||  |	  |||  |	   |  |td  |||  |||    || t| ||  t||| ||  |	  |||  |	   |  |  |||  |  | ||    | S r  r  r  r  r  r  r2       r2  c              	   C   s   t ||	 | |  | ||   | | ||   tt||| ||  |	  |||  |	   |  |td  | ||  |||    || t|||  t||| ||  |	  |||  |	   |  |  |||  | | ||    | S r  r  r  r  r  r  r3    r  r3  c                 C   s   t ||  | ||   tt||| ||  |	  |||  |	   |  | |||  td  ||t ||  | ||   t| ||  t||| ||  |	  |||  |	   |  |  |||  td  || S Nr  r  r  r  r  r  r  r4    r  r4  c                 C   s   t || | ||   tt||| ||  |	  |||  |	   |  | |||  td  ||t || | ||   t|||  t||| ||  |	  |||  |	   |  |  |||  td  || S r  r  r  r  r  r  r5    r  r5  c              
   C   s  t |	|
 | |  | ||   ||td   t|||  |td  t||| ||  |
  |||  |
   |	  |td   | ||  |||    || t|||  |td  t||| ||  |
  |||  |
   |	  |  ||td   | S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r6    s    r6  c                 C   s   t || |td  t| ||
  | |||
  | td   t||	|  |td   |
|
 t| ||
  |td  |||
  | td   t||	|  |  |td |  | ||    |
 S Nr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r7    s   r7  c	           	      C   s   t ||td  t| ||  | |||  | td   t||td   || t| ||  |td  |||  | td   t||  |td |  | ||    | S r  r  	r  r  r  r  r  r  r  r  r  r  r  r  r8    s   r8  c
           
      C   s   t |||  |td  |  | ||	  |td   |||	  | td   t|td t|||   |  ||  | ||    |	S r  r  )
r  r  r  r  r  r  r  r  r  r  r  r  r  r9    s   r9  c                 C   st   t || td  | ||  |td   |||  | td   t|td t|  |  | ||   |S r  r  )r  r  r  r  r  r  r  r  r  r  r  r:    r  r:  c                 C   s   t |td ||td   t| ||
  | |||
  | td   t||	|  |td   |
|
 t| ||
  |td  |||
  | td   t||	|  |td   ||td  |  | ||    |
 S r  r  r  r  r  r  r;    s   r;  c	           	      C   s   t |td |td  t| ||  | |||  | td   t||td   || t| ||  |td  |||  | td   t||td   |td |  | ||    | S r  r  r  r  r  r  r<    r  r<  c              	   C   s\   t || tt||| ||  |	  |||  |	   |  | |||  td  ||S r  r  r  r  r  r  r=    s   \r=  c                 C   sL   t ttd|||   | | |  ||||    | | ||   |S r  r  r  r  r  r  r>    s   Lr>  c              
   C   s^  t ||	 | |  | ||   | | ||   tt||| ||  |	  |||  |	   |  |td  t|||  |  | ||   |||  |  | ||     | ||  |||    ||tt||| ||  |	  |||  |	   |  | t|||  |  | ||   |||  |  | ||     | | ||   | S r  r  r  r  r  r  r?    s   ` r?  c              	   C   sN   t |ttd|||   | | |  ||||     td| |  |S r  r  r  r  r  r  r@    r  r@  c              	   C   sv   t |td tt||| ||  |
  |||  |
   |	  | |||  | | ||  || |    ||S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rA       vrA  c              	   C   sj   t |td | tt||| ||  |	  |||  |	   |  | |||  |||    || S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rB    r  rB  c                 C   sj   t ||| |	 |  | ||    tt|| ||t||| ||  |	  |||  |	   |  |S r  )r  r+   r   r  r  r  r  r  rC    r  rC  c
           
      C   s   t || tttdttd| t|||  |td   | ||	  |||	    |	|	tttdttd| t|||  |  |  | ||   |	 S Nr  r  r  r  r   r  r  r   r  r  
r  r  r  r  r  r  r  r  r  r  r  r  r  rD    r  rD  c                 C   s   t |tttdttd| t||td   | ||  |||    ||tttdttd| t||  |  | ||   | S r  r  r  r  r  r  r  r  r  r  r  r  r  rE    r  rE  c
                 C   s   t d| | }
t|
||t d   tt|||  |t d  |||	  |  |
 ||
  | |   |	|	tt|t|||  |t d   ||t d  |  | ||    |	 S r  r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rF       rF  c           	      C   s   t d| | }t||t d  tt||t d  |||  |  | ||  | |   ||tt||t d  t| |t d |  | ||    | S r  r  	r  r  r  r  r  r  r  r  r  r  r  r  rG       rG  c
           
      C   s   t || tttdttd| t|||  |td   | ||	  |||	    |	|	 tttdttd| t|||  |  |  | ||   |	 S r  r  r  r  r  r  rH  	  s   rH  c                 C   s   t |tttdttd| t||td   | ||  |||    || tttdttd| t||  |  | ||   | S r  r  r  r  r  r  rI       rI  c
                 C   s   |t d|  }
t|
||t d   tt|||  |t d  | ||	  | | ||
  ||
    |	|	 tt|t|||  |t d   ||t d  |  | ||    |	 S r  r  r  r  r  r  rJ    r  rJ  c           	      C   s   |t d|  }t||t d  tt||t d  | ||  | | ||  ||    || tt||t d  t| |t d |  | ||    | S r  r  r  r  r  r  rK    r  rK  c                 C   s   t || tt|td |	t|||  |td   | ||
  |||
    |
|
 tt|td |	t|||  |  |  | ||   |
 S r  r  r   r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rL    s   rL  c	           	      C   s   t |tt|td |t||td   | ||  |||    || tt|td |t||  |  | ||   | S r  r   	r  r  r  r  r  r  r  r  r  r  r  r  rM    s   rM  c                 C   s   t td||td   tt|td |	t|||  |td   | ||
  |||
    |
|
 tt||	t|||  |td   ||td  |  | ||    |
 S r  r  r  r   r  r  r  r  r  r  r  rN  #     rN  c	           	      C   s   t td|td  tt|td |t||td   | ||  |||    || tt||t||td   |td |  | ||    | S r  r  r  r  r  r  rO  '  s   rO  c                 C   s   t || tt|td |	t|||  |td   | ||
  |||
    |
|
tt|td |	t|||  |  |  | ||   |
 S r  r   r  r  r  r  rP  +  s   rP  c	           	      C   s   t |tt|td |t||td   | ||  |||    ||tt|td |t||  |  | ||   | S r  r   r  r  r  r  rQ  /     rQ  c                 C   s   t td||td   tt|td |	t|||  |td   | ||
  |||
    |
|
tt||	t|||  |td   ||td  |  | ||    |
 S r  r  r  r  r  r  rR  3     rR  c	           	      C   s   t td|td  tt|td |t||td   | ||  |||    ||tt||t||td   |td |  | ||    | S r  r  r  r  r  r  rS  7  r  rS  c              
   C   sh   t || | t|t||| ||  |
  |||  |
   |	  |  | ||  |||    ||S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rT  ;  r  rT  c              
   C   sh   t || | t|t||| ||  |	  |||  |	   |  |  | ||  |||    ||S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rU  ?  r  rU  c              	   C   s   t td|||  ||td    |}t|	|  | ||   t|| ||  |||    || t|t||| ||  |
  |||  |  |	   | S r  r  r  r  r   r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rV  C  s   *xrV  c              	   C   s   t td|||td    |}t||  | ||   t|| ||  |||    || t|t||| ||  |	  |||  |
  |   | S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rW  H  s   "xrW  c                 C   sb   t |ttttfrdS tt|||||  |  |||  |	  |  |
 | |}t|r/dS dS r  r  r!  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  rX  M  s   <rX  c                 C   sF   t t|||||  |  |||  |	  |  |
 | |}t||S r  r  r  r  r  r  rY  V  s   <
rY  c                 C   sH   t |ttttfrdS t||}ttt| t	t
|tdr"dS dS )NFr  T)r  r  r  r  r  r   r6   r  r  r   r  r  r  r  r  r  lstr  r  r  rZ  \  s   
 rZ  c              	   C   s\   t ||}t|t|t|td t|td |t|td t|td  |   |S )Nr  r  r  r  )r   r   r  r  r  r	  r  r  r  r[  e  s   
Rr[  c              	   C   sV   t || | t|| | |||    || t|t|| |||   |   | S r  )r  r   r  r  )r  r  r  r  r  r  r  r  r  r\  k  r  r\  c                 C   s   t t| t|||  |S r  r  )r  r  r  r  r  r  r  r]  o  s   r]  c
           
   
   C   s   t || | | | t|	|td  t|||	   |||	|    |	|	 t| |t||||	|   |    t|||	   | |	 S r  r  r   r  r  r  
r  r  r  r  r  r  r  r  r  r  r  r  r  r^  s  s   r^  c              
   C   s   t || | |	 ||td   t|
|td  |||
  |td   |||
|    |
|
 t| |t||||
|   |	    |||
  |td   ||td   |
 S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r_  w  r  r_  c                 C   s2   t | |t|t|||    t|||  |S r  r  )r  r  r  r  r  r  r  r  r  r  r  r`  {  r  r`  c              
   C   s   t t|||
  | |
}t|| | |	 tt||
|td   |||
|    |
|
|
 t| |t||||
|   |	    ||
 S r  )r  r	  r  r   r-  r  r  )r  r  r  r  r  r  r  r  r  r  r  wr  r  r  ra    s   rra  c	           
      C   s   t td|||td    |}	ttd| | | t|	| |||td    || t|	| |t||||td   |     | S r  r  )
r  r  r  r  r  r  r  r  r  r  r  r  r  rb    s   "nrb  c                 C   s   t td| | | | t|td | |t||||td   |    |td   |||td    || t|| |t||||td   |    |  | S )Nr  r  r  r  r  r  r  r  r  r  r  r  r  r  rc    s   rc  c	           	      C   sf   t tdd tt||td tdd   | |t||||  |    |  |||td |S )Nr  r  r  r  	r  r  r  r  r  r  r  r  r  r  r  r  rd    s   frd  c	           	      C   s   t td| | | | |td  t||td  | |t||||td   |    |td   |||td    || t||td  | |t||||td   |    |  |td  | S r  r  r  r  r  r  re    s   re  c              	   C   sd   t |ttttfrdS zt|| td|  |}tt|}W n t	t
fy+   Y dS w |r0dS dS NFr  Tr  r  r  r  r  r  r  r6   r   	TypeErrorAttributeError)r  r  r  r  resr  r  r  rf       rf  c                 C   s<   t || td|  |}t|ttdttd|  |S r  )r  r  r  r  r   r  r  r  r  r  r  r  rg    s   $rg  c              	   C   sd   t |ttttfrdS zt||td|  |}tt|}W n t	t
fy+   Y dS w |r0dS dS r  r  )r  r  r  r  r  r  zr  r  r  r  ri    r  ri  c              
   C   s   t ||td|  |}t|tt|t|| ttdttd|  | ||| t|| |t	|   ttdttd|  | S r  )
r  r  r  r   r-  r  r  r   r  r  )r  r  r  r  r  r  r  r  r  r  rj    s   vrj  c              
   C   st   t || | ttd| |||  |   |  || t|||  t|| ||||  |   |   | | S r  r  r   r  r  r  r  r  r  r  rk    r  rk  c              
   C   s   t | | | ttd| ||||  |    ||t|||  t|| ||||  |   |   | | t|| | | S r  r  r  r  r  r  rl    r  rl  c
           
      C   s   t || | | ||  tt| |t||||	  |    |td  |	 |	|	td|||	   |	 t| |t||||||	    |    | ||||	   |  ||  |	 S r  )r  r+   r   r  r  r  r  r  r  r  rm    s   rm  c              
   C   sz   t || | tt|||t| | |   |td   t| | |  ||| t|||t| | |   |  | S r  )r  r   r-  r  r  r  r  )r!  r  r  r  r  r  r  r  r  r  rn    s   zrn  c	           	      C   s   t || | | t||t| | |   |td  t| | t|||   |  || t||t| | |   | t|||   | | S r  )r  r   r  r  r  r  )	r!  r  r  r  r  r  r  r  r  r  r  r  ro    r  ro  c
           
   	   C   s   t || | ||td   tt||t| | |   |td  |||	  |td   t| |	 |  |	|	|	 t||t| | |   | |||	  |td   ||td   |	 S r  )r  r  r   r-  r  r  r  )
r!  r  r  r  r  r  r  r  r  r  r  r  r  rp    r  rp  c                 C   sd   t td|||td    |}t|tt|t| | |  ||| t|t| | |  | S r  r  r  r  r   r-  r  r  r  )r!  r  r  r  r  r  r  r  r  r  rq    s   "Brq  c                 C   sT   t td| |}t|tt|t| | |  ||| t|t| | |  | S r  r  )r  r  r  r  r  r  r  r  r  rs    s   Brs  c           	      C   sJ   t |ttttfrdS t||t| | |   | ||}t|r#dS dS r  r  	r!  r"  r  r  r  r  r  r  r  r  r  r  ru    s   $ru  c           	      C   s.   t ||t| | |   | ||}t||S r  r  r  r  r  r  rv    s   $
rv  c           	      C   sL   t |ttttfrdS t|||t| | |   |  |}t|r$dS dS r  r  r  r  r  r  rw    s   &rw  c           	      C   s0   t |||t| | |   |  |}t||S r  r  r  r  r  r  rx    s   &
rx  c              	   C   sf   t |ttttfrdS zt| ||t|   |}tt|}W n t	t
fy,   Y dS w |r1dS dS r  )r  r  r  r  r  rO  r  r6   r   r  r  )r!  r  r  r  r  r
  r  r  r  r  ry    s   ry  c                 C   sv   t | ||t|   |}tt|tdt|td ttt|td||t|tdtdt|td  |S )Nr  r  r  r  )rO  r  r  r  r  r+   r   )r!  r  r  r  r  r
  r  r  r  rz    s   \rz  c
           
      C   s   t || || | t|   t|||	  |td  ttd| | ||||	    |   |	|	t|||	  | ttd| | ||||	    |   || | t|   |	 S r  )r  r  r   r  r  r  )
r  r  r  r  r  r  r  r  r  r  r  r  r  r{    r  r{  c                 C   s   t |||
  | ttd|| ||||
    |	  |   |
t|||
  |td  ttd|| ||||
    |	  |   ||td   |
 t|||
  |td  t||| ||||
    |	    ||td   |
 S r  )r   r  r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r|    s   r|  c                 C   s  t |td td |  | |td   td t|| t| ||  ||td    td |  | ||  || | td| |     | |td  td| |  | ||  ||td      ||t|t|||  |t| ||  ||td      | S )Nr  r  r  r  r   r  r  r  )r  r  r  r  r  r  r  r  r  r  r}    s    r}  c                 C   s   t | | |td  t||| | ||td    |t| ||td    | | || |     || t|t|||  |t| ||td      | S r  r  )r  r  r  r  r  r  r  r  r  r~    r  r~  c	           	      C   sZ  t |td td |  | |td   td| |td   t|| |td  | t| ||  ||td    td |  | ||  || | td| |     | |td  td| |  | ||  ||td      ||t|| |td  t|||  |t| ||  ||td      ||td   | S )Nr  r  r  r  )	r  r  r  r  r  r  r  r  r  r  r  r  r    s   \ r  c                 C   s   t | | |td  ||td   t|| |td  || | ||td    |t| ||td    | | || |     || t|| |td  t|||  |t| ||td      ||td   | S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  "  r  r  c              	   C   s,   t |t| ||  |tt||   |S r  )r   r  r  r2  )r  r  r  r  r  r  r  r  r  r  &  s   ,r  c                 C   s2   t t|t| | |  || t|t|  | S r  )r   r-  r  r  r  )r  r  r  r  r  r  *  r  r  c              	   C   s^   t td| ttt||t| ||   | ||| tt|t| ||   | | S r  )r  r  r   r-  r  r  r  )r  r  r  r  r  r  r  r  .  r  r  c                 C   s   t td||td   tt| ||  |td  t|| | ||| t| ||  |td  t| ||td   | S r  )r  r  r   r-  r  r  r  )r  r  r  r  r  r  r  r  r  2  s   r  c                 C   sD   t td|  |}tt|t|| | || t|t| | S r  )r  r  r   r-  r  r  r  )r  r  r  r  r  r  r  r  6  s   2r  c                 C   sF   t t|| | td  | t|| || t|| |  |  | S r  )r   r-  r  r  r  )r  r  r  r  r  r  r  ;  s   Fr  c                 C   s2   t |ttttfrdS t||}t||rdS dS r  r  r  r  r  r  r  r   r  r  r  r  r  ?     

r  c                 C   s8   t ||}tt| ||tt|t| | |  || S r  r  r  r  r   r-  r  r  r  r  r  r  H  s   
.r  c                 C   sh   t t|t| | t| |  || t t|t|| t|  | || t|t|  t| | S r  )r   r-  r  r  r  )r  r  r  r  r  r  r  N  r  r  c                 C   s2   t |ttttfrdS t| |}t||rdS dS r  r  r  r  r  r  r  r  r  r  r  R  r  r  c                 C   sn   t | |}tt|t| ||tt|t|| t| | || tt|t|| t| | || S r  r  r  r  r  r  r  [  s   
dr  c              	   C   sR   t || ttdt|||   || t|t| t|||  |   | S r  r  r  r  r  r  r  r  r  r  r  a  r  r  c                 C   s<   t | t| t|||  |   t|||   | |S r  r  r   r  r  r  r  e  r  r  c              	   C   sv   t || |td  t|| t|||   || t||td  t| t|||  |   |td  | S r  r  )r  r  r  r  r  r  r  r  r  r  i  r  r  c                 C   sp   t || tt||t|||    ||t | | ||  | ttdt||t|||     || S r  )r  r   r  r  r  )r  r  r  r  r  r  r  r  r  r  r  m  s   pr  c                 C   s   t || t|  |S r  r  )r  r  r  r  r  r  r  r  q  s   r  c              	   C   sZ   t |ttttfrdS zt| | |}tt|}W n tt	fy&   Y dS w |r+dS dS r  )
r  r  r  r  r  rz  r6   r   r  r  )r  r  r
  r  r  r  r  r  u  s   r  c              
   C   sR   t | | |}ttdt|td ttt|td||tt|td|S )Nr  r  r  )rz  r  r  r  r+   r   r  )r  r  r
  r  r  r  r    s   Dr  c                 C   s6   t t| tt| t| ||t| t| | S r  )r  r  r  r  r   )r  r  r  r  r  r  r       6r  c                 C   s*   t |||  | |t||   |  |S r  r  )r  r  r  r  r  r  r  r  r  r  r  r    r  r  c              
   C   s6   t |	| |t|||||
  |  |    |  |
S r  r  )r  r  r  r  r  r  r  r  r  r  r  r  r  r  r    r!  r  (  __doc__Zsympy.externalr   r   r   r   r   r   Z%sympy.integrals.rubi.utility_functionr   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   r>   r?   r@   rA   rB   rC   rD   rE   rF   rG   rH   rI   rJ   rK   rL   rM   rN   rO   rP   rQ   rR   rS   rT   rU   rV   rW   rX   rY   rZ   r[   r\   r]   r^   r_   r`   ra   rb   rc   rd   re   rf   rg   rh   ri   rj   rk   rl   rm   rn   ro   rp   rq   rr   rs   rt   ru   rv   rw   rx   ry   rz   r{   r|   r}   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r  r  r	  r
  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r!  r"  r#  r$  r%  r&  r'  r(  r)  r*  r+  r,  r-  r.  r/  r0  r1  r2  r3  r4  r5  r6  r7  r8  r9  r:  r;  r<  r=  r>  r?  r@  rA  rB  rC  rD  rE  rF  rG  rH  rI  rJ  rK  rL  rM  rN  rO  rP  rQ  rR  rS  rT  rU  rV  rW  rX  rY  rZ  r[  r\  r]  r^  r_  r`  ra  rb  rc  rd  re  rf  rg  rh  ri  rj  rk  rl  rm  rn  ro  rp  rq  rr  rs  rt  ru  rv  rw  rx  ry  rz  r{  r|  r}  r~  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zsympyr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  Zsympy.integrals.rubi.symbolr  Zsympy.core.symbolr  r  Zsympy.functionsr  r  r  r  r  r  r  Z%sympy.functions.elementary.hyperbolicr  r  r  r  r  r   r  r  r  r  r  r  Z(sympy.functions.elementary.trigonometricr  r  r	  r
  r  r  r  r  r  ZA_ZB_ZC_r  ZG_ZH_r  Zb_Zc_r  r  r  r  Zh_Zi_Zj_Zk_Zl_r  r  r  r$  r  Zt_r  r  Zs_rh  r  Zy_Zz_Za1_Za2_Zb1_Zb2_Zc1_Zc2_Zd1_Zd2_Zn1_r(  Ze1_Ze2_Zf1_Zf2_r  r  Zn3_ZPq_ZPm_r  ZQm_ZQr_rr  Zjn_r  Znon2_r  rt  r  iiZPqqQRr  Cr  r  Z	_UseGammaZ	ShowStepsZStepCounterr  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r  r   r  r  r  r  r  r	  r
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