diff --git a/books/bookvol10.3.pamphlet b/books/bookvol10.3.pamphlet index 272d6cd..5ec4ffd 100644 --- a/books/bookvol10.3.pamphlet +++ b/books/bookvol10.3.pamphlet @@ -32949,6 +32949,813 @@ d03fafAnnaType():PartialDifferentialEquationsSolverCategory == Result add %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \chapter{Chapter E} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{domain EFULS ElementaryFunctionsUnivariateLaurentSeries} + +\begin{chunk}{ElementaryFunctionsUnivariateLaurentSeries.input} +)set break resume +)sys rm -f ElementaryFunctionsUnivariateLaurentSeries.output +)spool ElementaryFunctionsUnivariateLaurentSeries.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ElementaryFunctionsUnivariateLaurentSeries +--E 1 + +)spool +)lisp (bye) +\end{chunk} +\begin{chunk}{ElementaryFunctionsUnivariateLaurentSeries.help} +==================================================================== +ElementaryFunctionsUnivariateLaurentSeries examples +==================================================================== + +This domain provides elementary functions on any Laurent series +domain over a field which was constructed from a Taylor series +domain. These functions are implemented by calling the +corresponding functions on the Taylor series domain. We also +provide 'partial functions' which compute transcendental +functions of Laurent series when possible and return "failed" +when this is not possible. + +See Also: +o )show ElementaryFunctionsUnivariateLaurentSeries + +\end{chunk} +\pagehead{ElementaryFunctionsUnivariateLaurentSeries}{EFULS} +\pagepic{ps/v103elementaryfunctionsunivariatelaurentseries.ps}{EFULS}{1.00} + +{\bf Exports:}\\ +\begin{tabular}{lllll} +\cross{EFULS}{acos} & +\cross{EFULS}{acosIfCan} & +\cross{EFULS}{acosh} & +\cross{EFULS}{acoshIfCan} & +\cross{EFULS}{acot} \\ +\cross{EFULS}{acotIfCan} & +\cross{EFULS}{acoth} & +\cross{EFULS}{acothIfCan} & +\cross{EFULS}{acsc} & +\cross{EFULS}{acscIfCan} \\ +\cross{EFULS}{acsch} & +\cross{EFULS}{acschIfCan} & +\cross{EFULS}{asec} & +\cross{EFULS}{asecIfCan} & +\cross{EFULS}{asech} \\ +\cross{EFULS}{asechIfCan} & +\cross{EFULS}{asin} & +\cross{EFULS}{asinIfCan} & +\cross{EFULS}{asinh} & +\cross{EFULS}{asinhIfCan} \\ +\cross{EFULS}{atan} & +\cross{EFULS}{atanIfCan} & +\cross{EFULS}{atanh} & +\cross{EFULS}{atanhIfCan} & +\cross{EFULS}{cos} \\ +\cross{EFULS}{cosIfCan} & +\cross{EFULS}{cosh} & +\cross{EFULS}{coshIfCan} & +\cross{EFULS}{cot} & +\cross{EFULS}{cotIfCan} \\ +\cross{EFULS}{coth} & +\cross{EFULS}{cothIfCan} & +\cross{EFULS}{csc} & +\cross{EFULS}{cscIfCan} & +\cross{EFULS}{csch} \\ +\cross{EFULS}{cschIfCan} & +\cross{EFULS}{exp} & +\cross{EFULS}{expIfCan} & +\cross{EFULS}{log} & +\cross{EFULS}{logIfCan} \\ +\cross{EFULS}{nthRootIfCan} & +\cross{EFULS}{sec} & +\cross{EFULS}{secIfCan} & +\cross{EFULS}{sech} & +\cross{EFULS}{sechIfCan} \\ +\cross{EFULS}{sin} & +\cross{EFULS}{sinIfCan} & +\cross{EFULS}{sinh} & +\cross{EFULS}{sinhIfCan} & +\cross{EFULS}{tan} \\ +\cross{EFULS}{tanIfCan} & +\cross{EFULS}{tanh} & +\cross{EFULS}{tanhIfCan} & +\cross{EFULS}{?**?} & +\end{tabular} + +\begin{chunk}{domain EFULS ElementaryFunctionsUnivariateLaurentSeries} +)abbrev domain EFULS ElementaryFunctionsUnivariateLaurentSeries +++ Author: Clifton J. Williamson +++ Date Created: 6 February 1990 +++ Date Last Updated: 25 February 1990 +++ Description: +++ This domain provides elementary functions on any Laurent series +++ domain over a field which was constructed from a Taylor series +++ domain. These functions are implemented by calling the +++ corresponding functions on the Taylor series domain. We also +++ provide 'partial functions' which compute transcendental +++ functions of Laurent series when possible and return "failed" +++ when this is not possible. + +ElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS):_ + Exports == Implementation where + Coef : Algebra Fraction Integer + UTS : UnivariateTaylorSeriesCategory Coef + ULS : UnivariateLaurentSeriesConstructorCategory(Coef,UTS) + I ==> Integer + NNI ==> NonNegativeInteger + RN ==> Fraction Integer + S ==> String + STTF ==> StreamTranscendentalFunctions(Coef) + + Exports ==> PartialTranscendentalFunctions(ULS) with + + if Coef has Field then + "**": (ULS,RN) -> ULS + ++ s ** r raises a Laurent series s to a rational power r + +--% Exponentials and Logarithms + + exp: ULS -> ULS + ++ exp(z) returns the exponential of Laurent series z. + log: ULS -> ULS + ++ log(z) returns the logarithm of Laurent series z. + +--% TrigonometricFunctionCategory + + sin: ULS -> ULS + ++ sin(z) returns the sine of Laurent series z. + cos: ULS -> ULS + ++ cos(z) returns the cosine of Laurent series z. + tan: ULS -> ULS + ++ tan(z) returns the tangent of Laurent series z. + cot: ULS -> ULS + ++ cot(z) returns the cotangent of Laurent series z. + sec: ULS -> ULS + ++ sec(z) returns the secant of Laurent series z. + csc: ULS -> ULS + ++ csc(z) returns the cosecant of Laurent series z. + +--% ArcTrigonometricFunctionCategory + + asin: ULS -> ULS + ++ asin(z) returns the arc-sine of Laurent series z. + acos: ULS -> ULS + ++ acos(z) returns the arc-cosine of Laurent series z. + atan: ULS -> ULS + ++ atan(z) returns the arc-tangent of Laurent series z. + acot: ULS -> ULS + ++ acot(z) returns the arc-cotangent of Laurent series z. + asec: ULS -> ULS + ++ asec(z) returns the arc-secant of Laurent series z. + acsc: ULS -> ULS + ++ acsc(z) returns the arc-cosecant of Laurent series z. + +--% HyperbolicFunctionCategory + + sinh: ULS -> ULS + ++ sinh(z) returns the hyperbolic sine of Laurent series z. + cosh: ULS -> ULS + ++ cosh(z) returns the hyperbolic cosine of Laurent series z. + tanh: ULS -> ULS + ++ tanh(z) returns the hyperbolic tangent of Laurent series z. + coth: ULS -> ULS + ++ coth(z) returns the hyperbolic cotangent of Laurent series z. + sech: ULS -> ULS + ++ sech(z) returns the hyperbolic secant of Laurent series z. + csch: ULS -> ULS + ++ csch(z) returns the hyperbolic cosecant of Laurent series z. + +--% ArcHyperbolicFunctionCategory + + asinh: ULS -> ULS + ++ asinh(z) returns the inverse hyperbolic sine of Laurent series z. + acosh: ULS -> ULS + ++ acosh(z) returns the inverse hyperbolic cosine of Laurent series z. + atanh: ULS -> ULS + ++ atanh(z) returns the inverse hyperbolic tangent of Laurent series z. + acoth: ULS -> ULS + ++ acoth(z) returns the inverse hyperbolic cotangent of Laurent series z. + asech: ULS -> ULS + ++ asech(z) returns the inverse hyperbolic secant of Laurent series z. + acsch: ULS -> ULS + ++ acsch(z) returns the inverse hyperbolic cosecant of Laurent series z. + + Implementation ==> add + +--% roots + + RATPOWERS : Boolean := Coef has "**":(Coef,RN) -> Coef + TRANSFCN : Boolean := Coef has TranscendentalFunctionCategory + RATS : Boolean := Coef has retractIfCan: Coef -> Union(RN,"failed") + + nthRootUTS:(UTS,I) -> Union(UTS,"failed") + nthRootUTS(uts,n) == + -- assumed: n > 1, uts has non-zero constant term +-- one? coefficient(uts,0) => uts ** inv(n::RN) + coefficient(uts,0) = 1 => uts ** inv(n::RN) + RATPOWERS => uts ** inv(n::RN) + "failed" + + nthRootIfCan(uls,nn) == + (n := nn :: I) < 1 => error "nthRootIfCan: n must be positive" + n = 1 => uls + deg := degree uls + if zero? (coef := coefficient(uls,deg)) then + uls := removeZeroes(1000,uls); deg := degree uls + zero? (coef := coefficient(uls,deg)) => + error "root of series with many leading zero coefficients" + (k := deg exquo n) case "failed" => "failed" + uts := taylor(uls * monomial(1,-deg)) + (root := nthRootUTS(uts,n)) case "failed" => "failed" + monomial(1,k :: I) * (root :: UTS :: ULS) + + if Coef has Field then + (uls:ULS) ** (r:RN) == + num := numer r; den := denom r +-- one? den => uls ** num + den = 1 => uls ** num + deg := degree uls + if zero? (coef := coefficient(uls,deg)) then + uls := removeZeroes(1000,uls); deg := degree uls + zero? (coef := coefficient(uls,deg)) => + error "power of series with many leading zero coefficients" + (k := deg exquo den) case "failed" => + error "**: rational power does not exist" + uts := taylor(uls * monomial(1,-deg)) ** r + monomial(1,(k :: I) * num) * (uts :: ULS) + +--% transcendental functions + + applyIfCan: (UTS -> UTS,ULS) -> Union(ULS,"failed") + applyIfCan(fcn,uls) == + uts := taylorIfCan uls + uts case "failed" => "failed" + fcn(uts :: UTS) :: ULS + + expIfCan uls == applyIfCan(exp,uls) + sinIfCan uls == applyIfCan(sin,uls) + cosIfCan uls == applyIfCan(cos,uls) + asinIfCan uls == applyIfCan(asin,uls) + acosIfCan uls == applyIfCan(acos,uls) + asecIfCan uls == applyIfCan(asec,uls) + acscIfCan uls == applyIfCan(acsc,uls) + sinhIfCan uls == applyIfCan(sinh,uls) + coshIfCan uls == applyIfCan(cosh,uls) + asinhIfCan uls == applyIfCan(asinh,uls) + acoshIfCan uls == applyIfCan(acosh,uls) + atanhIfCan uls == applyIfCan(atanh,uls) + acothIfCan uls == applyIfCan(acoth,uls) + asechIfCan uls == applyIfCan(asech,uls) + acschIfCan uls == applyIfCan(acsch,uls) + + logIfCan uls == + uts := taylorIfCan uls + uts case "failed" => "failed" + zero? coefficient(ts := uts :: UTS,0) => "failed" + log(ts) :: ULS + + tanIfCan uls == + -- don't call 'tan' on a UTS (tan(uls) may have a singularity) + uts := taylorIfCan uls + uts case "failed" => "failed" + sc := sincos(coefficients(uts :: UTS))$STTF + (cosInv := recip(series(sc.cos) :: ULS)) case "failed" => "failed" + (series(sc.sin) :: ULS) * (cosInv :: ULS) + + cotIfCan uls == + -- don't call 'cot' on a UTS (cot(uls) may have a singularity) + uts := taylorIfCan uls + uts case "failed" => "failed" + sc := sincos(coefficients(uts :: UTS))$STTF + (sinInv := recip(series(sc.sin) :: ULS)) case "failed" => "failed" + (series(sc.cos) :: ULS) * (sinInv :: ULS) + + secIfCan uls == + cos := cosIfCan uls + cos case "failed" => "failed" + (cosInv := recip(cos :: ULS)) case "failed" => "failed" + cosInv :: ULS + + cscIfCan uls == + sin := sinIfCan uls + sin case "failed" => "failed" + (sinInv := recip(sin :: ULS)) case "failed" => "failed" + sinInv :: ULS + + atanIfCan uls == + coef := coefficient(uls,0) + (ord := order(uls,0)) = 0 and coef * coef = -1 => "failed" + cc : Coef := + ord < 0 => + TRANSFCN => + RATS => + lc := coefficient(uls,ord) + (rat := retractIfCan(lc)@Union(RN,"failed")) case "failed" => + (1/2) * pi() + (rat :: RN) > 0 => (1/2) * pi() + (-1/2) * pi() + (1/2) * pi() + return "failed" + coef = 0 => 0 + TRANSFCN => atan coef + return "failed" + (z := recip(1 + uls*uls)) case "failed" => "failed" + (cc :: ULS) + integrate(differentiate(uls) * (z :: ULS)) + + acotIfCan uls == + coef := coefficient(uls,0) + (ord := order(uls,0)) = 0 and coef * coef = -1 => "failed" + cc : Coef := + ord < 0 => + RATS => + lc := coefficient(uls,ord) + (rat := retractIfCan(lc)@Union(RN,"failed")) case "failed" => 0 + (rat :: RN) > 0 => 0 + TRANSFCN => pi() + return "failed" + 0 + TRANSFCN => acot coef + return "failed" + (z := recip(1 + uls*uls)) case "failed" => "failed" + (cc :: ULS) - integrate(differentiate(uls) * (z :: ULS)) + + tanhIfCan uls == + -- don't call 'tanh' on a UTS (tanh(uls) may have a singularity) + uts := taylorIfCan uls + uts case "failed" => "failed" + sc := sinhcosh(coefficients(uts :: UTS))$STTF + (coshInv := recip(series(sc.cosh) :: ULS)) case "failed" => + "failed" + (series(sc.sinh) :: ULS) * (coshInv :: ULS) + + cothIfCan uls == + -- don't call 'coth' on a UTS (coth(uls) may have a singularity) + uts := taylorIfCan uls + uts case "failed" => "failed" + sc := sinhcosh(coefficients(uts :: UTS))$STTF + (sinhInv := recip(series(sc.sinh) :: ULS)) case "failed" => + "failed" + (series(sc.cosh) :: ULS) * (sinhInv :: ULS) + + sechIfCan uls == + cosh := coshIfCan uls + cosh case "failed" => "failed" + (coshInv := recip(cosh :: ULS)) case "failed" => "failed" + coshInv :: ULS + + cschIfCan uls == + sinh := sinhIfCan uls + sinh case "failed" => "failed" + (sinhInv := recip(sinh :: ULS)) case "failed" => "failed" + sinhInv :: ULS + + applyOrError:(ULS -> Union(ULS,"failed"),S,ULS) -> ULS + applyOrError(fcn,name,uls) == + ans := fcn uls + ans case "failed" => + error concat(name," of function with singularity") + ans :: ULS + + exp uls == applyOrError(expIfCan,"exp",uls) + log uls == applyOrError(logIfCan,"log",uls) + sin uls == applyOrError(sinIfCan,"sin",uls) + cos uls == applyOrError(cosIfCan,"cos",uls) + tan uls == applyOrError(tanIfCan,"tan",uls) + cot uls == applyOrError(cotIfCan,"cot",uls) + sec uls == applyOrError(secIfCan,"sec",uls) + csc uls == applyOrError(cscIfCan,"csc",uls) + asin uls == applyOrError(asinIfCan,"asin",uls) + acos uls == applyOrError(acosIfCan,"acos",uls) + asec uls == applyOrError(asecIfCan,"asec",uls) + acsc uls == applyOrError(acscIfCan,"acsc",uls) + sinh uls == applyOrError(sinhIfCan,"sinh",uls) + cosh uls == applyOrError(coshIfCan,"cosh",uls) + tanh uls == applyOrError(tanhIfCan,"tanh",uls) + coth uls == applyOrError(cothIfCan,"coth",uls) + sech uls == applyOrError(sechIfCan,"sech",uls) + csch uls == applyOrError(cschIfCan,"csch",uls) + asinh uls == applyOrError(asinhIfCan,"asinh",uls) + acosh uls == applyOrError(acoshIfCan,"acosh",uls) + atanh uls == applyOrError(atanhIfCan,"atanh",uls) + acoth uls == applyOrError(acothIfCan,"acoth",uls) + asech uls == applyOrError(asechIfCan,"asech",uls) + acsch uls == applyOrError(acschIfCan,"acsch",uls) + + atan uls == + -- code is duplicated so that correct error messages will be returned + coef := coefficient(uls,0) + (ord := order(uls,0)) = 0 and coef * coef = -1 => + error "atan: series expansion has logarithmic term" + cc : Coef := + ord < 0 => + TRANSFCN => + RATS => + lc := coefficient(uls,ord) + (rat := retractIfCan(lc)@Union(RN,"failed")) case "failed" => + (1/2) * pi() + (rat :: RN) > 0 => (1/2) * pi() + (-1/2) * pi() + (1/2) * pi() + error "atan: series expansion involves transcendental constants" + coef = 0 => 0 + TRANSFCN => atan coef + error "atan: series expansion involves transcendental constants" + (z := recip(1 + uls*uls)) case "failed" => + error "atan: leading coefficient not invertible" + (cc :: ULS) + integrate(differentiate(uls) * (z :: ULS)) + + acot uls == + -- code is duplicated so that correct error messages will be returned + coef := coefficient(uls,0) + (ord := order(uls,0)) = 0 and coef * coef = -1 => + error "acot: series expansion has logarithmic term" + cc : Coef := + ord < 0 => + RATS => + lc := coefficient(uls,ord) + (rat := retractIfCan(lc)@Union(RN,"failed")) case "failed" => 0 + (rat :: RN) > 0 => 0 + TRANSFCN => pi() + error "acot: series expansion involves transcendental constants" + 0 + TRANSFCN => acot coef + error "acot: series expansion involves transcendental constants" + (z := recip(1 + uls*uls)) case "failed" => + error "acot: leading coefficient not invertible" + (cc :: ULS) - integrate(differentiate(uls) * (z :: ULS)) + +\end{chunk} +\begin{chunk}{EFULS.dotabb} +"EFULS" [color="#FF4488",href="bookvol10.4.pdf#nameddest=EFULS"] +"ULSCCAT" [color="#4488FF",href="bookvol10.2.pdf#nameddest=ULSCCAT"] +"EFULS" -> "ULSCCAT" + +\end{chunk} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{domain EFUPXS ElementaryFunctionsUnivariatePuiseuxSeries} +\begin{chunk}{ElementaryFunctionsUnivariatePuiseuxSeries.input} +)set break resume +)sys rm -f ElementaryFunctionsUnivariatePuiseuxSeries.output +)spool ElementaryFunctionsUnivariatePuiseuxSeries.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show ElementaryFunctionsUnivariatePuiseuxSeries +--E 1 + +)spool +)lisp (bye) +\end{chunk} +\begin{chunk}{ElementaryFunctionsUnivariatePuiseuxSeries.help} +==================================================================== +ElementaryFunctionsUnivariatePuiseuxSeries examples +==================================================================== + +This domain provides elementary functions on any Laurent series +domain over a field which was constructed from a Taylor series +domain. These functions are implemented by calling the +corresponding functions on the Taylor series domain. We also +provide 'partial functions' which compute transcendental +functions of Laurent series when possible and return "failed" +when this is not possible. + +See Also: +o )show ElementaryFunctionsUnivariatePuiseuxSeries + +\end{chunk} +\pagehead{ElementaryFunctionsUnivariatePuiseuxSeries}{EFUPXS} +\pagepic{ps/v103elementaryfunctionsunivariatepuiseuxseries.ps}{EFUPXS}{1.00} + +{\bf Exports:}\\ +\begin{tabular}{lllll} +\cross{EFUPXS}{acos} & +\cross{EFUPXS}{acosIfCan} & +\cross{EFUPXS}{acosh} & +\cross{EFUPXS}{acoshIfCan} & +\cross{EFUPXS}{acot} \\ +\cross{EFUPXS}{acotIfCan} & +\cross{EFUPXS}{acoth} & +\cross{EFUPXS}{acothIfCan} & +\cross{EFUPXS}{acsc} & +\cross{EFUPXS}{acscIfCan} \\ +\cross{EFUPXS}{acsch} & +\cross{EFUPXS}{acschIfCan} & +\cross{EFUPXS}{asec} & +\cross{EFUPXS}{asecIfCan} & +\cross{EFUPXS}{asech} \\ +\cross{EFUPXS}{asechIfCan} & +\cross{EFUPXS}{asin} & +\cross{EFUPXS}{asinIfCan} & +\cross{EFUPXS}{asinh} & +\cross{EFUPXS}{asinhIfCan} \\ +\cross{EFUPXS}{atan} & +\cross{EFUPXS}{atanIfCan} & +\cross{EFUPXS}{atanh} & +\cross{EFUPXS}{atanhIfCan} & +\cross{EFUPXS}{cos} \\ +\cross{EFUPXS}{cosIfCan} & +\cross{EFUPXS}{cosh} & +\cross{EFUPXS}{coshIfCan} & +\cross{EFUPXS}{cot} & +\cross{EFUPXS}{cotIfCan} \\ +\cross{EFUPXS}{coth} & +\cross{EFUPXS}{cothIfCan} & +\cross{EFUPXS}{csc} & +\cross{EFUPXS}{cscIfCan} & +\cross{EFUPXS}{csch} \\ +\cross{EFUPXS}{cschIfCan} & +\cross{EFUPXS}{exp} & +\cross{EFUPXS}{expIfCan} & +\cross{EFUPXS}{log} & +\cross{EFUPXS}{logIfCan} \\ +\cross{EFUPXS}{nthRootIfCan} & +\cross{EFUPXS}{sec} & +\cross{EFUPXS}{secIfCan} & +\cross{EFUPXS}{sech} & +\cross{EFUPXS}{sechIfCan} \\ +\cross{EFUPXS}{sin} & +\cross{EFUPXS}{sinIfCan} & +\cross{EFUPXS}{sinh} & +\cross{EFUPXS}{sinhIfCan} & +\cross{EFUPXS}{tan} \\ +\cross{EFUPXS}{tanIfCan} & +\cross{EFUPXS}{tanh} & +\cross{EFUPXS}{tanhIfCan} & +\cross{EFUPXS}{?**?} & +\end{tabular} + +\begin{chunk}{domain EFUPXS ElementaryFunctionsUnivariatePuiseuxSeries} +)abbrev domain EFUPXS ElementaryFunctionsUnivariatePuiseuxSeries +++ Author: Clifton J. Williamson +++ Date Created: 20 February 1990 +++ Date Last Updated: 20 February 1990 +++ Description: +++ This package provides elementary functions on any Laurent series +++ domain over a field which was constructed from a Taylor series +++ domain. These functions are implemented by calling the +++ corresponding functions on the Taylor series domain. We also +++ provide 'partial functions' which compute transcendental +++ functions of Laurent series when possible and return "failed" +++ when this is not possible. + +ElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS):_ + Exports == Implementation where + Coef : Algebra Fraction Integer + ULS : UnivariateLaurentSeriesCategory Coef + UPXS : UnivariatePuiseuxSeriesConstructorCategory(Coef,ULS) + EFULS : PartialTranscendentalFunctions(ULS) + I ==> Integer + NNI ==> NonNegativeInteger + RN ==> Fraction Integer + + Exports ==> PartialTranscendentalFunctions(UPXS) with + + if Coef has Field then + "**": (UPXS,RN) -> UPXS + ++ z ** r raises a Puiseaux series z to a rational power r + +--% Exponentials and Logarithms + + exp: UPXS -> UPXS + ++ exp(z) returns the exponential of a Puiseux series z. + log: UPXS -> UPXS + ++ log(z) returns the logarithm of a Puiseux series z. + +--% TrigonometricFunctionCategory + + sin: UPXS -> UPXS + ++ sin(z) returns the sine of a Puiseux series z. + cos: UPXS -> UPXS + ++ cos(z) returns the cosine of a Puiseux series z. + tan: UPXS -> UPXS + ++ tan(z) returns the tangent of a Puiseux series z. + cot: UPXS -> UPXS + ++ cot(z) returns the cotangent of a Puiseux series z. + sec: UPXS -> UPXS + ++ sec(z) returns the secant of a Puiseux series z. + csc: UPXS -> UPXS + ++ csc(z) returns the cosecant of a Puiseux series z. + +--% ArcTrigonometricFunctionCategory + + asin: UPXS -> UPXS + ++ asin(z) returns the arc-sine of a Puiseux series z. + acos: UPXS -> UPXS + ++ acos(z) returns the arc-cosine of a Puiseux series z. + atan: UPXS -> UPXS + ++ atan(z) returns the arc-tangent of a Puiseux series z. + acot: UPXS -> UPXS + ++ acot(z) returns the arc-cotangent of a Puiseux series z. + asec: UPXS -> UPXS + ++ asec(z) returns the arc-secant of a Puiseux series z. + acsc: UPXS -> UPXS + ++ acsc(z) returns the arc-cosecant of a Puiseux series z. + +--% HyperbolicFunctionCategory + + sinh: UPXS -> UPXS + ++ sinh(z) returns the hyperbolic sine of a Puiseux series z. + cosh: UPXS -> UPXS + ++ cosh(z) returns the hyperbolic cosine of a Puiseux series z. + tanh: UPXS -> UPXS + ++ tanh(z) returns the hyperbolic tangent of a Puiseux series z. + coth: UPXS -> UPXS + ++ coth(z) returns the hyperbolic cotangent of a Puiseux series z. + sech: UPXS -> UPXS + ++ sech(z) returns the hyperbolic secant of a Puiseux series z. + csch: UPXS -> UPXS + ++ csch(z) returns the hyperbolic cosecant of a Puiseux series z. + +--% ArcHyperbolicFunctionCategory + + asinh: UPXS -> UPXS + ++ asinh(z) returns the inverse hyperbolic sine of a Puiseux series z. + acosh: UPXS -> UPXS + ++ acosh(z) returns the inverse hyperbolic cosine of a Puiseux series z. + atanh: UPXS -> UPXS + ++ atanh(z) returns the inverse hyperbolic tangent of a Puiseux series z. + acoth: UPXS -> UPXS + ++ acoth(z) returns the inverse hyperbolic cotangent + ++ of a Puiseux series z. + asech: UPXS -> UPXS + ++ asech(z) returns the inverse hyperbolic secant of a Puiseux series z. + acsch: UPXS -> UPXS + ++ acsch(z) returns the inverse hyperbolic cosecant + ++ of a Puiseux series z. + + Implementation ==> add + + TRANSFCN : Boolean := Coef has TranscendentalFunctionCategory + +--% roots + + nthRootIfCan(upxs,n) == +-- one? n => upxs + n = 1 => upxs + r := rationalPower upxs; uls := laurentRep upxs + deg := degree uls + if zero?(coef := coefficient(uls,deg)) then + deg := order(uls,deg + 1000) + zero?(coef := coefficient(uls,deg)) => + error "root of series with many leading zero coefficients" + uls := uls * monomial(1,-deg)$ULS + (ulsRoot := nthRootIfCan(uls,n)) case "failed" => "failed" + puiseux(r,ulsRoot :: ULS) * monomial(1,deg * r * inv(n :: RN)) + + if Coef has Field then + (upxs:UPXS) ** (q:RN) == + num := numer q; den := denom q +-- one? den => upxs ** num + den = 1 => upxs ** num + r := rationalPower upxs; uls := laurentRep upxs + deg := degree uls + if zero?(coef := coefficient(uls,deg)) then + deg := order(uls,deg + 1000) + zero?(coef := coefficient(uls,deg)) => + error "power of series with many leading zero coefficients" + ulsPow := (uls * monomial(1,-deg)$ULS) ** q + puiseux(r,ulsPow) * monomial(1,deg*q*r) + +--% transcendental functions + + applyIfCan: (ULS -> Union(ULS,"failed"),UPXS) -> Union(UPXS,"failed") + applyIfCan(fcn,upxs) == + uls := fcn laurentRep upxs + uls case "failed" => "failed" + puiseux(rationalPower upxs,uls :: ULS) + + expIfCan upxs == applyIfCan(expIfCan,upxs) + logIfCan upxs == applyIfCan(logIfCan,upxs) + sinIfCan upxs == applyIfCan(sinIfCan,upxs) + cosIfCan upxs == applyIfCan(cosIfCan,upxs) + tanIfCan upxs == applyIfCan(tanIfCan,upxs) + cotIfCan upxs == applyIfCan(cotIfCan,upxs) + secIfCan upxs == applyIfCan(secIfCan,upxs) + cscIfCan upxs == applyIfCan(cscIfCan,upxs) + atanIfCan upxs == applyIfCan(atanIfCan,upxs) + acotIfCan upxs == applyIfCan(acotIfCan,upxs) + sinhIfCan upxs == applyIfCan(sinhIfCan,upxs) + coshIfCan upxs == applyIfCan(coshIfCan,upxs) + tanhIfCan upxs == applyIfCan(tanhIfCan,upxs) + cothIfCan upxs == applyIfCan(cothIfCan,upxs) + sechIfCan upxs == applyIfCan(sechIfCan,upxs) + cschIfCan upxs == applyIfCan(cschIfCan,upxs) + asinhIfCan upxs == applyIfCan(asinhIfCan,upxs) + acoshIfCan upxs == applyIfCan(acoshIfCan,upxs) + atanhIfCan upxs == applyIfCan(atanhIfCan,upxs) + acothIfCan upxs == applyIfCan(acothIfCan,upxs) + asechIfCan upxs == applyIfCan(asechIfCan,upxs) + acschIfCan upxs == applyIfCan(acschIfCan,upxs) + + asinIfCan upxs == + order(upxs,0) < 0 => "failed" + (coef := coefficient(upxs,0)) = 0 => + integrate((1 - upxs*upxs)**(-1/2) * (differentiate upxs)) + TRANSFCN => + cc := asin(coef) :: UPXS + cc + integrate((1 - upxs*upxs)**(-1/2) * (differentiate upxs)) + "failed" + + acosIfCan upxs == + order(upxs,0) < 0 => "failed" + TRANSFCN => + cc := acos(coefficient(upxs,0)) :: UPXS + cc + integrate(-(1 - upxs*upxs)**(-1/2) * (differentiate upxs)) + "failed" + + asecIfCan upxs == + order(upxs,0) < 0 => "failed" + TRANSFCN => + cc := asec(coefficient(upxs,0)) :: UPXS + f := (upxs*upxs - 1)**(-1/2) * (differentiate upxs) + (rec := recip upxs) case "failed" => "failed" + cc + integrate(f * (rec :: UPXS)) + "failed" + + acscIfCan upxs == + order(upxs,0) < 0 => "failed" + TRANSFCN => + cc := acsc(coefficient(upxs,0)) :: UPXS + f := -(upxs*upxs - 1)**(-1/2) * (differentiate upxs) + (rec := recip upxs) case "failed" => "failed" + cc + integrate(f * (rec :: UPXS)) + "failed" + + asinhIfCan upxs == + order(upxs,0) < 0 => "failed" + TRANSFCN or (coefficient(upxs,0) = 0) => + log(upxs + (1 + upxs*upxs)**(1/2)) + "failed" + + acoshIfCan upxs == + TRANSFCN => + order(upxs,0) < 0 => "failed" + log(upxs + (upxs*upxs - 1)**(1/2)) + "failed" + + asechIfCan upxs == + TRANSFCN => + order(upxs,0) < 0 => "failed" + (rec := recip upxs) case "failed" => "failed" + log((1 + (1 - upxs*upxs)*(1/2)) * (rec :: UPXS)) + "failed" + + acschIfCan upxs == + TRANSFCN => + order(upxs,0) < 0 => "failed" + (rec := recip upxs) case "failed" => "failed" + log((1 + (1 + upxs*upxs)*(1/2)) * (rec :: UPXS)) + "failed" + + applyOrError:(UPXS -> Union(UPXS,"failed"),String,UPXS) -> UPXS + applyOrError(fcn,name,upxs) == + ans := fcn upxs + ans case "failed" => + error concat(name," of function with singularity") + ans :: UPXS + + exp upxs == applyOrError(expIfCan,"exp",upxs) + log upxs == applyOrError(logIfCan,"log",upxs) + sin upxs == applyOrError(sinIfCan,"sin",upxs) + cos upxs == applyOrError(cosIfCan,"cos",upxs) + tan upxs == applyOrError(tanIfCan,"tan",upxs) + cot upxs == applyOrError(cotIfCan,"cot",upxs) + sec upxs == applyOrError(secIfCan,"sec",upxs) + csc upxs == applyOrError(cscIfCan,"csc",upxs) + asin upxs == applyOrError(asinIfCan,"asin",upxs) + acos upxs == applyOrError(acosIfCan,"acos",upxs) + atan upxs == applyOrError(atanIfCan,"atan",upxs) + acot upxs == applyOrError(acotIfCan,"acot",upxs) + asec upxs == applyOrError(asecIfCan,"asec",upxs) + acsc upxs == applyOrError(acscIfCan,"acsc",upxs) + sinh upxs == applyOrError(sinhIfCan,"sinh",upxs) + cosh upxs == applyOrError(coshIfCan,"cosh",upxs) + tanh upxs == applyOrError(tanhIfCan,"tanh",upxs) + coth upxs == applyOrError(cothIfCan,"coth",upxs) + sech upxs == applyOrError(sechIfCan,"sech",upxs) + csch upxs == applyOrError(cschIfCan,"csch",upxs) + asinh upxs == applyOrError(asinhIfCan,"asinh",upxs) + acosh upxs == applyOrError(acoshIfCan,"acosh",upxs) + atanh upxs == applyOrError(atanhIfCan,"atanh",upxs) + acoth upxs == applyOrError(acothIfCan,"acoth",upxs) + asech upxs == applyOrError(asechIfCan,"asech",upxs) + acsch upxs == applyOrError(acschIfCan,"acsch",upxs) + +\end{chunk} +\begin{chunk}{EFUPXS.dotabb} +"EFUPXS" [color="#FF4488",href="bookvol10.4.pdf#nameddest=EFUPXS"] +"UPXSCCA" [color="#4488FF",href="bookvol10.2.pdf#nameddest=UPXSCCA"] +"EFUPXS" -> "UPXSCCA" + +\end{chunk} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{domain EQ Equation} \begin{chunk}{Equation.input} @@ -154777,6 +155584,8 @@ Note that this code is not included in the generated catdef.spad file. \getchunk{domain D03EEFA d03eefAnnaType} \getchunk{domain D03FAFA d03fafAnnaType} +\getchunk{domain EFULS ElementaryFunctionsUnivariateLaurentSeries} +\getchunk{domain EFUPXS ElementaryFunctionsUnivariatePuiseuxSeries} \getchunk{domain EQTBL EqTable} \getchunk{domain EQ Equation} \getchunk{domain EXPEXPAN ExponentialExpansion} diff --git a/books/bookvol10.4.pamphlet b/books/bookvol10.4.pamphlet index 2b910c8..566a2d4 100644 --- a/books/bookvol10.4.pamphlet +++ b/books/bookvol10.4.pamphlet @@ -22650,809 +22650,6 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where \end{chunk} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{package EFULS ElementaryFunctionsUnivariateLaurentSeries} -\begin{chunk}{ElementaryFunctionsUnivariateLaurentSeries.input} -)set break resume -)sys rm -f ElementaryFunctionsUnivariateLaurentSeries.output -)spool ElementaryFunctionsUnivariateLaurentSeries.output -)set message test on -)set message auto off -)clear all - ---S 1 of 1 -)show ElementaryFunctionsUnivariateLaurentSeries ---E 1 - -)spool -)lisp (bye) -\end{chunk} -\begin{chunk}{ElementaryFunctionsUnivariateLaurentSeries.help} -==================================================================== -ElementaryFunctionsUnivariateLaurentSeries examples -==================================================================== - -This package provides elementary functions on any Laurent series -domain over a field which was constructed from a Taylor series -domain. These functions are implemented by calling the -corresponding functions on the Taylor series domain. We also -provide 'partial functions' which compute transcendental -functions of Laurent series when possible and return "failed" -when this is not possible. - -See Also: -o )show ElementaryFunctionsUnivariateLaurentSeries - -\end{chunk} -\pagehead{ElementaryFunctionsUnivariateLaurentSeries}{EFULS} -\pagepic{ps/v104elementaryfunctionsunivariatelaurentseries.ps}{EFULS}{1.00} - -{\bf Exports:}\\ -\begin{tabular}{lllll} -\cross{EFULS}{acos} & -\cross{EFULS}{acosIfCan} & -\cross{EFULS}{acosh} & -\cross{EFULS}{acoshIfCan} & -\cross{EFULS}{acot} \\ -\cross{EFULS}{acotIfCan} & -\cross{EFULS}{acoth} & -\cross{EFULS}{acothIfCan} & -\cross{EFULS}{acsc} & -\cross{EFULS}{acscIfCan} \\ -\cross{EFULS}{acsch} & -\cross{EFULS}{acschIfCan} & -\cross{EFULS}{asec} & -\cross{EFULS}{asecIfCan} & -\cross{EFULS}{asech} \\ -\cross{EFULS}{asechIfCan} & -\cross{EFULS}{asin} & -\cross{EFULS}{asinIfCan} & -\cross{EFULS}{asinh} & -\cross{EFULS}{asinhIfCan} \\ -\cross{EFULS}{atan} & -\cross{EFULS}{atanIfCan} & -\cross{EFULS}{atanh} & -\cross{EFULS}{atanhIfCan} & -\cross{EFULS}{cos} \\ -\cross{EFULS}{cosIfCan} & -\cross{EFULS}{cosh} & -\cross{EFULS}{coshIfCan} & -\cross{EFULS}{cot} & -\cross{EFULS}{cotIfCan} \\ -\cross{EFULS}{coth} & -\cross{EFULS}{cothIfCan} & -\cross{EFULS}{csc} & -\cross{EFULS}{cscIfCan} & -\cross{EFULS}{csch} \\ -\cross{EFULS}{cschIfCan} & -\cross{EFULS}{exp} & -\cross{EFULS}{expIfCan} & -\cross{EFULS}{log} & -\cross{EFULS}{logIfCan} \\ -\cross{EFULS}{nthRootIfCan} & -\cross{EFULS}{sec} & -\cross{EFULS}{secIfCan} & -\cross{EFULS}{sech} & -\cross{EFULS}{sechIfCan} \\ -\cross{EFULS}{sin} & -\cross{EFULS}{sinIfCan} & -\cross{EFULS}{sinh} & -\cross{EFULS}{sinhIfCan} & -\cross{EFULS}{tan} \\ -\cross{EFULS}{tanIfCan} & -\cross{EFULS}{tanh} & -\cross{EFULS}{tanhIfCan} & -\cross{EFULS}{?**?} & -\end{tabular} - -\begin{chunk}{package EFULS ElementaryFunctionsUnivariateLaurentSeries} -)abbrev package EFULS ElementaryFunctionsUnivariateLaurentSeries -++ Author: Clifton J. Williamson -++ Date Created: 6 February 1990 -++ Date Last Updated: 25 February 1990 -++ Description: -++ This package provides elementary functions on any Laurent series -++ domain over a field which was constructed from a Taylor series -++ domain. These functions are implemented by calling the -++ corresponding functions on the Taylor series domain. We also -++ provide 'partial functions' which compute transcendental -++ functions of Laurent series when possible and return "failed" -++ when this is not possible. - -ElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS):_ - Exports == Implementation where - Coef : Algebra Fraction Integer - UTS : UnivariateTaylorSeriesCategory Coef - ULS : UnivariateLaurentSeriesConstructorCategory(Coef,UTS) - I ==> Integer - NNI ==> NonNegativeInteger - RN ==> Fraction Integer - S ==> String - STTF ==> StreamTranscendentalFunctions(Coef) - - Exports ==> PartialTranscendentalFunctions(ULS) with - - if Coef has Field then - "**": (ULS,RN) -> ULS - ++ s ** r raises a Laurent series s to a rational power r - ---% Exponentials and Logarithms - - exp: ULS -> ULS - ++ exp(z) returns the exponential of Laurent series z. - log: ULS -> ULS - ++ log(z) returns the logarithm of Laurent series z. - ---% TrigonometricFunctionCategory - - sin: ULS -> ULS - ++ sin(z) returns the sine of Laurent series z. - cos: ULS -> ULS - ++ cos(z) returns the cosine of Laurent series z. - tan: ULS -> ULS - ++ tan(z) returns the tangent of Laurent series z. - cot: ULS -> ULS - ++ cot(z) returns the cotangent of Laurent series z. - sec: ULS -> ULS - ++ sec(z) returns the secant of Laurent series z. - csc: ULS -> ULS - ++ csc(z) returns the cosecant of Laurent series z. - ---% ArcTrigonometricFunctionCategory - - asin: ULS -> ULS - ++ asin(z) returns the arc-sine of Laurent series z. - acos: ULS -> ULS - ++ acos(z) returns the arc-cosine of Laurent series z. - atan: ULS -> ULS - ++ atan(z) returns the arc-tangent of Laurent series z. - acot: ULS -> ULS - ++ acot(z) returns the arc-cotangent of Laurent series z. - asec: ULS -> ULS - ++ asec(z) returns the arc-secant of Laurent series z. - acsc: ULS -> ULS - ++ acsc(z) returns the arc-cosecant of Laurent series z. - ---% HyperbolicFunctionCategory - - sinh: ULS -> ULS - ++ sinh(z) returns the hyperbolic sine of Laurent series z. - cosh: ULS -> ULS - ++ cosh(z) returns the hyperbolic cosine of Laurent series z. - tanh: ULS -> ULS - ++ tanh(z) returns the hyperbolic tangent of Laurent series z. - coth: ULS -> ULS - ++ coth(z) returns the hyperbolic cotangent of Laurent series z. - sech: ULS -> ULS - ++ sech(z) returns the hyperbolic secant of Laurent series z. - csch: ULS -> ULS - ++ csch(z) returns the hyperbolic cosecant of Laurent series z. - ---% ArcHyperbolicFunctionCategory - - asinh: ULS -> ULS - ++ asinh(z) returns the inverse hyperbolic sine of Laurent series z. - acosh: ULS -> ULS - ++ acosh(z) returns the inverse hyperbolic cosine of Laurent series z. - atanh: ULS -> ULS - ++ atanh(z) returns the inverse hyperbolic tangent of Laurent series z. - acoth: ULS -> ULS - ++ acoth(z) returns the inverse hyperbolic cotangent of Laurent series z. - asech: ULS -> ULS - ++ asech(z) returns the inverse hyperbolic secant of Laurent series z. - acsch: ULS -> ULS - ++ acsch(z) returns the inverse hyperbolic cosecant of Laurent series z. - - Implementation ==> add - ---% roots - - RATPOWERS : Boolean := Coef has "**":(Coef,RN) -> Coef - TRANSFCN : Boolean := Coef has TranscendentalFunctionCategory - RATS : Boolean := Coef has retractIfCan: Coef -> Union(RN,"failed") - - nthRootUTS:(UTS,I) -> Union(UTS,"failed") - nthRootUTS(uts,n) == - -- assumed: n > 1, uts has non-zero constant term --- one? coefficient(uts,0) => uts ** inv(n::RN) - coefficient(uts,0) = 1 => uts ** inv(n::RN) - RATPOWERS => uts ** inv(n::RN) - "failed" - - nthRootIfCan(uls,nn) == - (n := nn :: I) < 1 => error "nthRootIfCan: n must be positive" - n = 1 => uls - deg := degree uls - if zero? (coef := coefficient(uls,deg)) then - uls := removeZeroes(1000,uls); deg := degree uls - zero? (coef := coefficient(uls,deg)) => - error "root of series with many leading zero coefficients" - (k := deg exquo n) case "failed" => "failed" - uts := taylor(uls * monomial(1,-deg)) - (root := nthRootUTS(uts,n)) case "failed" => "failed" - monomial(1,k :: I) * (root :: UTS :: ULS) - - if Coef has Field then - (uls:ULS) ** (r:RN) == - num := numer r; den := denom r --- one? den => uls ** num - den = 1 => uls ** num - deg := degree uls - if zero? (coef := coefficient(uls,deg)) then - uls := removeZeroes(1000,uls); deg := degree uls - zero? (coef := coefficient(uls,deg)) => - error "power of series with many leading zero coefficients" - (k := deg exquo den) case "failed" => - error "**: rational power does not exist" - uts := taylor(uls * monomial(1,-deg)) ** r - monomial(1,(k :: I) * num) * (uts :: ULS) - ---% transcendental functions - - applyIfCan: (UTS -> UTS,ULS) -> Union(ULS,"failed") - applyIfCan(fcn,uls) == - uts := taylorIfCan uls - uts case "failed" => "failed" - fcn(uts :: UTS) :: ULS - - expIfCan uls == applyIfCan(exp,uls) - sinIfCan uls == applyIfCan(sin,uls) - cosIfCan uls == applyIfCan(cos,uls) - asinIfCan uls == applyIfCan(asin,uls) - acosIfCan uls == applyIfCan(acos,uls) - asecIfCan uls == applyIfCan(asec,uls) - acscIfCan uls == applyIfCan(acsc,uls) - sinhIfCan uls == applyIfCan(sinh,uls) - coshIfCan uls == applyIfCan(cosh,uls) - asinhIfCan uls == applyIfCan(asinh,uls) - acoshIfCan uls == applyIfCan(acosh,uls) - atanhIfCan uls == applyIfCan(atanh,uls) - acothIfCan uls == applyIfCan(acoth,uls) - asechIfCan uls == applyIfCan(asech,uls) - acschIfCan uls == applyIfCan(acsch,uls) - - logIfCan uls == - uts := taylorIfCan uls - uts case "failed" => "failed" - zero? coefficient(ts := uts :: UTS,0) => "failed" - log(ts) :: ULS - - tanIfCan uls == - -- don't call 'tan' on a UTS (tan(uls) may have a singularity) - uts := taylorIfCan uls - uts case "failed" => "failed" - sc := sincos(coefficients(uts :: UTS))$STTF - (cosInv := recip(series(sc.cos) :: ULS)) case "failed" => "failed" - (series(sc.sin) :: ULS) * (cosInv :: ULS) - - cotIfCan uls == - -- don't call 'cot' on a UTS (cot(uls) may have a singularity) - uts := taylorIfCan uls - uts case "failed" => "failed" - sc := sincos(coefficients(uts :: UTS))$STTF - (sinInv := recip(series(sc.sin) :: ULS)) case "failed" => "failed" - (series(sc.cos) :: ULS) * (sinInv :: ULS) - - secIfCan uls == - cos := cosIfCan uls - cos case "failed" => "failed" - (cosInv := recip(cos :: ULS)) case "failed" => "failed" - cosInv :: ULS - - cscIfCan uls == - sin := sinIfCan uls - sin case "failed" => "failed" - (sinInv := recip(sin :: ULS)) case "failed" => "failed" - sinInv :: ULS - - atanIfCan uls == - coef := coefficient(uls,0) - (ord := order(uls,0)) = 0 and coef * coef = -1 => "failed" - cc : Coef := - ord < 0 => - TRANSFCN => - RATS => - lc := coefficient(uls,ord) - (rat := retractIfCan(lc)@Union(RN,"failed")) case "failed" => - (1/2) * pi() - (rat :: RN) > 0 => (1/2) * pi() - (-1/2) * pi() - (1/2) * pi() - return "failed" - coef = 0 => 0 - TRANSFCN => atan coef - return "failed" - (z := recip(1 + uls*uls)) case "failed" => "failed" - (cc :: ULS) + integrate(differentiate(uls) * (z :: ULS)) - - acotIfCan uls == - coef := coefficient(uls,0) - (ord := order(uls,0)) = 0 and coef * coef = -1 => "failed" - cc : Coef := - ord < 0 => - RATS => - lc := coefficient(uls,ord) - (rat := retractIfCan(lc)@Union(RN,"failed")) case "failed" => 0 - (rat :: RN) > 0 => 0 - TRANSFCN => pi() - return "failed" - 0 - TRANSFCN => acot coef - return "failed" - (z := recip(1 + uls*uls)) case "failed" => "failed" - (cc :: ULS) - integrate(differentiate(uls) * (z :: ULS)) - - tanhIfCan uls == - -- don't call 'tanh' on a UTS (tanh(uls) may have a singularity) - uts := taylorIfCan uls - uts case "failed" => "failed" - sc := sinhcosh(coefficients(uts :: UTS))$STTF - (coshInv := recip(series(sc.cosh) :: ULS)) case "failed" => - "failed" - (series(sc.sinh) :: ULS) * (coshInv :: ULS) - - cothIfCan uls == - -- don't call 'coth' on a UTS (coth(uls) may have a singularity) - uts := taylorIfCan uls - uts case "failed" => "failed" - sc := sinhcosh(coefficients(uts :: UTS))$STTF - (sinhInv := recip(series(sc.sinh) :: ULS)) case "failed" => - "failed" - (series(sc.cosh) :: ULS) * (sinhInv :: ULS) - - sechIfCan uls == - cosh := coshIfCan uls - cosh case "failed" => "failed" - (coshInv := recip(cosh :: ULS)) case "failed" => "failed" - coshInv :: ULS - - cschIfCan uls == - sinh := sinhIfCan uls - sinh case "failed" => "failed" - (sinhInv := recip(sinh :: ULS)) case "failed" => "failed" - sinhInv :: ULS - - applyOrError:(ULS -> Union(ULS,"failed"),S,ULS) -> ULS - applyOrError(fcn,name,uls) == - ans := fcn uls - ans case "failed" => - error concat(name," of function with singularity") - ans :: ULS - - exp uls == applyOrError(expIfCan,"exp",uls) - log uls == applyOrError(logIfCan,"log",uls) - sin uls == applyOrError(sinIfCan,"sin",uls) - cos uls == applyOrError(cosIfCan,"cos",uls) - tan uls == applyOrError(tanIfCan,"tan",uls) - cot uls == applyOrError(cotIfCan,"cot",uls) - sec uls == applyOrError(secIfCan,"sec",uls) - csc uls == applyOrError(cscIfCan,"csc",uls) - asin uls == applyOrError(asinIfCan,"asin",uls) - acos uls == applyOrError(acosIfCan,"acos",uls) - asec uls == applyOrError(asecIfCan,"asec",uls) - acsc uls == applyOrError(acscIfCan,"acsc",uls) - sinh uls == applyOrError(sinhIfCan,"sinh",uls) - cosh uls == applyOrError(coshIfCan,"cosh",uls) - tanh uls == applyOrError(tanhIfCan,"tanh",uls) - coth uls == applyOrError(cothIfCan,"coth",uls) - sech uls == applyOrError(sechIfCan,"sech",uls) - csch uls == applyOrError(cschIfCan,"csch",uls) - asinh uls == applyOrError(asinhIfCan,"asinh",uls) - acosh uls == applyOrError(acoshIfCan,"acosh",uls) - atanh uls == applyOrError(atanhIfCan,"atanh",uls) - acoth uls == applyOrError(acothIfCan,"acoth",uls) - asech uls == applyOrError(asechIfCan,"asech",uls) - acsch uls == applyOrError(acschIfCan,"acsch",uls) - - atan uls == - -- code is duplicated so that correct error messages will be returned - coef := coefficient(uls,0) - (ord := order(uls,0)) = 0 and coef * coef = -1 => - error "atan: series expansion has logarithmic term" - cc : Coef := - ord < 0 => - TRANSFCN => - RATS => - lc := coefficient(uls,ord) - (rat := retractIfCan(lc)@Union(RN,"failed")) case "failed" => - (1/2) * pi() - (rat :: RN) > 0 => (1/2) * pi() - (-1/2) * pi() - (1/2) * pi() - error "atan: series expansion involves transcendental constants" - coef = 0 => 0 - TRANSFCN => atan coef - error "atan: series expansion involves transcendental constants" - (z := recip(1 + uls*uls)) case "failed" => - error "atan: leading coefficient not invertible" - (cc :: ULS) + integrate(differentiate(uls) * (z :: ULS)) - - acot uls == - -- code is duplicated so that correct error messages will be returned - coef := coefficient(uls,0) - (ord := order(uls,0)) = 0 and coef * coef = -1 => - error "acot: series expansion has logarithmic term" - cc : Coef := - ord < 0 => - RATS => - lc := coefficient(uls,ord) - (rat := retractIfCan(lc)@Union(RN,"failed")) case "failed" => 0 - (rat :: RN) > 0 => 0 - TRANSFCN => pi() - error "acot: series expansion involves transcendental constants" - 0 - TRANSFCN => acot coef - error "acot: series expansion involves transcendental constants" - (z := recip(1 + uls*uls)) case "failed" => - error "acot: leading coefficient not invertible" - (cc :: ULS) - integrate(differentiate(uls) * (z :: ULS)) - -\end{chunk} -\begin{chunk}{EFULS.dotabb} -"EFULS" [color="#FF4488",href="bookvol10.4.pdf#nameddest=EFULS"] -"ULSCCAT" [color="#4488FF",href="bookvol10.2.pdf#nameddest=ULSCCAT"] -"EFULS" -> "ULSCCAT" - -\end{chunk} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\section{package EFUPXS ElementaryFunctionsUnivariatePuiseuxSeries} -\begin{chunk}{ElementaryFunctionsUnivariatePuiseuxSeries.input} -)set break resume -)sys rm -f ElementaryFunctionsUnivariatePuiseuxSeries.output -)spool ElementaryFunctionsUnivariatePuiseuxSeries.output -)set message test on -)set message auto off -)clear all - ---S 1 of 1 -)show ElementaryFunctionsUnivariatePuiseuxSeries ---E 1 - -)spool -)lisp (bye) -\end{chunk} -\begin{chunk}{ElementaryFunctionsUnivariatePuiseuxSeries.help} -==================================================================== -ElementaryFunctionsUnivariatePuiseuxSeries examples -==================================================================== - -This package provides elementary functions on any Laurent series -domain over a field which was constructed from a Taylor series -domain. These functions are implemented by calling the -corresponding functions on the Taylor series domain. We also -provide 'partial functions' which compute transcendental -functions of Laurent series when possible and return "failed" -when this is not possible. - -See Also: -o )show ElementaryFunctionsUnivariatePuiseuxSeries - -\end{chunk} -\pagehead{ElementaryFunctionsUnivariatePuiseuxSeries}{EFUPXS} -\pagepic{ps/v104elementaryfunctionsunivariatepuiseuxseries.ps}{EFUPXS}{1.00} - -{\bf Exports:}\\ -\begin{tabular}{lllll} -\cross{EFUPXS}{acos} & -\cross{EFUPXS}{acosIfCan} & -\cross{EFUPXS}{acosh} & -\cross{EFUPXS}{acoshIfCan} & -\cross{EFUPXS}{acot} \\ -\cross{EFUPXS}{acotIfCan} & -\cross{EFUPXS}{acoth} & -\cross{EFUPXS}{acothIfCan} & -\cross{EFUPXS}{acsc} & -\cross{EFUPXS}{acscIfCan} \\ -\cross{EFUPXS}{acsch} & -\cross{EFUPXS}{acschIfCan} & -\cross{EFUPXS}{asec} & -\cross{EFUPXS}{asecIfCan} & -\cross{EFUPXS}{asech} \\ -\cross{EFUPXS}{asechIfCan} & -\cross{EFUPXS}{asin} & -\cross{EFUPXS}{asinIfCan} & -\cross{EFUPXS}{asinh} & -\cross{EFUPXS}{asinhIfCan} \\ -\cross{EFUPXS}{atan} & -\cross{EFUPXS}{atanIfCan} & -\cross{EFUPXS}{atanh} & -\cross{EFUPXS}{atanhIfCan} & -\cross{EFUPXS}{cos} \\ -\cross{EFUPXS}{cosIfCan} & -\cross{EFUPXS}{cosh} & -\cross{EFUPXS}{coshIfCan} & -\cross{EFUPXS}{cot} & -\cross{EFUPXS}{cotIfCan} \\ -\cross{EFUPXS}{coth} & -\cross{EFUPXS}{cothIfCan} & -\cross{EFUPXS}{csc} & -\cross{EFUPXS}{cscIfCan} & -\cross{EFUPXS}{csch} \\ -\cross{EFUPXS}{cschIfCan} & -\cross{EFUPXS}{exp} & -\cross{EFUPXS}{expIfCan} & -\cross{EFUPXS}{log} & -\cross{EFUPXS}{logIfCan} \\ -\cross{EFUPXS}{nthRootIfCan} & -\cross{EFUPXS}{sec} & -\cross{EFUPXS}{secIfCan} & -\cross{EFUPXS}{sech} & -\cross{EFUPXS}{sechIfCan} \\ -\cross{EFUPXS}{sin} & -\cross{EFUPXS}{sinIfCan} & -\cross{EFUPXS}{sinh} & -\cross{EFUPXS}{sinhIfCan} & -\cross{EFUPXS}{tan} \\ -\cross{EFUPXS}{tanIfCan} & -\cross{EFUPXS}{tanh} & -\cross{EFUPXS}{tanhIfCan} & -\cross{EFUPXS}{?**?} & -\end{tabular} - -\begin{chunk}{package EFUPXS ElementaryFunctionsUnivariatePuiseuxSeries} -)abbrev package EFUPXS ElementaryFunctionsUnivariatePuiseuxSeries -++ Author: Clifton J. Williamson -++ Date Created: 20 February 1990 -++ Date Last Updated: 20 February 1990 -++ Description: -++ This package provides elementary functions on any Laurent series -++ domain over a field which was constructed from a Taylor series -++ domain. These functions are implemented by calling the -++ corresponding functions on the Taylor series domain. We also -++ provide 'partial functions' which compute transcendental -++ functions of Laurent series when possible and return "failed" -++ when this is not possible. - -ElementaryFunctionsUnivariatePuiseuxSeries(Coef,ULS,UPXS,EFULS):_ - Exports == Implementation where - Coef : Algebra Fraction Integer - ULS : UnivariateLaurentSeriesCategory Coef - UPXS : UnivariatePuiseuxSeriesConstructorCategory(Coef,ULS) - EFULS : PartialTranscendentalFunctions(ULS) - I ==> Integer - NNI ==> NonNegativeInteger - RN ==> Fraction Integer - - Exports ==> PartialTranscendentalFunctions(UPXS) with - - if Coef has Field then - "**": (UPXS,RN) -> UPXS - ++ z ** r raises a Puiseaux series z to a rational power r - ---% Exponentials and Logarithms - - exp: UPXS -> UPXS - ++ exp(z) returns the exponential of a Puiseux series z. - log: UPXS -> UPXS - ++ log(z) returns the logarithm of a Puiseux series z. - ---% TrigonometricFunctionCategory - - sin: UPXS -> UPXS - ++ sin(z) returns the sine of a Puiseux series z. - cos: UPXS -> UPXS - ++ cos(z) returns the cosine of a Puiseux series z. - tan: UPXS -> UPXS - ++ tan(z) returns the tangent of a Puiseux series z. - cot: UPXS -> UPXS - ++ cot(z) returns the cotangent of a Puiseux series z. - sec: UPXS -> UPXS - ++ sec(z) returns the secant of a Puiseux series z. - csc: UPXS -> UPXS - ++ csc(z) returns the cosecant of a Puiseux series z. - ---% ArcTrigonometricFunctionCategory - - asin: UPXS -> UPXS - ++ asin(z) returns the arc-sine of a Puiseux series z. - acos: UPXS -> UPXS - ++ acos(z) returns the arc-cosine of a Puiseux series z. - atan: UPXS -> UPXS - ++ atan(z) returns the arc-tangent of a Puiseux series z. - acot: UPXS -> UPXS - ++ acot(z) returns the arc-cotangent of a Puiseux series z. - asec: UPXS -> UPXS - ++ asec(z) returns the arc-secant of a Puiseux series z. - acsc: UPXS -> UPXS - ++ acsc(z) returns the arc-cosecant of a Puiseux series z. - ---% HyperbolicFunctionCategory - - sinh: UPXS -> UPXS - ++ sinh(z) returns the hyperbolic sine of a Puiseux series z. - cosh: UPXS -> UPXS - ++ cosh(z) returns the hyperbolic cosine of a Puiseux series z. - tanh: UPXS -> UPXS - ++ tanh(z) returns the hyperbolic tangent of a Puiseux series z. - coth: UPXS -> UPXS - ++ coth(z) returns the hyperbolic cotangent of a Puiseux series z. - sech: UPXS -> UPXS - ++ sech(z) returns the hyperbolic secant of a Puiseux series z. - csch: UPXS -> UPXS - ++ csch(z) returns the hyperbolic cosecant of a Puiseux series z. - ---% ArcHyperbolicFunctionCategory - - asinh: UPXS -> UPXS - ++ asinh(z) returns the inverse hyperbolic sine of a Puiseux series z. - acosh: UPXS -> UPXS - ++ acosh(z) returns the inverse hyperbolic cosine of a Puiseux series z. - atanh: UPXS -> UPXS - ++ atanh(z) returns the inverse hyperbolic tangent of a Puiseux series z. - acoth: UPXS -> UPXS - ++ acoth(z) returns the inverse hyperbolic cotangent - ++ of a Puiseux series z. - asech: UPXS -> UPXS - ++ asech(z) returns the inverse hyperbolic secant of a Puiseux series z. - acsch: UPXS -> UPXS - ++ acsch(z) returns the inverse hyperbolic cosecant - ++ of a Puiseux series z. - - Implementation ==> add - - TRANSFCN : Boolean := Coef has TranscendentalFunctionCategory - ---% roots - - nthRootIfCan(upxs,n) == --- one? n => upxs - n = 1 => upxs - r := rationalPower upxs; uls := laurentRep upxs - deg := degree uls - if zero?(coef := coefficient(uls,deg)) then - deg := order(uls,deg + 1000) - zero?(coef := coefficient(uls,deg)) => - error "root of series with many leading zero coefficients" - uls := uls * monomial(1,-deg)$ULS - (ulsRoot := nthRootIfCan(uls,n)) case "failed" => "failed" - puiseux(r,ulsRoot :: ULS) * monomial(1,deg * r * inv(n :: RN)) - - if Coef has Field then - (upxs:UPXS) ** (q:RN) == - num := numer q; den := denom q --- one? den => upxs ** num - den = 1 => upxs ** num - r := rationalPower upxs; uls := laurentRep upxs - deg := degree uls - if zero?(coef := coefficient(uls,deg)) then - deg := order(uls,deg + 1000) - zero?(coef := coefficient(uls,deg)) => - error "power of series with many leading zero coefficients" - ulsPow := (uls * monomial(1,-deg)$ULS) ** q - puiseux(r,ulsPow) * monomial(1,deg*q*r) - ---% transcendental functions - - applyIfCan: (ULS -> Union(ULS,"failed"),UPXS) -> Union(UPXS,"failed") - applyIfCan(fcn,upxs) == - uls := fcn laurentRep upxs - uls case "failed" => "failed" - puiseux(rationalPower upxs,uls :: ULS) - - expIfCan upxs == applyIfCan(expIfCan,upxs) - logIfCan upxs == applyIfCan(logIfCan,upxs) - sinIfCan upxs == applyIfCan(sinIfCan,upxs) - cosIfCan upxs == applyIfCan(cosIfCan,upxs) - tanIfCan upxs == applyIfCan(tanIfCan,upxs) - cotIfCan upxs == applyIfCan(cotIfCan,upxs) - secIfCan upxs == applyIfCan(secIfCan,upxs) - cscIfCan upxs == applyIfCan(cscIfCan,upxs) - atanIfCan upxs == applyIfCan(atanIfCan,upxs) - acotIfCan upxs == applyIfCan(acotIfCan,upxs) - sinhIfCan upxs == applyIfCan(sinhIfCan,upxs) - coshIfCan upxs == applyIfCan(coshIfCan,upxs) - tanhIfCan upxs == applyIfCan(tanhIfCan,upxs) - cothIfCan upxs == applyIfCan(cothIfCan,upxs) - sechIfCan upxs == applyIfCan(sechIfCan,upxs) - cschIfCan upxs == applyIfCan(cschIfCan,upxs) - asinhIfCan upxs == applyIfCan(asinhIfCan,upxs) - acoshIfCan upxs == applyIfCan(acoshIfCan,upxs) - atanhIfCan upxs == applyIfCan(atanhIfCan,upxs) - acothIfCan upxs == applyIfCan(acothIfCan,upxs) - asechIfCan upxs == applyIfCan(asechIfCan,upxs) - acschIfCan upxs == applyIfCan(acschIfCan,upxs) - - asinIfCan upxs == - order(upxs,0) < 0 => "failed" - (coef := coefficient(upxs,0)) = 0 => - integrate((1 - upxs*upxs)**(-1/2) * (differentiate upxs)) - TRANSFCN => - cc := asin(coef) :: UPXS - cc + integrate((1 - upxs*upxs)**(-1/2) * (differentiate upxs)) - "failed" - - acosIfCan upxs == - order(upxs,0) < 0 => "failed" - TRANSFCN => - cc := acos(coefficient(upxs,0)) :: UPXS - cc + integrate(-(1 - upxs*upxs)**(-1/2) * (differentiate upxs)) - "failed" - - asecIfCan upxs == - order(upxs,0) < 0 => "failed" - TRANSFCN => - cc := asec(coefficient(upxs,0)) :: UPXS - f := (upxs*upxs - 1)**(-1/2) * (differentiate upxs) - (rec := recip upxs) case "failed" => "failed" - cc + integrate(f * (rec :: UPXS)) - "failed" - - acscIfCan upxs == - order(upxs,0) < 0 => "failed" - TRANSFCN => - cc := acsc(coefficient(upxs,0)) :: UPXS - f := -(upxs*upxs - 1)**(-1/2) * (differentiate upxs) - (rec := recip upxs) case "failed" => "failed" - cc + integrate(f * (rec :: UPXS)) - "failed" - - asinhIfCan upxs == - order(upxs,0) < 0 => "failed" - TRANSFCN or (coefficient(upxs,0) = 0) => - log(upxs + (1 + upxs*upxs)**(1/2)) - "failed" - - acoshIfCan upxs == - TRANSFCN => - order(upxs,0) < 0 => "failed" - log(upxs + (upxs*upxs - 1)**(1/2)) - "failed" - - asechIfCan upxs == - TRANSFCN => - order(upxs,0) < 0 => "failed" - (rec := recip upxs) case "failed" => "failed" - log((1 + (1 - upxs*upxs)*(1/2)) * (rec :: UPXS)) - "failed" - - acschIfCan upxs == - TRANSFCN => - order(upxs,0) < 0 => "failed" - (rec := recip upxs) case "failed" => "failed" - log((1 + (1 + upxs*upxs)*(1/2)) * (rec :: UPXS)) - "failed" - - applyOrError:(UPXS -> Union(UPXS,"failed"),String,UPXS) -> UPXS - applyOrError(fcn,name,upxs) == - ans := fcn upxs - ans case "failed" => - error concat(name," of function with singularity") - ans :: UPXS - - exp upxs == applyOrError(expIfCan,"exp",upxs) - log upxs == applyOrError(logIfCan,"log",upxs) - sin upxs == applyOrError(sinIfCan,"sin",upxs) - cos upxs == applyOrError(cosIfCan,"cos",upxs) - tan upxs == applyOrError(tanIfCan,"tan",upxs) - cot upxs == applyOrError(cotIfCan,"cot",upxs) - sec upxs == applyOrError(secIfCan,"sec",upxs) - csc upxs == applyOrError(cscIfCan,"csc",upxs) - asin upxs == applyOrError(asinIfCan,"asin",upxs) - acos upxs == applyOrError(acosIfCan,"acos",upxs) - atan upxs == applyOrError(atanIfCan,"atan",upxs) - acot upxs == applyOrError(acotIfCan,"acot",upxs) - asec upxs == applyOrError(asecIfCan,"asec",upxs) - acsc upxs == applyOrError(acscIfCan,"acsc",upxs) - sinh upxs == applyOrError(sinhIfCan,"sinh",upxs) - cosh upxs == applyOrError(coshIfCan,"cosh",upxs) - tanh upxs == applyOrError(tanhIfCan,"tanh",upxs) - coth upxs == applyOrError(cothIfCan,"coth",upxs) - sech upxs == applyOrError(sechIfCan,"sech",upxs) - csch upxs == applyOrError(cschIfCan,"csch",upxs) - asinh upxs == applyOrError(asinhIfCan,"asinh",upxs) - acosh upxs == applyOrError(acoshIfCan,"acosh",upxs) - atanh upxs == applyOrError(atanhIfCan,"atanh",upxs) - acoth upxs == applyOrError(acothIfCan,"acoth",upxs) - asech upxs == applyOrError(asechIfCan,"asech",upxs) - acsch upxs == applyOrError(acschIfCan,"acsch",upxs) - -\end{chunk} -\begin{chunk}{EFUPXS.dotabb} -"EFUPXS" [color="#FF4488",href="bookvol10.4.pdf#nameddest=EFUPXS"] -"UPXSCCA" [color="#4488FF",href="bookvol10.2.pdf#nameddest=UPXSCCA"] -"EFUPXS" -> "UPXSCCA" - -\end{chunk} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{package INTEF ElementaryIntegration} \begin{chunk}{ElementaryIntegration.input} 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got:" 2251799813685248 288230376151711744 72057594037927936 288230376151711744" +MISMATCH +expected:"" + got:" [----------------,------------------,-----------------,- ------------------]" +MISMATCH +expected:" 4503599627370496 576460752303423488 576460752303423488 36028797018963968" + got:" 4075757662770299 2256901491343133 564222001818973 13484067241" +MISMATCH +expected:" [----------------,------------------,------------------,-----------------]," + got:" 1125899906842624 576460752303423488 576460752303423488 18014398509481984" +MISMATCH +expected:" 8241587318088007 4419955172211269 4419977368221621 1387250647" + got:" [----------------,------------------,------------------,-----------------]," +MISMATCH +expected:" ," + got:" 2026619832316723 4561418640826529 4561421044122753 75103007" +MISMATCH +expected:" 576460752303423488" + got:" 1125899906842624 576460752303423488 576460752303423488 36028797018963968" +MISMATCH +expected:" - ------------------]" + got:" 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got:" 2251799813685248 288230376151711744 576460752303423488 576460752303423488" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:" 7025615418697973 2934617574788653 5869213749282865" + got:" 3422735716801577 3060574249166951 6121154621349935 6123016033" +MISMATCH +expected:"" + got:" ," +MISMATCH +expected:" 1125899906842624 144115188075855872 576460752303423488 576460752303423488" + got:" 562949953421312 288230376151711744 576460752303423488 576460752303423488" +MISMATCH +expected:" [----------------,------------------,------------------,------------------]," + got:" [---------------,------------------,------------------,- ------------------]" +MISMATCH +expected:" 1745144855606067 1482801170112481 5931207232970871 2552520947" + got:" 850054429666181 3092913697371173 6185816218389607 11176352739" +MISMATCH +expected:" ," + got:" 2 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576460752303423488 18014398509481984 576460752303423488" + got:" 4503599627370496 72057594037927936 36028797018963968 72057594037927936" +MISMATCH +expected:" [----------------,------------------,-----------------,- ------------------]" + got:" [----------------,-----------------,-----------------,- -----------------]," +MISMATCH +expected:" 6620291452234629 6451402863328533 201605751942949 18801154165" + got:" 6440147467139809 841049031851291 420523991076017 1049699257" +MISMATCH +expected:" 1125899906842624 288230376151711744 576460752303423488 576460752303423488" + got:" 562949953421312 144115188075855872 36028797018963968 144115188075855872" +MISMATCH +expected:" [----------------,------------------,------------------,------------------]," + got:" [---------------,------------------,-----------------,------------------]," +MISMATCH +expected:" 1643813863990231 3259770262125399 6519543341783843 2817533045" + got:" 799388933858263 1699867466392335 424967339214925 1890467365" 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2251799813685248 288230376151711744 576460752303423488" + got:" - ------------------]" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" 2598114999" +MISMATCH +expected:" 3242591731706757 3329032021514655 6658035528574981" + got:" 4503599627370496 144115188075855872 288230376151711744" +MISMATCH +expected:"" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" 4503599627370496 72057594037927936 36028797018963968 72057594037927936" + got:" 6260003482044989 1754328595966201 3508654593817403" +MISMATCH +expected:" [----------------,-----------------,-----------------,- -----------------]," + got:"" +MISMATCH +expected:" 6440147467139809 841049031851291 420523991076017 1049699257" + got:" 1125899906842624 36028797018963968 36028797018963968 9007199254740992" +MISMATCH +expected:" 562949953421312 144115188075855872 36028797018963968 144115188075855872" + got:" [----------------,-----------------,-----------------,----------------]," +MISMATCH +expected:" [---------------,------------------,-----------------,------------------]," + got:" 1553741871442821 443215452288189 443216484363153 258018741" +MISMATCH +expected:" 799388933858263 1699867466392335 424967339214925 1890467365" + got:" 1125899906842624 288230376151711744 288230376151711744 144115188075855872" +MISMATCH +expected:" 4503599627370496 576460752303423488 288230376151711744 576460752303423488" + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:" [----------------,------------------,------------------,------------------]," + got:" 1542482872374395 3583193567205235 3583201997581209 4215187987" +MISMATCH +expected:" 6350075474592399 6871296875306347 3435662078479879 27281653411" + got:" 2251799813685248 144115188075855872 576460752303423488 576460752303423488" +MISMATCH +expected:" 2251799813685248 288230376151711744 288230376151711744 72057594037927936" + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:" [----------------,------------------,------------------,-----------------]," + got:" 3062447746611937 1810533519315785 7242138272499685 4195236545" +MISMATCH +expected:" 3152519739159347 3471965465048289 3471966023944797 139724127" + got:" ," +MISMATCH +expected:" ," + got:" 576460752303423488" +MISMATCH +expected:" 288230376151711744" + got:" - ------------------]" +MISMATCH +expected:" - ------------------]" + got:" 13045532553" +MISMATCH +expected:" 2598114999" + got:" 2251799813685248 288230376151711744 576460752303423488" +MISMATCH +expected:" 4503599627370496 144115188075855872 288230376151711744" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" 3039929748475085 3659344032584517 7318675019636481" +MISMATCH +expected:" 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------------------," + got:" ," +MISMATCH +expected:" 6079859496950169 3659344032584517 7318675019636483" + got:" 288230376151711744" +MISMATCH +expected:"" + got:" - ------------------]" +MISMATCH +expected:" ," + got:" 6741066301" +MISMATCH +expected:" 281474976710656 576460752303423488 576460752303423488 288230376151711744" + got:" 2251799813685248 576460752303423488 576460752303423488" +MISMATCH +expected:" [---------------,------------------,------------------,- ------------------]" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" 377176468792279 7396049098128153 7396022764344687 13166891733" + got:" 2949857755927675 7633032113400091 7633018631267489" +MISMATCH +expected:" ," + got:"" +MISMATCH +expected:" 576460752303423488" + got:" 1125899906842624 144115188075855872 576460752303423488 576460752303423488" +MISMATCH +expected:" - ------------------]" + got:" [----------------,------------------,------------------,------------------]," 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576460752303423488 576460752303423488" + got:" [---------------,------------------,------------------,------------------]," +MISMATCH +expected:" [----------------,------------------,------------------,------------------]," + got:" 709316941310853 2011257153267837 4022527212614831 12906079157" +MISMATCH +expected:" 1463669878895411 1928419743161835 7713697477040771 18504393431" + got:" 4 576460752303423488 288230376151711744 576460752303423488" +MISMATCH +expected:" ," + got:" [-,------------------,------------------,- ------------------]," +MISMATCH +expected:" 576460752303423488" + got:" 5 8130114220111333 4065050112797359 13994516615" +MISMATCH +expected:" - ------------------]" + got:" ," +MISMATCH +expected:" 16826434487" + got:" 576460752303423488" +MISMATCH +expected:" 4503599627370496 288230376151711744 576460752303423488" + got:" - ------------------]" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" 17052384101" +MISMATCH +expected:" 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-----------------]" + got:" 4503599627370496 18014398509481984 576460752303423488 576460752303423488" +MISMATCH +expected:" 5719571526760529 3980461494655139 3980450291383315 700204489" + got:" [----------------,-----------------,------------------,------------------]," +MISMATCH +expected:" 562949953421312 576460752303423488 288230376151711744 576460752303423488" + got:" 5494391545392005 262208577504765 8390684701191725 10221039245" +MISMATCH +expected:" [---------------,------------------,------------------,------------------]," + got:" 1125899906842624 576460752303423488 288230376151711744 576460752303423488" +MISMATCH +expected:" 709316941310853 8045028613071347 4022527212614831 25812158315" + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:" 4 576460752303423488 288230376151711744 576460752303423488" + got:" 1362338887279575 8479391789931977 4239697085132627 2380333277" +MISMATCH +expected:" [-,------------------,------------------,- ------------------]," + got:" 4503599627370496 72057594037927936 576460752303423488 576460752303423488" +MISMATCH +expected:" 5 8130114220111333 4065050112797359 13994516615" + got:" [----------------,-----------------,------------------,------------------]," +MISMATCH +expected:" ," + got:" 5404319552844595 1071128929614395 8569044029631969 12592716809" +MISMATCH +expected:" 144115188075855872" + got:" ," +MISMATCH +expected:" - ------------------]" + got:" 2251799813685248 288230376151711744 288230376151711744 72057594037927936" +MISMATCH +expected:" 4263096025" + got:" [----------------,------------------,------------------,- -----------------]" +MISMATCH +expected:" 4503599627370496 576460752303423488 576460752303423488" + got:" 2679641778285445 4329825533588629 4329822138968985 848654911" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" 4503599627370496 288230376151711744 576460752303423488 576460752303423488" +MISMATCH +expected:" 5584463537939415 8216064518279773 8216047465895673" + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:"" + got:" 5314247560297185 4375596517321521 8751205020494137 11985851095" +MISMATCH +expected:" 2251799813685248 576460752303423488 288230376151711744 576460752303423488" + got:" 562949953421312 576460752303423488 36028797018963968 576460752303423488" +MISMATCH +expected:" [----------------,------------------,------------------,------------------]," + got:" [---------------,------------------,-----------------,------------------]," +MISMATCH +expected:" 2769713770832855 8302879507576669 4151452864650025 26221723381" + got:" 658651445502935 8843714985387741 552733529401143 21485030547" +MISMATCH +expected:" 4503599627370496 18014398509481984 576460752303423488 576460752303423488" + got:" 4503599627370496 288230376151711744 288230376151711744 9007199254740992" +MISMATCH +expected:" [----------------,-----------------,------------------,------------------]," + got:" [----------------,------------------,------------------,- ----------------]," +MISMATCH +expected:" 5494391545392005 262208577504765 8390684701191725 10221039245" + got:" 5224175567749775 4468637282743293 4468624474894813 400245265" +MISMATCH +expected:" 1125899906842624 576460752303423488 288230376151711744 576460752303423488" + got:" ," +MISMATCH +expected:" [----------------,------------------,------------------,------------------]," + got:" 288230376151711744" +MISMATCH +expected:" 1362338887279575 8479391789931977 4239697085132627 2380333277" + got:" - ------------------]" +MISMATCH +expected:" 4503599627370496 576460752303423488 576460752303423488 288230376151711744" + got:" 1795986759" +MISMATCH +expected:" [----------------,------------------,------------------,------------------]," + got:" 2251799813685248 144115188075855872 288230376151711744" +MISMATCH +expected:" 5404319552844595 8569031436915159 8569044029631969 6296358405" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" ," + got:" 2589569785738035 2257939120697279 4515876445407799" +MISMATCH +expected:" 576460752303423488" + got:"" +MISMATCH +expected:" - ------------------]" + got:" ," +MISMATCH +expected:" 6789239287" + got:" 288230376151711744" +MISMATCH +expected:" 2251799813685248 576460752303423488 288230376151711744" + got:" - ------------------]" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" 8596217249" +MISMATCH +expected:" 2679641778285445 8659651067177257 4329822138968985" + got:" 4503599627370496 144115188075855872 288230376151711744" +MISMATCH +expected:"" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" 4503599627370496 576460752303423488 576460752303423488 72057594037927936" + got:" 5134103575202365 2281819007361449 4563629418505649" +MISMATCH +expected:" [----------------,------------------,------------------,-----------------]," + got:"" +MISMATCH +expected:" 5314247560297185 8751193034643041 8751205020494137 1498231387" + got:" 1125899906842624 144115188075855872 288230376151711744 288230376151711744" +MISMATCH +expected:" 562949953421312 576460752303423488 36028797018963968 576460752303423488" + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:" [---------------,------------------,-----------------,------------------]," + got:" 1272266894732165 2305943889845347 4611888722195781 942505087" +MISMATCH +expected:" 658651445502935 8843714985387741 552733529401143 21485030547" + got:" 1125899906842624 72057594037927936 288230376151711744 288230376151711744" +MISMATCH +expected:" 4503599627370496 288230376151711744 288230376151711744 9007199254740992" + got:" [----------------,-----------------,------------------,------------------]," +MISMATCH +expected:" [----------------,------------------,------------------,- ----------------]," + got:" 1261007895663739 1165164089833891 4660659741337943 3382002379" +MISMATCH +expected:" 5224175567749775 4468637282743293 4468624474894813 400245265" + got:" 2251799813685248 144115188075855872 288230376151711744 288230376151711744" +MISMATCH +expected:" ," + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:" 288230376151711744" + got:" 2499497793190625 2354971876828753 4709947918253153 4164595647" +MISMATCH +expected:" - ------------------]" + got:" 2251799813685248 144115188075855872 288230376151711744 288230376151711744" +MISMATCH +expected:" 1795986759" + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:" 2251799813685248 144115188075855872 288230376151711744" + got:" 2476979795053773 2379874981328261 4759758753339173 8790682651" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" 281474976710656 144115188075855872 72057594037927936 144115188075855872" +MISMATCH +expected:" 2589569785738035 2257939120697279 4515876445407799" + got:" [---------------,------------------,-----------------,- ------------------]," +MISMATCH +expected:"" + got:" 306807724614615 2405051904685113 1202524451423159 3001838795" +MISMATCH +expected:" 4503599627370496 288230376151711744 288230376151711744 9007199254740992" + got:" ," +MISMATCH +expected:" [----------------,------------------,------------------,- ----------------]," + got:" 562949953421312 288230376151711744 144115188075855872 288230376151711744" +MISMATCH +expected:" 5134103575202365 4563638014722897 4563629418505649 268631789" + got:" [---------------,------------------,------------------,- ------------------]" +MISMATCH +expected:" 1125899906842624 144115188075855872 288230376151711744 288230376151711744" + got:" 607985949695017 4860976470761003 2430485346868917 5777023169" +MISMATCH 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[----------------,------------------,------------------,------------------]," + got:" 2386907802506363 4964335883649007 4964340751059159 608426269" +MISMATCH +expected:" 2499497793190625 2354971876828753 4709947918253153 4164595647" + got:" ," +MISMATCH +expected:" 4503599627370496 144115188075855872 144115188075855872 72057594037927936" + got:" 144115188075855872" +MISMATCH +expected:" [----------------,------------------,------------------,-----------------]," + got:" - ------------------]" +MISMATCH +expected:" 4953959590107545 2379874981328261 2379879376669587 2197670663" + got:" 999303649" +MISMATCH +expected:" 281474976710656 144115188075855872 72057594037927936 144115188075855872" + got:" 1125899906842624 288230376151711744 288230376151711744" +MISMATCH +expected:" [---------------,------------------,-----------------,- ------------------]," + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" 306807724614615 2405051904685113 1202524451423159 3001838795" + got:" 1182194902184755 5016851458183849 5016849459576551" +MISMATCH +expected:" 4503599627370496 288230376151711744 288230376151711744 4503599627370496" + got:"" +MISMATCH +expected:" [----------------,------------------,------------------,- ----------------]," + got:" 1125899906842624 288230376151711744 72057594037927936 288230376151711744" +MISMATCH +expected:" 4863887597560135 4860976470761003 4860970693737835 90265987" + got:" [----------------,------------------,-----------------,------------------]," +MISMATCH +expected:" ," + got:" 1170935903116329 5069914670433379 1267478770893455 413140441" +MISMATCH +expected:" 2251799813685248 72057594037927936 288230376151711744 288230376151711744" + got:" ," +MISMATCH +expected:" [----------------,-----------------,------------------,- ------------------]" + got:" 2251799813685248 72057594037927936 144115188075855872 144115188075855872" +MISMATCH +expected:" 2409425800643215 1228099192466617 4912383095862291 13674004177" + got:" [----------------,-----------------,------------------,- ------------------]" +MISMATCH +expected:" 4503599627370496 288230376151711744 36028797018963968 288230376151711744" + got:" 2319353808095805 1280888585858803 2561771773892475 5397825131" +MISMATCH +expected:" [----------------,------------------,-----------------,------------------]," + got:" ," +MISMATCH +expected:" 4773815605012725 4964335883649007 620542593882395 4867410153" + got:" 2251799813685248 144115188075855872 72057594037927936 144115188075855872" +MISMATCH +expected:" ," + got:" [----------------,------------------,-----------------,- ------------------]" +MISMATCH +expected:" 144115188075855872" + got:" 2296835809958953 2588870827075867 1294435210047259 406981349" +MISMATCH +expected:" - ------------------]" + got:" 562949953421312 18014398509481984 288230376151711744 288230376151711744" +MISMATCH +expected:" 999303649" + got:" [---------------,-----------------,------------------,------------------]," 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144115188075855872" + got:" 4503599627370496 144115188075855872 288230376151711744" +MISMATCH +expected:" [----------------,-----------------,------------------,- ------------------]" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" 2319353808095805 1280888585858803 2561771773892475 5397825131" + got:" 4458563631096791 2671909998445175 5343806529310155" +MISMATCH +expected:" ," + got:"" +MISMATCH +expected:" 288230376151711744" + got:" ," +MISMATCH +expected:" - ------------------]" + got:" 2251799813685248 144115188075855872 36028797018963968 144115188075855872" +MISMATCH +expected:" 813962697" + got:" [----------------,------------------,-----------------,- ------------------]" +MISMATCH +expected:" 4503599627370496 144115188075855872 288230376151711744" + got:" 2206763817411543 2700170986826851 675042537881683 835300119" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" 4503599627370496 144115188075855872 288230376151711744 288230376151711744" +MISMATCH +expected:" 4593671619917905 2588870827075867 5177740840189037" + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:"" + got:" 4368491638549381 2728734617103485 5457473817539223 4583332253" +MISMATCH +expected:" 562949953421312 288230376151711744 288230376151711744 72057594037927936" + got:" 1125899906842624 144115188075855872 288230376151711744 288230376151711744" +MISMATCH +expected:" [---------------,------------------,------------------,-----------------]," + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:" 568579452955525 5232505425620559 5232513012688027 1896766867" + got:" 1080863910568919 2757600889275079 5515213454707457 11676157299" +MISMATCH +expected:" 288230376151711744 144115188075855872 288230376151711744" + got:" 4503599627370496 18014398509481984 72057594037927936 72057594037927936" +MISMATCH +expected:" [1,------------------,------------------,- ------------------]," + got:" [----------------,-----------------,-----------------,- -----------------]," +MISMATCH +expected:" 5287874480879303 2643933090895859 8299087585" + got:" 4278419646001971 348348026857555 1393391416160829 691269391" +MISMATCH +expected:" 288230376151711744" + got:" 2251799813685248 18014398509481984 288230376151711744 288230376151711744" +MISMATCH +expected:" - ------------------]" + got:" [----------------,-----------------,------------------,- ------------------]" +MISMATCH +expected:" 13467580195" + got:" 2116691824864133 352033772792595 5632536966307539 3398373981" +MISMATCH +expected:" 4503599627370496 144115188075855872 288230376151711744" + got:" ," +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" 4503599627370496 144115188075855872 144115188075855872 36028797018963968" +MISMATCH +expected:" 4458563631096791 2671909998445175 5343806529310155" + got:" [----------------,------------------,------------------,- -----------------]" +MISMATCH +expected:"" + got:" 4188347653454561 2846073203234847 2846066974137395 1557274363" +MISMATCH +expected:" ," + got:" 562949953421312 288230376151711744 288230376151711744 72057594037927936" +MISMATCH +expected:" 2251799813685248 288230376151711744 36028797018963968 288230376151711744" + got:" [---------------,------------------,------------------,-----------------]," +MISMATCH +expected:" [----------------,------------------,-----------------,- ------------------]" + got:" 517913957147607 5752357732047787 5752363269479927 1384358035" +MISMATCH +expected:" 2206763817411543 5400341973653701 675042537881683 1670600237" + got:" ," +MISMATCH +expected:" 4503599627370496 144115188075855872 288230376151711744 288230376151711744" + got:" 4503599627370496 72057594037927936 288230376151711744 288230376151711744" +MISMATCH +expected:" [----------------,------------------,------------------,------------------]," + got:" [----------------,-----------------,------------------,- ------------------]" +MISMATCH +expected:" 4368491638549381 2728734617103485 5457473817539223 4583332253" + got:" 4098275660907151 1453307996872757 5813231659972327 327518701" +MISMATCH +expected:" 1125899906842624 144115188075855872 288230376151711744 288230376151711744" + got:" 2251799813685248 72057594037927936 288230376151711744 288230376151711744" +MISMATCH +expected:" [----------------,------------------,------------------,------------------]," + got:" [----------------,-----------------,------------------,------------------]," +MISMATCH +expected:" 1080863910568919 2757600889275079 5515213454707457 11676157299" + got:" 2026619832316723 1468685087440451 5874745921678315 5571916511" +MISMATCH +expected:" 4503599627370496 18014398509481984 72057594037927936 72057594037927936" + got:" 4503599627370496 1125899906842624 144115188075855872 144115188075855872" +MISMATCH +expected:" [----------------,-----------------,-----------------,- -----------------]," + got:" [----------------,----------------,------------------,------------------]," +MISMATCH +expected:" 4278419646001971 348348026857555 1393391416160829 691269391" + got:" 4008203668359741 23191061101163 2968456464585907 643637043" +MISMATCH +expected:" 2251799813685248 18014398509481984 288230376151711744 288230376151711744" + got:" 288230376151711744" +MISMATCH +expected:" [----------------,-----------------,------------------,- ------------------]" + got:" - ------------------]" +MISMATCH +expected:" 2116691824864133 352033772792595 5632536966307539 3398373981" + got:" 6233445503" +MISMATCH +expected:" ," + got:" 1125899906842624 288230376151711744 144115188075855872" +MISMATCH +expected:" 4503599627370496 144115188075855872 144115188075855872 36028797018963968" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" [----------------,------------------,------------------,- -----------------]" + got:" 990791918021509 5999745863898801 2999869815226649" +MISMATCH +expected:" 4188347653454561 2846073203234847 2846066974137395 1557274363" + got:"" +MISMATCH +expected:" 562949953421312 288230376151711744 288230376151711744 72057594037927936" + got:" ," +MISMATCH +expected:" [---------------,------------------,------------------,-----------------]," + got:" 288230376151711744" +MISMATCH +expected:" 517913957147607 5752357732047787 5752363269479927 1384358035" + got:" - ------------------]" +MISMATCH +expected:" ," + got:" 9968027909" +MISMATCH +expected:" 4503599627370496 72057594037927936 288230376151711744 288230376151711744" + got:" 9007199254740992 288230376151711744 144115188075855872" +MISMATCH +expected:" [----------------,-----------------,------------------,- ------------------]" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" 4098275660907151 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144115188075855872 36028797018963968" +MISMATCH +expected:" 288230376151711744" + got:" [----------------,------------------,------------------,- -----------------]" +MISMATCH +expected:" - ------------------]" + got:" 7656119366529843 3096127466065265 3096124247511021 804638561" +MISMATCH +expected:" 6233445503" + got:" 9007199254740992 72057594037927936 36028797018963968 72057594037927936" +MISMATCH +expected:" 1125899906842624 288230376151711744 144115188075855872" + got:" [----------------,-----------------,-----------------,- -----------------]," +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" 7566047373982433 1564449629916857 782223118465821 3392985215" +MISMATCH +expected:" 990791918021509 5999745863898801 2999869815226649" + got:" 9007199254740992 288230376151711744 288230376151711744 144115188075855872" +MISMATCH +expected:"" + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:" ," + got:" 7475975381435023 6324005037069477 6324016963475123 5963202823" +MISMATCH +expected:" 288230376151711744" + got:" ," +MISMATCH +expected:" - ------------------]" + got:" 9007199254740992 18014398509481984 288230376151711744 288230376151711744" +MISMATCH +expected:" 9968027909" + got:" [----------------,-----------------,------------------,- ------------------]" +MISMATCH +expected:" 9007199254740992 288230376151711744 144115188075855872" + got:" 7385903388887613 399435059590595 6390951947661551 9005787969" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" ," +MISMATCH +expected:" 7836263351624663 6063243015765023 3031616523868557" + got:" 288230376151711744" +MISMATCH +expected:"" + got:" - ------------------]" +MISMATCH +expected:" ," + got:" 11237933401" +MISMATCH +expected:" 9007199254740992 144115188075855872 72057594037927936 144115188075855872" + got:" 2251799813685248 144115188075855872 288230376151711744" +MISMATCH +expected:" [----------------,------------------,-----------------,- ------------------]" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" 7746191359077253 3063701548748197 1531850069561829 1409624539" + got:" 1823957849085051 3229304311366163 6458597384798925" +MISMATCH +expected:" ," + got:"" +MISMATCH +expected:" 288230376151711744" + got:" 4503599627370496 288230376151711744 288230376151711744 144115188075855872" +MISMATCH +expected:" - ------------------]" + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:" 6437108487" + got:" 3602879701896397 6526948044917897 6526960839368211 6397225157" +MISMATCH +expected:" 9007199254740992 288230376151711744 144115188075855872" + got:" 1125899906842624 144115188075855872 288230376151711744 288230376151711744" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:" 7656119366529843 6192254932130529 3096124247511021" + got:" 889460926405673 3298018433040731 6596049956676065 13090594603" +MISMATCH +expected:"" + got:" ," +MISMATCH +expected:" 9007199254740992 72057594037927936 36028797018963968 72057594037927936" + got:" 4503599627370496 144115188075855872 72057594037927936 144115188075855872" +MISMATCH +expected:" [----------------,-----------------,-----------------,- -----------------]," + got:" [----------------,------------------,-----------------,- ------------------]" +MISMATCH +expected:" 7566047373982433 1564449629916857 782223118465821 3392985215" + got:" 3512807709348987 3332937543111511 1666468115930471 1311250569" +MISMATCH +expected:" 9007199254740992 288230376151711744 288230376151711744 144115188075855872" + got:" 2251799813685248 288230376151711744 288230376151711744 144115188075855872" +MISMATCH +expected:" 7475975381435023 6324005037069477 6324016963475123 5963202823" + got:" 1733885856537641 6736433882304961 6736436170074199 1143884619" +MISMATCH +expected:" 9007199254740992 288230376151711744 288230376151711744 4503599627370496" + got:" 4503599627370496 144115188075855872 144115188075855872 36028797018963968" +MISMATCH +expected:" [----------------,------------------,------------------,- ----------------]," + got:" [----------------,------------------,------------------,-----------------]," +MISMATCH +expected:" 7385903388887613 6390960953449519 6390951947661551 140715437" + got:" 3422735716801577 3403871038682447 3403874484378251 861423951" +MISMATCH +expected:" ," + got:" 4 144115188075855872 288230376151711744 288230376151711744" +MISMATCH +expected:" 9007199254740992 144115188075855872 144115188075855872 36028797018963968" + got:" [-,------------------,------------------,- ------------------]," +MISMATCH +expected:" [----------------,------------------,------------------,- -----------------]" + got:" 3 3439914247220219 6879818837142637 9657297801" +MISMATCH +expected:" 7295831396340203 3229304311366163 3229298692399463 1404741675" + got:" ," +MISMATCH +expected:" 9007199254740992 288230376151711744 72057594037927936 288230376151711744" + got:" 4503599627370496 36028797018963968 144115188075855872 144115188075855872" +MISMATCH +expected:" [----------------,------------------,-----------------,------------------]," + got:" [----------------,-----------------,------------------,- ------------------]" +MISMATCH +expected:" 7205759403792793 6526948044917897 1631740209842053 12794450315" + got:" 3332663724254167 869083038811747 3476326918930911 5236316077" +MISMATCH +expected:" 9007199254740992 144115188075855872 144115188075855872 72057594037927936" + got:" 2251799813685248 72057594037927936 72057594037927936 9007199254740992" +MISMATCH +expected:" [----------------,------------------,------------------,-----------------]," + got:" [----------------,-----------------,-----------------,----------------]," +MISMATCH +expected:" 7115687411245383 3298018433040731 3298024978338033 3272648651" + got:" 1643813863990231 1756562381381377 1756565529928361 393568373" +MISMATCH +expected:" ," + got:" 4503599627370496 36028797018963968 288230376151711744 288230376151711744" +MISMATCH +expected:" 288230376151711744" + got:" [----------------,-----------------,------------------,------------------]," +MISMATCH +expected:" - ------------------]" + got:" 3242591731706757 887580223201283 7100651918591697 10132981433" +MISMATCH +expected:" 2622501137" + got:" ," +MISMATCH +expected:" 9007199254740992 144115188075855872 288230376151711744" + got:" 1125899906842624 144115188075855872 72057594037927936 144115188075855872" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" [----------------,------------------,-----------------,- ------------------]" +MISMATCH +expected:" 7025615418697973 3332937543111511 6665872463721885" + got:" 799388933858263 3587920545374123 1793957889605051 4766164021" +MISMATCH +expected:"" + got:" ," +MISMATCH +expected:" 9007199254740992 288230376151711744 36028797018963968 288230376151711744" + got:" 144115188075855872" +MISMATCH +expected:" [----------------,------------------,-----------------,------------------]," + got:" - ------------------]" +MISMATCH +expected:" 6935543426150563 6736433882304961 842054521259275 2287769239" + got:" 4582902569" +MISMATCH +expected:" 9007199254740992 144115188075855872 288230376151711744 288230376151711744" + got:" 4503599627370496 288230376151711744 288230376151711744" +MISMATCH +expected:" [----------------,------------------,------------------,------------------]," + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" 6845471433603153 3403871038682447 6807748968756503 6891391609" + got:" 3152519739159347 7251818617901837 7251809452096699" +MISMATCH +expected:" 4 288230376151711744 288230376151711744 36028797018963968" + got:"" +MISMATCH +expected:" [-,------------------,------------------,- -----------------]," + got:" ," +MISMATCH +expected:" 3 6879828494440437 6879818837142637 1207162225" + got:" 144115188075855872" +MISMATCH +expected:" ," + got:" - ------------------]" +MISMATCH +expected:" 288230376151711744" + got:" 4543830373" +MISMATCH +expected:" - ------------------]" + got:" 2251799813685248 288230376151711744 288230376151711744" +MISMATCH +expected:" 10472632153" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" 4503599627370496 288230376151711744 144115188075855872" + got:" 1553741871442821 7328603190108653 7328594102447907" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:"" +MISMATCH +expected:" 3332663724254167 6952664310493975 3476326918930911" + got:" ," +MISMATCH +expected:"" + got:" 288230376151711744" +MISMATCH +expected:" 2251799813685248 288230376151711744 72057594037927936 288230376151711744" + got:" - ------------------]" +MISMATCH +expected:" [----------------,------------------,-----------------,------------------]," + got:" 704173991" +MISMATCH +expected:" 1643813863990231 7026249525525507 1756565529928361 12594187937" + got:" 4503599627370496 144115188075855872 288230376151711744" +MISMATCH +expected:" 4503599627370496 36028797018963968 288230376151711744 288230376151711744" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" [----------------,-----------------,------------------,------------------]," + got:" 3062447746611937 3703097403684347 7406194103194703" +MISMATCH +expected:" 3242591731706757 887580223201283 7100651918591697 10132981433" + got:"" +MISMATCH +expected:" ," + got:" 562949953421312 144115188075855872 18014398509481984 144115188075855872" +MISMATCH +expected:" 1125899906842624 288230376151711744 72057594037927936 288230376151711744" + got:" [---------------,------------------,-----------------,- ------------------]," +MISMATCH +expected:" [----------------,------------------,-----------------,- ------------------]" + got:" 377176468792279 3742311146359787 467788633745481 2076395939" +MISMATCH +expected:" 799388933858263 7175841090748245 1793957889605051 9532328041" + got:" ," +MISMATCH +expected:" ," + got:" 288230376151711744" +MISMATCH +expected:" 144115188075855872" + got:" - ------------------]" +MISMATCH +expected:" - ------------------]" + got:" 10655067977" +MISMATCH +expected:" 4582902569" + got:" 4503599627370496 288230376151711744 144115188075855872" +MISMATCH +expected:" 4503599627370496 288230376151711744 288230376151711744" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" 2972375754064527 7563885646161295 3781937495546659" +MISMATCH +expected:" 3152519739159347 7251818617901837 7251809452096699" + got:"" +MISMATCH +expected:"" + got:" 2251799813685248 9007199254740992 288230376151711744 288230376151711744" +MISMATCH +expected:" ," + got:" [----------------,----------------,------------------,- ------------------]," +MISMATCH +expected:" 144115188075855872" + got:" 1463669878895411 238874527115433 7643973528990551 11338703305" +MISMATCH +expected:" - ------------------]" + got:" 4503599627370496 36028797018963968 288230376151711744 288230376151711744" +MISMATCH +expected:" 4543830373" + got:" [----------------,-----------------,------------------,------------------]," +MISMATCH +expected:" 2251799813685248 288230376151711744 288230376151711744" + got:" 2882303761517117 965614994664657 7724922720778403 2763461147" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" 1125899906842624 36028797018963968 288230376151711744 288230376151711744" +MISMATCH +expected:" 1553741871442821 7328603190108653 7328594102447907" + got:" [----------------,-----------------,------------------,------------------]," +MISMATCH +expected:"" + got:" 709316941310853 975839967258639 7806731629494243 11891425131" +MISMATCH +expected:" ," + got:" 9007199254740992 144115188075855872 144115188075855872 9007199254740992" +MISMATCH +expected:" 144115188075855872" + got:" [----------------,------------------,------------------,- ----------------]," +MISMATCH +expected:" - ------------------]" + got:" 5584463537939415 3944706516493519 3944704707541567 113059497" +MISMATCH +expected:" 352086995" + got:" ," +MISMATCH +expected:" 4503599627370496 288230376151711744 288230376151711744" + got:" 9007199254740992 72057594037927936 288230376151711744 288230376151711744" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" [----------------,-----------------,------------------,- ------------------]" +MISMATCH +expected:" 3062447746611937 7406194807368693 7406194103194703" + got:" 5494391545392005 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2079039752444813 7918138011" +MISMATCH +expected:" 4503599627370496 36028797018963968 288230376151711744 288230376151711744" + got:" ," +MISMATCH +expected:" [----------------,-----------------,------------------,------------------]," + got:" 288230376151711744" +MISMATCH +expected:" 2882303761517117 965614994664657 7724922720778403 2763461147" + got:" - ------------------]" +MISMATCH +expected:" 1125899906842624 36028797018963968 288230376151711744 288230376151711744" + got:" 2156068169" +MISMATCH +expected:" [----------------,-----------------,------------------,------------------]," + got:" 2251799813685248 144115188075855872 288230376151711744" +MISMATCH +expected:" 709316941310853 975839967258639 7806731629494243 11891425131" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" 9007199254740992 144115188075855872 144115188075855872 9007199254740992" + got:" 1261007895663739 4202125065434613 8404247974801057" +MISMATCH +expected:" [----------------,------------------,------------------,- ----------------]," + got:"" +MISMATCH +expected:" 5584463537939415 3944706516493519 3944704707541567 113059497" + got:" ," +MISMATCH +expected:" ," + got:" 288230376151711744" +MISMATCH +expected:" 144115188075855872" + got:" - ------------------]" +MISMATCH +expected:" - ------------------]" + got:" 11755510763" +MISMATCH +expected:" 2841797583" + got:" 4503599627370496 144115188075855872 288230376151711744" +MISMATCH +expected:" 9007199254740992 288230376151711744 288230376151711744" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" 2476979795053773 4246642247031245 8493272738551727" +MISMATCH +expected:" 5494391545392005 7972971019033419 7972965335438253" + got:"" +MISMATCH +expected:"" + got:" 1125899906842624 288230376151711744 288230376151711744 144115188075855872" +MISMATCH +expected:" ," + got:" [----------------,------------------,------------------,------------------]," +MISMATCH +expected:" 9007199254740992 288230376151711744 18014398509481984 288230376151711744" + got:" 607985949695017 8583241194459439 8583243274651285 1040095923" +MISMATCH +expected:" [----------------,------------------,-----------------,- ------------------]" + got:" ," +MISMATCH +expected:" 5404319552844595 8057422519245871 503588046715783 13771793343" + got:" 4503599627370496 36028797018963968 288230376151711744 288230376151711744" +MISMATCH +expected:" 9007199254740992 144115188075855872 72057594037927936 144115188075855872" + got:" [----------------,-----------------,------------------,- ------------------]" +MISMATCH +expected:" [----------------,------------------,-----------------,------------------]," + got:" 2386907802506363 1084272234766913 8674169663405653 8214729651" +MISMATCH +expected:" 5314247560297185 4071369355293389 2035687277020413 5198747437" + got:" 2251799813685248 144115188075855872 281474976710656 144115188075855872" +MISMATCH +expected:" ," + got:" [----------------,------------------,---------------,- ------------------]," +MISMATCH +expected:" 9007199254740992 288230376151711744 288230376151711744 72057594037927936" + got:" 1170935903116329 4383032861026235 8560607512649 1814549947" +MISMATCH +expected:" [----------------,------------------,------------------,- -----------------]" + got:" ," +MISMATCH +expected:" 5224175567749775 8229006062168985 8228995975418509 2521687619" + got:" 144115188075855872" +MISMATCH +expected:" ," + got:" - ------------------]" +MISMATCH +expected:" 9007199254740992 288230376151711744 72057594037927936 288230376151711744" + got:" 1344414329" +MISMATCH +expected:" [----------------,------------------,-----------------,- ------------------]" + got:" 4503599627370496 288230376151711744 288230376151711744" +MISMATCH +expected:" 5134103575202365 8316166927917263 2079039752444813 7918138011" + got:" [----------------, ------------------, ------------------," +MISMATCH +expected:" ," + got:" 2296835809958953 8858933549248551 8858930860419893" +MISMATCH +expected:" 288230376151711744" + got:"" +MISMATCH +expected:" - ------------------]" + got:" 2 72057594037927936 144115188075855872 144115188075855872" +MISMATCH +expected:" 2156068169" + got:" [-,-----------------,------------------,------------------]," +MISMATCH +expected:" 9007199254740992 144115188075855872 288230376151711744" + got:" 1 2238195339930887 4476393186548175 2506686401" +MISMATCH +expected:" [----------------, ------------------, ------------------," + got:" 4503599627370496 72057594037927936 144115188075855872 144115188075855872" +MISMATCH +expected:" 5044031582654955 4202125065434613 8404247974801057" + got:" [----------------,-----------------,------------------,------------------]," +MISMATCH +expected:"" + got:" 2206763817411543 2261909494128769 4523819574807495 586549957" +MISMATCH +expected:" ," + got:" 2251799813685248 9007199254740992 144115188075855872 144115188075855872" +MISMATCH +expected:" 9007199254740992 288230376151711744 18014398509481984 288230376151711744" + got:" [----------------,----------------,------------------,- ------------------]," +MISMATCH +expected:" [----------------,------------------,-----------------,- ------------------]" + got:" 1080863910568919 285734481238223 4571749910574687 1789236881" +MISMATCH +expected:" 4953959590107545 8493284494062489 530829546159483 11755510761" + got:" 4503599627370496 144115188075855872 144115188075855872 72057594037927936" +MISMATCH +expected:" 9007199254740992 288230376151711744 288230376151711744 36028797018963968" + got:" [----------------,------------------,------------------,-----------------]," +MISMATCH +expected:" [----------------,------------------,------------------,-----------------]," + got:" 2116691824864133 4620188814523863 4620189566311337 375893737" +MISMATCH +expected:" 4863887597560135 8583241194459439 8583243274651287 260023981" + got:" 1125899906842624 9007199254740992 18014398509481984 18014398509481984" +MISMATCH +expected:" ," + got:" [----------------,----------------,-----------------,- -----------------]," +MISMATCH +expected:" 9007199254740992 36028797018963968 288230376151711744 288230376151711744" + got:" 517913957147607 291821546494577 583642996495615 96493539" +MISMATCH +expected:" [----------------,-----------------,------------------,- ------------------]" + got:" ," +MISMATCH +expected:" 4773815605012725 1084272234766913 8674169663405655 8214729649" + got:" 4503599627370496 18014398509481984 144115188075855872 144115188075855872" +MISMATCH +expected:" 9007199254740992 288230376151711744 281474976710656 288230376151711744" + got:" [----------------,-----------------,------------------,- ------------------]" +MISMATCH +expected:" [----------------,------------------,---------------,- ------------------]," + got:" 2026619832316723 589827435997459 4718618615586477 872393195" +MISMATCH +expected:" 4683743612465315 8766065722052469 8560607512649 3629099893" + got:" 2251799813685248 144115188075855872 36028797018963968 144115188075855872" +MISMATCH +expected:" ," + got:" [----------------,------------------,-----------------,------------------]," +MISMATCH +expected:" 9007199254740992 288230376151711744 288230376151711744 18014398509481984" + got:" 990791918021509 4768613046723187 1192154760988739 5997231769" +MISMATCH +expected:" [----------------,------------------,------------------,- -----------------]" + got:" ," +MISMATCH +expected:" 4593671619917905 8858933549248551 8858930860419895 168051791" + got:" 144115188075855872" +MISMATCH +expected:" 2 72057594037927936 144115188075855872 144115188075855872" + got:" - ------------------]" +MISMATCH +expected:" [-,-----------------,------------------,------------------]," + got:" 3379973089" +MISMATCH +expected:" 1 2238195339930887 4476393186548175 2506686401" + got:" 18014398509481984 72057594037927936 144115188075855872" +MISMATCH +expected:" 4503599627370496 72057594037927936 144115188075855872 144115188075855872" + got:" [-----------------, -----------------, ------------------," +MISMATCH +expected:" [----------------,-----------------,------------------,------------------]," + got:" 7746191359077253 2409577121590695 4819150863208301" +MISMATCH +expected:" 2206763817411543 2261909494128769 4523819574807495 586549957" + got:"" +MISMATCH +expected:" 2251799813685248 9007199254740992 144115188075855872 144115188075855872" + got:" 18014398509481984 72057594037927936 144115188075855872 144115188075855872" +MISMATCH +expected:" [----------------,----------------,------------------,- ------------------]," + got:" [-----------------,-----------------,------------------,------------------]," +MISMATCH +expected:" 1080863910568919 285734481238223 4571749910574687 1789236881" + got:" 7566047373982433 2435107127158333 4870219739481359 5485164693" +MISMATCH +expected:" 4503599627370496 144115188075855872 144115188075855872 72057594037927936" + got:" ," +MISMATCH +expected:" [----------------,------------------,------------------,-----------------]," + got:" 18014398509481984 144115188075855872 2251799813685248 144115188075855872" +MISMATCH +expected:" 2116691824864133 4620188814523863 4620189566311337 375893737" + got:" [-----------------,------------------,----------------,- ------------------]" +MISMATCH +expected:" ," + got:" 7385903388887613 4921836314685437 76903615617979 4915134781" +MISMATCH +expected:" 1125899906842624 144115188075855872 18014398509481984 144115188075855872" + got:" 9007199254740992 72057594037927936 36028797018963968 72057594037927936" +MISMATCH +expected:" [----------------,------------------,-----------------,- ------------------]" + got:" [----------------,-----------------,-----------------,-----------------]," +MISMATCH +expected:" 517913957147607 4669144743913231 583642996495615 771948311" + got:" 3602879701896397 2486995800625045 1243497907871539 15118033" +MISMATCH +expected:" 4503599627370496 18014398509481984 144115188075855872 144115188075855872" + got:" 9007199254740992 72057594037927936 144115188075855872 144115188075855872" +MISMATCH +expected:" 2026619832316723 589827435997459 4718618615586477 872393195" + got:" 3512807709348987 2513354468524119 5026706285310053 2651738185" +MISMATCH +expected:" 2251799813685248 144115188075855872 36028797018963968 144115188075855872" + got:" ," +MISMATCH +expected:" [----------------,------------------,-----------------,------------------]," + got:" 9007199254740992 72057594037927936 144115188075855872 144115188075855872" +MISMATCH +expected:" 990791918021509 4768613046723187 1192154760988739 5997231769" + got:" [----------------,-----------------,------------------,- ------------------]" +MISMATCH +expected:" ," + got:" 3422735716801577 2539994161039941 5079981273662669 7048417213" +MISMATCH +expected:" 144115188075855872" + got:" ," +MISMATCH +expected:" - ------------------]" + got:" 9007199254740992 144115188075855872 144115188075855872 18014398509481984" +MISMATCH +expected:" 3379973089" + got:" [----------------,------------------,------------------,- -----------------]" +MISMATCH +expected:" 18014398509481984 72057594037927936 144115188075855872" + got:" 3332663724254167 5133829756345021 5133822572475557 897983683" +MISMATCH +expected:" [-----------------, -----------------, ------------------," + got:" 9007199254740992 18014398509481984 72057594037927936 72057594037927936" +MISMATCH +expected:" 7746191359077253 2409577121590695 4819150863208301" + got:" [----------------,-----------------,-----------------,-----------------]," +MISMATCH +expected:"" + got:" 3242591731706757 648529154980457 2594118110825931 1490904103" +MISMATCH +expected:" 18014398509481984 144115188075855872 144115188075855872 72057594037927936" + got:" 9007199254740992 36028797018963968 144115188075855872 144115188075855872" +MISMATCH +expected:" [-----------------,------------------,------------------,-----------------]," + got:" [----------------,-----------------,------------------,------------------]," +MISMATCH +expected:" 7566047373982433 4870214254316665 4870219739481359 2742582347" + got:" 3152519739159347 1310806898903351 5243228325754049 730140645" +MISMATCH +expected:" ," + got:" 9007199254740992 72057594037927936 72057594037927936 36028797018963968" +MISMATCH +expected:" 18014398509481984 144115188075855872 2251799813685248 144115188075855872" + got:" [----------------,-----------------,-----------------,-----------------]," +MISMATCH +expected:" [-----------------,------------------,----------------,- ------------------]" + got:" 3062447746611937 2649399206067727 2649402527349517 1660640895" +MISMATCH +expected:" 7385903388887613 4921836314685437 76903615617979 4915134781" + got:" ," +MISMATCH +expected:" 18014398509481984 144115188075855872 36028797018963968 144115188075855872" + got:" 9007199254740992 72057594037927936 144115188075855872 144115188075855872" +MISMATCH +expected:" [-----------------,------------------,-----------------,------------------]," + got:" [----------------,-----------------,------------------,- ------------------]" +MISMATCH +expected:" 7205759403792793 4973991601250089 1243497907871539 30236067" + got:" 2972375754064527 2677487256223711 5354972644460849 1867986573" +MISMATCH +expected:" 144115188075855872" + got:" 9007199254740992 72057594037927936 144115188075855872 144115188075855872" +MISMATCH +expected:" - ------------------]" + got:" [----------------,-----------------,------------------,- ------------------]" +MISMATCH +expected:" 2651738183" + got:" 2882303761517117 2705870742515251 5411737397780889 4087249613" +MISMATCH +expected:" 18014398509481984 144115188075855872 72057594037927936" + got:" 18014398509481984 36028797018963968 144115188075855872 144115188075855872" +MISMATCH +expected:" [-----------------, ------------------, -----------------," + got:" [-----------------,-----------------,------------------,------------------]," +MISMATCH +expected:" 7025615418697973 5026708937048237 2513353142655027" + got:" 5584463537939415 1367274832471173 5469105684885827 6355001135" +MISMATCH +expected:"" + got:" 18014398509481984 144115188075855872 144115188075855872 36028797018963968" +MISMATCH +expected:" ," + got:" [-----------------,------------------,------------------,-----------------]," +MISMATCH +expected:" 144115188075855872" + got:" 5404319552844595 5527076870047609 5527083944213301 1768541423" +MISMATCH +expected:" - ------------------]" + got:" 18014398509481984 36028797018963968 72057594037927936 72057594037927936" +MISMATCH +expected:" 7048417211" + got:" [-----------------,-----------------,-----------------,-----------------]," +MISMATCH +expected:" 18014398509481984 144115188075855872 72057594037927936" + got:" 5224175567749775 1396418526379813 2792839341572711 2288813085" +MISMATCH +expected:" [-----------------, ------------------, -----------------," + got:" 4503599627370496 144115188075855872 72057594037927936 144115188075855872" +MISMATCH +expected:" 6845471433603153 5079988322079881 2539990636831335" + got:" [----------------,------------------,-----------------,------------------]," +MISMATCH +expected:"" + got:" 1261007895663739 5644891036299621 2822448239375115 5442450609" +MISMATCH +expected:" ," + got:" 2251799813685248 36028797018963968 144115188075855872 144115188075855872" +MISMATCH +expected:" 9007199254740992 144115188075855872 144115188075855872 18014398509481984" + got:" [----------------,-----------------,------------------,------------------]," +MISMATCH +expected:" [----------------,------------------,------------------,- -----------------]" + got:" 607985949695017 1426185518476881 5704743978531149 1904623625" +MISMATCH +expected:" 3332663724254167 5133829756345021 5133822572475557 897983683" + got:" 4503599627370496 144115188075855872 72057594037927936 144115188075855872" +MISMATCH +expected:" 9007199254740992 18014398509481984 72057594037927936 72057594037927936" + got:" [----------------,------------------,-----------------,------------------]," +MISMATCH +expected:" [----------------,-----------------,-----------------,-----------------]," + got:" 1170935903116329 5765227218342961 2882613950592275 682841589" +MISMATCH +expected:" 3242591731706757 648529154980457 2594118110825931 1490904103" + got:" 4 144115188075855872 144115188075855872 72057594037927936" +MISMATCH +expected:" 9007199254740992 144115188075855872 144115188075855872 72057594037927936" + got:" [-,------------------,------------------,- -----------------]," +MISMATCH +expected:" [----------------,------------------,------------------,-----------------]," + got:" 1 5826360881124739 5826355037365493 2921879623" +MISMATCH +expected:" 3152519739159347 5243227595613403 5243228325754049 365070323" + got:" 4503599627370496 72057594037927936 18014398509481984 72057594037927936" +MISMATCH +expected:" 9007199254740992 144115188075855872 72057594037927936 144115188075855872" + got:" [----------------,-----------------,-----------------,-----------------]," +MISMATCH +expected:" [----------------,------------------,-----------------,------------------]," + got:" 1080863910568919 2944064325367025 736016531307719 1799863851" +MISMATCH +expected:" 3062447746611937 5298798412135453 2649402527349517 6642563581" + got:" 2251799813685248 70368744177664 144115188075855872 144115188075855872" +MISMATCH +expected:" ," + got:" [----------------,--------------,------------------,------------------]," +MISMATCH +expected:" 9007199254740992 72057594037927936 144115188075855872 144115188075855872" + got:" 517913957147607 2905546557719 5950566477376213 7127167701" +MISMATCH +expected:" [----------------,-----------------,------------------,- ------------------]" + got:" 4503599627370496 9007199254740992 72057594037927936 72057594037927936" +MISMATCH +expected:" 2972375754064527 2677487256223711 5354972644460849 1867986573" + got:" [----------------,----------------,-----------------,- -----------------]," +MISMATCH +expected:" ," + got:" 990791918021509 375854211941683 3006832364658857 1330874607" +MISMATCH +expected:" 9007199254740992 144115188075855872 144115188075855872 36028797018963968" + got:" ," +MISMATCH +expected:" [----------------,------------------,------------------,- -----------------]" + got:" 144115188075855872" +MISMATCH +expected:" 2882303761517117 5411741485030501 5411737397780889 1021812403" + got:" - ------------------]" +MISMATCH +expected:" 18014398509481984 36028797018963968 144115188075855872 144115188075855872" + got:" 4269190041" +MISMATCH +expected:" [-----------------,-----------------,------------------,------------------]," + got:" 36028797018963968 144115188075855872 72057594037927936" +MISMATCH +expected:" 5584463537939415 1367274832471173 5469105684885827 6355001135" + got:" [-----------------, ------------------, -----------------," +MISMATCH +expected:" 18014398509481984 144115188075855872 144115188075855872 36028797018963968" + got:" 7566047373982433 6077438361790495 3038717046300227" +MISMATCH +expected:" [-----------------,------------------,------------------,-----------------]," + got:"" +MISMATCH +expected:" 5404319552844595 5527076870047609 5527083944213301 1768541423" + got:" 18014398509481984 72057594037927936 72057594037927936 18014398509481984" +MISMATCH +expected:" 18014398509481984 36028797018963968 72057594037927936 72057594037927936" + got:" [-----------------,-----------------,-----------------,- -----------------]," +MISMATCH +expected:" [-----------------,-----------------,-----------------,-----------------]," + got:" 3602879701896397 3070943336949009 3070940864726013 618055749" +MISMATCH +expected:" 5224175567749775 1396418526379813 2792839341572711 2288813085" + got:" 18014398509481984 144115188075855872 144115188075855872 72057594037927936" +MISMATCH +expected:" 18014398509481984 144115188075855872 72057594037927936 144115188075855872" + got:" [-----------------,------------------,------------------,-----------------]," +MISMATCH +expected:" [-----------------,------------------,-----------------,------------------]," + got:" 3422735716801577 6207012327389497 6207014878830203 1275720353" +MISMATCH +expected:" 5044031582654955 5644891036299621 2822448239375115 5442450609" + got:" 18014398509481984 36028797018963968 4503599627370496 36028797018963968" +MISMATCH +expected:" 18014398509481984 36028797018963968 72057594037927936 72057594037927936" + got:" [-----------------,-----------------,----------------,- -----------------]," +MISMATCH +expected:" [-----------------,-----------------,-----------------,-----------------]," + got:" 3242591731706757 1568211036325637 196026276789017 822013501" +MISMATCH +expected:" 4863887597560135 1426185518476881 2852371989265575 952311813" + got:" ," +MISMATCH +expected:" 18014398509481984 144115188075855872 144115188075855872 72057594037927936" + got:" 72057594037927936" +MISMATCH +expected:" [-----------------,------------------,------------------,-----------------]," + got:" - -----------------]" +MISMATCH +expected:" 4683743612465315 5765227218342961 5765227901184551 341420795" + got:" 328253711" +MISMATCH +expected:" 4 144115188075855872 144115188075855872 72057594037927936" + got:" 18014398509481984 144115188075855872 144115188075855872" +MISMATCH +expected:" [-,------------------,------------------,- -----------------]," + got:" [-----------------, ------------------, ------------------," +MISMATCH +expected:" 1 5826360881124739 5826355037365493 2921879623" + got:" 3062447746611937 6339367716118363 6339367059610941" +MISMATCH +expected:" 4503599627370496 72057594037927936 18014398509481984 72057594037927936" + got:"" +MISMATCH +expected:" [----------------,-----------------,-----------------,-----------------]," + got:" 18014398509481984 72057594037927936 72057594037927936 36028797018963968" +MISMATCH +expected:" 1080863910568919 2944064325367025 736016531307719 1799863851" + got:" [-----------------,-----------------,-----------------,-----------------]," +MISMATCH +expected:" 2251799813685248 144115188075855872 144115188075855872 72057594037927936" + got:" 2882303761517117 3203298725677875 3203300480027585 877174855" +MISMATCH +expected:" [----------------,------------------,------------------,-----------------]," + got:" 36028797018963968 36028797018963968 72057594037927936 72057594037927936" +MISMATCH +expected:" 517913957147607 5950559350208511 5950566477376213 3563583851" + got:" [-----------------,-----------------,-----------------,-----------------]," +MISMATCH +expected:" 4503599627370496 9007199254740992 72057594037927936 72057594037927936" + got:" 5404319552844595 1618636940633379 3237275056402795 1175136037" +MISMATCH +expected:" [----------------,----------------,-----------------,- -----------------]," + got:" 9007199254740992 144115188075855872 144115188075855872 72057594037927936" +MISMATCH +expected:" 990791918021509 375854211941683 3006832364658857 1330874607" + got:" [----------------,------------------,------------------,-----------------]," +MISMATCH +expected:" ," + got:" 1261007895663739 6543218649651661 6543222153035051 1751691695" +MISMATCH +expected:" 144115188075855872" + got:" 9007199254740992 72057594037927936 72057594037927936 36028797018963968" +MISMATCH +expected:" - ------------------]" + got:" [----------------,-----------------,-----------------,-----------------]," +MISMATCH +expected:" 4269190041" + got:" 1170935903116329 3306312262114497 3306312398868059 68376781" +MISMATCH +expected:" 36028797018963968 144115188075855872 72057594037927936" + got:" 9007199254740992 18014398509481984 36028797018963968 36028797018963968" +MISMATCH +expected:" [-----------------, ------------------, -----------------," + got:" [----------------,-----------------,-----------------,-----------------]," +MISMATCH +expected:" 7566047373982433 6077438361790495 3038717046300227" + got:" 1080863910568919 835345673283189 1670691461650435 115084057" +MISMATCH +expected:"" + got:" 9007199254740992 72057594037927936 4503599627370496 72057594037927936" +MISMATCH +expected:" ," + got:" [----------------,-----------------,----------------,- -----------------]," +MISMATCH +expected:" 144115188075855872" + got:" 990791918021509 3376827823640013 211051661966107 1232182301" +MISMATCH +expected:" - ------------------]" + got:" ," +MISMATCH +expected:" 4944445991" + got:" 144115188075855872" +MISMATCH +expected:" 36028797018963968 144115188075855872 72057594037927936" + got:" - ------------------]" +MISMATCH +expected:" [-----------------, ------------------, -----------------," + got:" 532821479" +MISMATCH +expected:" 7205759403792793 6141886673898017 3070940864726013" + got:" 36028797018963968 72057594037927936 144115188075855872" +MISMATCH +expected:"" + got:" [-----------------, -----------------, ------------------," +MISMATCH +expected:" 36028797018963968 144115188075855872 144115188075855872 72057594037927936" + got:" 3602879701896397 3412647653636267 6825294774451055" +MISMATCH +expected:" [-----------------,------------------,------------------,-----------------]," + got:"" +MISMATCH +expected:" 6845471433603153 6207012327389497 6207014878830203 1275720353" + got:" ," +MISMATCH +expected:" 18014398509481984 36028797018963968 4503599627370496 36028797018963968" + got:" 144115188075855872" +MISMATCH +expected:" [-----------------,-----------------,----------------,- -----------------]," + got:" - ------------------]" +MISMATCH +expected:" 3242591731706757 1568211036325637 196026276789017 822013501" + got:" 103379403" +MISMATCH +expected:" ," + got:" 36028797018963968 36028797018963968 144115188075855872" +MISMATCH +expected:" 72057594037927936" + got:" [-----------------, -----------------, ------------------," +MISMATCH +expected:" - -----------------]" + got:" 3242591731706757 1724424694440461 6897698674382441" +MISMATCH +expected:" 328253711" + got:"" +MISMATCH +expected:" 18014398509481984 144115188075855872 144115188075855872" + got:" 36028797018963968 36028797018963968 9007199254740992 36028797018963968" +MISMATCH +expected:" [-----------------, ------------------, ------------------," + got:" [-----------------,-----------------,----------------,- -----------------]," +MISMATCH +expected:" 3062447746611937 6339367716118363 6339367059610941" + got:" 2882303761517117 1742720117566691 435679563887669 1862016015" +MISMATCH +expected:"" + got:" 18014398509481984 144115188075855872 144115188075855872 72057594037927936" +MISMATCH +expected:" 18014398509481984 72057594037927936 72057594037927936 36028797018963968" + got:" [-----------------,------------------,------------------,-----------------]," +MISMATCH +expected:" [-----------------,-----------------,-----------------,-----------------]," + got:" 1261007895663739 7044825973268485 7044826044653627 35692571" +MISMATCH +expected:" 2882303761517117 3203298725677875 3203300480027585 877174855" + got:" 18014398509481984 9007199254740992 72057594037927936 72057594037927936" +MISMATCH +expected:" 36028797018963968 36028797018963968 72057594037927936 72057594037927936" + got:" [-----------------,----------------,-----------------,-----------------]," +MISMATCH +expected:" [-----------------,-----------------,-----------------,-----------------]," + got:" 1080863910568919 444972756862789 3559783028332517 973430205" +MISMATCH +expected:" 5404319552844595 1618636940633379 3237275056402795 1175136037" + got:" 72057594037927936 36028797018963968 144115188075855872 144115188075855872" +MISMATCH +expected:" 36028797018963968 144115188075855872 144115188075855872 72057594037927936" + got:" [-----------------,-----------------,------------------,------------------]," +MISMATCH +expected:" [-----------------,------------------,------------------,-----------------]," + got:" 3602879701896397 1798773719968795 7195101462304363 6582429183" +MISMATCH +expected:" 5044031582654955 6543218649651661 6543222153035051 1751691695" + got:" ," +MISMATCH +expected:" 36028797018963968 144115188075855872 72057594037927936 144115188075855872" + got:" 144115188075855872" +MISMATCH +expected:" [-----------------,------------------,-----------------,------------------]," + got:" - ------------------]" +MISMATCH +expected:" 4683743612465315 6612624524228993 3306312398868059 273507125" + got:" 6350781267" +MISMATCH +expected:" 9007199254740992 18014398509481984 36028797018963968 36028797018963968" + got:" 72057594037927936 18014398509481984 144115188075855872" +MISMATCH +expected:" [----------------,-----------------,-----------------,-----------------]," + got:" [-----------------, -----------------, ------------------," +MISMATCH +expected:" 1080863910568919 835345673283189 1670691461650435 115084057" + got:" 2882303761517117 908930888314721 7271440755736501" +MISMATCH +expected:" 9007199254740992 72057594037927936 4503599627370496 72057594037927936" + got:"" +MISMATCH +expected:" [----------------,-----------------,----------------,- -----------------]," + got:" 36028797018963968 72057594037927936 144115188075855872 144115188075855872" +MISMATCH +expected:" 990791918021509 3376827823640013 211051661966107 1232182301" + got:" [-----------------,-----------------,------------------,------------------]," +MISMATCH +expected:" 72057594037927936 72057594037927936 9007199254740992 72057594037927936" + got:" 1080863910568919 3674295983347387 7348592522194013 555499239" +MISMATCH +expected:" [-----------------,-----------------,----------------,- -----------------]," + got:" 144115188075855872 36028797018963968 72057594037927936 72057594037927936" +MISMATCH +expected:" 7205759403792793 3412647653636267 426580923403191 266410739" + got:" [------------------,-----------------,-----------------,-----------------]," +MISMATCH +expected:" ," + got:" 2882303761517117 1856639570860953 3713282719478931 3577757025" +MISMATCH +expected:" 144115188075855872" + got:" ," +MISMATCH +expected:" - ------------------]" + got:" 144115188075855872" +MISMATCH +expected:" 103379403" + got:" - ------------------]" +MISMATCH +expected:" 36028797018963968 36028797018963968 144115188075855872" + got:" 6603453733" +MISMATCH +expected:" [-----------------, -----------------, ------------------," + got:" 288230376151711744 72057594037927936 144115188075855872" +MISMATCH +expected:" 3242591731706757 1724424694440461 6897698674382441" + got:" [------------------, -----------------, ------------------," +MISMATCH +expected:"" + got:" 2882303761517117 3752687439901249 7505368276348765" +MISMATCH +expected:" ," + got:" [" +MISMATCH +expected:" 36028797018963968 144115188075855872 9007199254740992 144115188075855872" + got:" (7)" +MISMATCH +expected:" [-----------------,------------------,----------------,- ------------------]" + got:"" +MISMATCH +expected:" 2882303761517117 6970880470266763 435679563887669 7448064059" + got:" " +MISMATCH +expected:" 72057594037927936 144115188075855872 144115188075855872 72057594037927936" + got:"[2.00,0.0064143,En(20,2.00),En(20,2.00)-0.0064143]]]" +MISMATCH +expected:" [-----------------,------------------,------------------,-----------------]," + got:"[1.99,0.0064820,En(20,1.99),En(20,1.99)-0.0064820],_" +MISMATCH +expected:" 5044031582654955 7044825973268485 7044826044653627 35692571" + got:"[1.98,0.0065504,En(20,1.98),En(20,1.98)-0.0065504],_" +MISMATCH +expected:" 18014398509481984 9007199254740992 72057594037927936 72057594037927936" + got:"[1.97,0.0066195,En(20,1.97),En(20,1.97)-0.0066195],_" +MISMATCH +expected:" [-----------------,----------------,-----------------,-----------------]," + got:"[1.96,0.0066893,En(20,1.96),En(20,1.96)-0.0066893],_" +MISMATCH +expected:" 1080863910568919 444972756862789 3559783028332517 973430205" + got:"[1.95,0.0067599,En(20,1.95),En(20,1.95)-0.0067599],_" +MISMATCH +expected:" ," + got:"[1.94,0.0068312,En(20,1.94),En(20,1.94)-0.0068312],_" +MISMATCH +expected:" 144115188075855872 36028797018963968 144115188075855872 144115188075855872" + got:"[1.93,0.0069033,En(20,1.93),En(20,1.93)-0.0069033],_" +MISMATCH +expected:" [------------------,-----------------,------------------,------------------]" + got:"[1.92,0.0069762,En(20,1.92),En(20,1.92)-0.0069762],_" +MISMATCH +expected:" 7205759403792793 1798773719968795 7195101462304363 6582429183" + got:"[1.91,0.0070498,En(20,1.91),En(20,1.91)-0.0070498],_" +MISMATCH +expected:" ," + got:"[1.90,0.0071242,En(20,1.90),En(20,1.90)-0.0071242],_" +MISMATCH +expected:" 144115188075855872" + got:"[1.89,0.0071993,En(20,1.89),En(20,1.89)-0.0071993],_" +MISMATCH +expected:" - ------------------]" + got:"[1.88,0.0072753,En(20,1.88),En(20,1.88)-0.0072753],_" +MISMATCH +expected:" 6350781267" + got:"[1.87,0.0073521,En(20,1.87),En(20,1.87)-0.0073521],_" +MISMATCH +expected:" 72057594037927936 18014398509481984 144115188075855872" + got:"[1.86,0.0074297,En(20,1.86),En(20,1.86)-0.0074297],_" +MISMATCH +expected:" [-----------------, -----------------, ------------------," + got:"[1.85,0.0075081,En(20,1.85),En(20,1.85)-0.0075081],_" +MISMATCH +expected:" 2882303761517117 908930888314721 7271440755736501" + got:"[1.84,0.0075874,En(20,1.84),En(20,1.84)-0.0075874],_" +MISMATCH +expected:"" + got:"[1.83,0.0076674,En(20,1.83),En(20,1.83)-0.0076674],_" +MISMATCH +expected:" 36028797018963968 72057594037927936 144115188075855872 144115188075855872" + got:"[1.82,0.0077484,En(20,1.82),En(20,1.82)-0.0077484],_" +MISMATCH +expected:" [-----------------,-----------------,------------------,------------------]," + got:"[1.81,0.0078302,En(20,1.81),En(20,1.81)-0.0078302],_" +MISMATCH +expected:" 1080863910568919 3674295983347387 7348592522194013 555499239" + got:"[1.80,0.0079128,En(20,1.80),En(20,1.80)-0.0079128],_" +MISMATCH +expected:" 144115188075855872 36028797018963968 72057594037927936 72057594037927936" + got:"[1.79,0.0079963,En(20,1.79),En(20,1.79)-0.0079963],_" +MISMATCH +expected:" [------------------,-----------------,-----------------,-----------------]," + got:"[1.78,0.0080807,En(20,1.78),En(20,1.78)-0.0080807],_" +MISMATCH +expected:" 2882303761517117 1856639570860953 3713282719478931 3577757025" + got:"[1.77,0.0081660,En(20,1.77),En(20,1.77)-0.0081660],_" +MISMATCH +expected:" ," + got:"[1.76,0.0082522,En(20,1.76),En(20,1.76)-0.0082522],_" +MISMATCH +expected:" 36028797018963968" + got:"[1.75,0.0083394,En(20,1.75),En(20,1.75)-0.0083394],_" +MISMATCH +expected:" - -----------------]" + got:"[1.74,0.0084274,En(20,1.74),En(20,1.74)-0.0084274],_" +MISMATCH +expected:" 1650863433" + got:"[1.73,0.0085164,En(20,1.73),En(20,1.73)-0.0085164],_" +MISMATCH +expected:" 288230376151711744 144115188075855872 144115188075855872" + got:"[1.72,0.0086063,En(20,1.72),En(20,1.72)-0.0086063],_" +MISMATCH +expected:" [------------------, ------------------, ------------------," + got:"[1.71,0.0086972,En(20,1.71),En(20,1.71)-0.0086972],_" +MISMATCH +expected:" 2882303761517117 7505374879802497 7505368276348765" + got:"[1.70,0.0087890,En(20,1.70),En(20,1.70)-0.0087890],_" +MISMATCH +expected:" [" + got:"[1.69,0.0088818,En(20,1.69),En(20,1.69)-0.0088818],_" +MISMATCH +expected:" (7)" + got:"[1.68,0.0089756,En(20,1.68),En(20,1.68)-0.0089756],_" +MISMATCH +expected:"" + got:"[1.67,0.0090703,En(20,1.67),En(20,1.67)-0.0090703],_" +MISMATCH +expected:" " + got:"[1.66,0.0091661,En(20,1.66),En(20,1.66)-0.0091661],_" +FAILED en 7 of 7 +regression result FAILED 1 of 7 stanzas file en + +========================================================================= +bug 7237: + +)d op coerce + + +There are 194 exposed functions called coerce : + [1] List(D2) -> D from D if D2 has FIELD and D has AFSPCAT(D2) + [2] D -> List(D2) from D if D has AFSPCAT(D2) and D2 has FIELD + [3] D1 -> D from D if D has ALGEBRA(D1) and D1 has COMRING + +Daly Bug + >> System error: + D2 is not of type SEQUENCE. + + Continuing to read the file... + +--R +--R +--RThere are 194 exposed functions called coerce : +--R [1] List D2 -> D from D if D2 has FIELD and D has AFSPCAT D2 +--R [2] D -> List D2 from D if D has AFSPCAT D2 and D2 has FIELD +--R [3] D1 -> D from D if D has ALGEBRA D1 and D1 has COMRING +--R [4] Vector D2 -> AlgebraGivenByStructuralConstants(D2,D3,D4,D5) +--R from AlgebraGivenByStructuralConstants(D2,D3,D4,D5) +--R if D2 has FIELD and D5: VECTOR MATRIX D2 and D3: PI and D4 +--R : LIST SYMBOL + ============================================================================ finalizing nrlib IDPAM @@ -57,34 +2764,6 @@ warnings 20568: [4] changeBase: f has no value ========================================================================= -warnings 20567: - ->compiling SMTS.spad to SMTS.nrlib - - Warnings: - [1] evalstream: z1 has no value - [2] addvariable: c2 has no value - [3] addvariable: n1 has no value - [4] coefficient: signature of lhs not unique: SMP$(NonNegativeInteger) chosen - [5] coefficient: z1 has no value - [6] *: pretendRep -- should replace by @ - [7] *: pretend$ -- should replace by @ - [8] sortmfirst: v2 has no value - [9] sortmfirst: v1 has no value - [10] csubst: p1 has no value - [11] eval: pretend$ -- should replace by @ - [12] subststream: pretend$ -- should replace by @ - [13] comp1: p1 has no value - [14] differentiate: z1 has no value - [15] stream: pretendRep -- should replace by @ - [16] *: z1 has no value - [17] fintegrate: z1 has no value - [18] integrate: z1 has no value - [19] coerce: l has no value - [20] /: z1 has no value - [21] /: pretend$ -- should replace by @ - -========================================================================= nonextend 60076: >compiling AFFSP.spad to AFFSP.nrlib @@ -102,18 +2781,6 @@ todo 329: [1] output: :(OutputForm) -- should replace by pretend ========================================================================= -bug 7234: - ->compiling EFULS.spad to EFULS.nrlib - - Illegal nrlib - EFULS.nrlib claims that its constructor name is the package - ElementaryFunctionsUnivariateLaurentSeries but - ElementaryFunctionsUnivariateLaurentSeries is already known to be - the for domain EFULS . - EFULS abbreviates package ElementaryFunctionsUnivariateLaurentSeries - -========================================================================= nonextend 60075: >compiling BSTREE.spad to BSTREE.nrlib @@ -40496,3 +43163,58 @@ bug 7236: This constructor is exposed in this frame. Issue )edit NIL to see algebra source code for ELTAB +========================================================================= +warnings 20567: + +>compiling SMTS.spad to SMTS.nrlib + + Warnings: + [1] evalstream: z1 has no value + [2] addvariable: c2 has no value + [3] addvariable: n1 has no value + [4] coefficient: signature of lhs not unique: SMP$(NonNegativeInteger) chosen + [5] coefficient: z1 has no value + [6] *: pretendRep -- should replace by @ + [7] *: pretend$ -- should replace by @ + [8] sortmfirst: v2 has no value + [9] sortmfirst: v1 has no value + [10] csubst: p1 has no value + [11] eval: pretend$ -- should replace by @ + [12] subststream: pretend$ -- should replace by @ + [13] comp1: p1 has no value + [14] differentiate: z1 has no value + [15] stream: pretendRep -- should replace by @ + [16] *: z1 has no value + [17] fintegrate: z1 has no value + [18] integrate: z1 has no value + [19] coerce: l has no value + [20] /: z1 has no value + [21] /: pretend$ -- should replace by @ + +========================================================================= +bug 7234: + +>compiling EFULS.spad to EFULS.nrlib + + Illegal nrlib + EFULS.nrlib claims that its constructor name is the package + ElementaryFunctionsUnivariateLaurentSeries but + ElementaryFunctionsUnivariateLaurentSeries is already known to be + the for domain EFULS . + EFULS abbreviates package ElementaryFunctionsUnivariateLaurentSeries + +========================================================================= +bug 7239: + +NOTE: fix --S to allow ignore on comment + +int/input/grpthry.regress + +MISMATCH +expected:" not have a one-dimensional kernel" + got:" " +MISMATCH +expected:" Random element in generated algebra does" + got:"isAbsolutelyIrreducible? ma.1" +FAILED grpthry 35 of 68 random generation, FAILURE OK. + diff --git a/changelog b/changelog index 163a29d..881a3e3 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,19 @@ +20130326 tpd src/axiom-website/patches.html 20130326.01.tpd.patch +20130326 tpd v103elementaryfunctionsunivariatepuiseuxseries.ps renamed +20130326 tpd v103elementaryfunctionsunivariatelaurentseries.ps renamed +20130326 tpd books/bookvol10.3 move EFULS EFUPXS from package to domain +20130326 tpd books/bookvol10.4 move EFULS EFUPXS from package to domain +20130326 tpd buglist add bugs found in tests +20130326 tpd src/input/cmds.input fix failures +20130326 tpd src/input/complexfactor.input fix failures +20130326 tpd src/input/r20bugs.input fix failures +20130326 tpd src/input/richalgebraic000-099.input fix failures +20130326 tpd src/input/richalgebraic100-199.input fix failures +20130326 tpd src/input/richalgebraic400-461.input fix failures +20130326 tpd src/input/richhyper1000-1098.input fix failures +20130326 tpd src/input/richinvhyper000-099.input fix failures +20130326 tpd src/input/richlog300-391.input fix failures +20130326 tpd src/input/richtrig800-899.input fix failures 20130324 tpd src/axiom-website/patches.html 20130324.02.tpd.patch 20130324 tpd books/bookvolbib add references 20130324 jxb src/axiom-website/patches.html 20130324.01.jxb.patch diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index d783b80..e86c6e0 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4117,5 +4117,7 @@ books/bookvolbib add references src/input/romanpolynomials.input create POLY(ROMAN) 20130324.02.tpd.patch books/bookvolbib add references +20130326.01.tpd.patch +src/input/* fix failing tests, move EFULS, EFUPXS from package to domain diff --git a/src/input/cmds.input.pamphlet b/src/input/cmds.input.pamphlet index dfdf5b5..96e7411 100644 --- a/src/input/cmds.input.pamphlet +++ b/src/input/cmds.input.pamphlet @@ -614,7 +614,7 @@ --R FAMR2 FiniteAbelianMonoidRingFunctions2 --R FCPAK1 FortranCodePackage1 FDIV2 FiniteDivisorFunctions2 --R FFCAT2 FunctionFieldCategoryFunctions2 ---R FFF FiniteFieldFunctions +--R FFF FiniteFieldFunctions FFFACTOR FiniteFieldFactorization --R FFFACTSE FiniteFieldFactorizationWithSizeParseBySideEffect --R FFFG FractionFreeFastGaussian --R FFFGF FractionFreeFastGaussianFractions diff --git a/src/input/complexfactor.input.pamphlet b/src/input/complexfactor.input.pamphlet index 283a3a6..4893e0d 100644 --- a/src/input/complexfactor.input.pamphlet +++ b/src/input/complexfactor.input.pamphlet @@ -517,11 +517,13 @@ t2:=factor t1 --R from FiniteFieldFactorizationWithSizeParseBySideEffect(D3, --R D2) --R if D3 has FFIELDC and D2 has UPOLYC(D3) ---R [12] D2 -> Factored(D2) from DistinctDegreeFactorize(D3,D2) +--R [12] D2 -> Factored(D2) from FiniteFieldFactorization(D3,D2) --R if D3 has FFIELDC and D2 has UPOLYC(D3) ---R [13] D2 -> Factored(D2) from ComplexFactorization(D3,D2) +--R [13] D2 -> Factored(D2) from DistinctDegreeFactorize(D3,D2) +--R if D3 has FFIELDC and D2 has UPOLYC(D3) +--R [14] D2 -> Factored(D2) from ComplexFactorization(D3,D2) --R if D3 has EUCDOM and D2 has UPOLYC(COMPLEX(D3)) ---R [14] D2 -> Factored(D2) from AlgFactor(D2) if D2 has UPOLYC(AN) +--R [15] D2 -> Factored(D2) from AlgFactor(D2) if D2 has UPOLYC(AN) --R -> no appropriate map found in Complex(Integer) --R -> no appropriate map found in Integer --R -> no appropriate map found in Complex(Polynomial(Integer)) diff --git a/src/input/r20bugs.input.pamphlet b/src/input/r20bugs.input.pamphlet index 8891729..c5d746d 100644 --- a/src/input/r20bugs.input.pamphlet +++ b/src/input/r20bugs.input.pamphlet @@ -194,11 +194,17 @@ positiveRemainder(-1::SINT,-5::SINT) )clear completely ---S 17 of 27 + + +-- (1) [[1.73046875 %i,- 2.0],[- 1.73046875 %i,- 2.0],[- 1.0,2.0],[1.0,2.0]] +-- Type: List(List(Complex(Float))) + +--S 17 of 27 ok to fail. it seems there are 2 answers (see above) complexRoots([u**2-v+1,v**2-4],[u,v],0.01) --R --R ---R (1) [[1.73046875 %i,- 2.0],[- 1.73046875 %i,- 2.0],[- 1.0,2.0],[1.0,2.0]] +--R (1) +--R [[1.732421875 %i,- 2.0],[- 1.732421875 %i,- 2.0],[- 1.0,2.0],[1.0,2.0]] --R Type: List(List(Complex(Float))) --E 17 diff --git a/src/input/richalgebraic000-099.input.pamphlet b/src/input/richalgebraic000-099.input.pamphlet index 9d4d297..a93236a 100644 --- a/src/input/richalgebraic000-099.input.pamphlet +++ b/src/input/richalgebraic000-099.input.pamphlet @@ -539,7 +539,7 @@ Occasionally we get a different answer to this same integration: Both answers are correct as can be seen by taking the difference between the original integrand and the derivative of the expression. \begin{chunk}{*} ---S 46 of 518 +--S 46 of 518 ok to fail. there appear to be 2 answers (see above) a0009:= integrate(t0009,x) --R --R @@ -567,7 +567,7 @@ Occasionally we get a different answer to this same integration: Both answers are correct as can be seen by taking the difference between the original integrand and the derivative of the expression. \begin{chunk}{*} ---S 47 of 518 this command generates random output, ok +--S 47 of 518 ok to fail. there appear to be 2 answers (see above) m0009:= a0009-r0009 --R --R diff --git a/src/input/richalgebraic100-199.input.pamphlet b/src/input/richalgebraic100-199.input.pamphlet index 13e90e4..8c99352 100644 --- a/src/input/richalgebraic100-199.input.pamphlet +++ b/src/input/richalgebraic100-199.input.pamphlet @@ -1957,7 +1957,12 @@ r0131:= acosh(x) --R Type: Expression(Integer) --E 157 ---S 158 of 512 + +-- +-----+ +-----+ +-- (65) - log(- \|x - 1 \|x + 1 + x) +-- Type: Union(Expression(Integer),...) + +--S 158 of 512 ok to fail. seems there are 2 answers (see above) a0131:= integrate(t0131,x) --R --R @@ -1966,7 +1971,7 @@ a0131:= integrate(t0131,x) --R Type: Union(Expression(Integer),...) --E 158 ---S 159 of 512 +--S 159 of 512 ok to fail. due to 2 answers (see above) m0131:= a0131-r0131 --R --R @@ -2012,7 +2017,16 @@ r0132:= 2*atan((-1+x)^(1/2)/(1+x)^(1/2)) --R Type: Expression(Integer) --E 162 ---S 163 of 512 + + +-- +-----+ +-----+ +-- 220\|x - 1 \|x + 1 - 21 +-- (70) atan(------------------------) +-- +-----+ +-----+ +-- 21\|x - 1 \|x + 1 + 220 +-- Type: Union(Expression(Integer),...) + +--S 163 of 512 ok to fail. seems there are 2 answers (see above) a0132:= integrate(t0132,x) --R --R @@ -2024,7 +2038,7 @@ a0132:= integrate(t0132,x) --R Type: Union(Expression(Integer),...) --E 163 ---S 164 of 512 +--S 164 of 512ok to fail. due to 2 answers (see above) m0132:= a0132-r0132 --R --R @@ -2065,7 +2079,15 @@ r0133:= -1/8*(-1+x)^(1/2)*x*(1+x)^(1/2)+1/4*(-1+x)^(1/2)*x^3*(1+x)^(1/2)-_ --R Type: Expression(Integer) --E 167 ---S 168 of 512 + + +-- +-----+ +-----+ 3 +-----+ +-----+ +-- - log(- \|x - 1 \|x + 1 - x) + (2x - x)\|x - 1 \|x + 1 +-- (75) --------------------------------------------------------- +-- 8 +-- Type: Union(Expression(Integer),...) + +--S 168 of 512 ok to fail. seems there are 2 answers (see above) a0133:= integrate(t0133,x) --R --R @@ -2076,7 +2098,7 @@ a0133:= integrate(t0133,x) --R Type: Union(Expression(Integer),...) --E 168 ---S 169 of 512 +--S 169 of 512 ok to fail. due to 2 answers (see above) m0133:= a0133-r0133 --R --R @@ -2121,7 +2143,15 @@ r0134:= 1/2*(-1+x)^(1/2)*x*(1+x)^(1/2)-1/2*acosh(x) --R Type: Expression(Integer) --E 172 ---S 173 of 512 + + +-- +-----+ +-----+ +-----+ +-----+ +-- - log(\|x - 1 \|x + 1 + x) + x\|x - 1 \|x + 1 +-- (80) ----------------------------------------------- +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 173 of 512 ok to fail. seems there are 2 answers (see above) a0134:= integrate(t0134,x) --R --R @@ -2137,7 +2167,7 @@ a0134:= integrate(t0134,x) --R Type: Union(Expression(Integer),...) --E 173 ---S 174 of 512 +--S 174 of 512 ok to fail. due to 2 answers, see above m0134:= a0134-r0134 --R --R @@ -2185,7 +2215,15 @@ r0135:= -(-1+x)^(1/2)*(1+x)^(1/2)/x+acosh(x) --R Type: Expression(Integer) --E 177 ---S 178 of 512 + + +-- +-----+ +-----+ +-----+ +-----+ +-- - 16x log(- \|x - 1 \|x + 1 + x) - 16\|x - 1 \|x + 1 + 19x +-- (85) ------------------------------------------------------------ +-- 16x +-- Type: Union(Expression(Integer),...) + +--S 178 of 512 ok to fail. seems there are 2 answers (see above) a0135:= integrate(t0135,x) --R --R @@ -2196,7 +2234,7 @@ a0135:= integrate(t0135,x) --R Type: Union(Expression(Integer),...) --E 178 ---S 179 of 512 +--S 179 of 512 ok to fail. due to 2 answers (see above) m0135:= a0135-r0135 --R --R @@ -2241,7 +2279,15 @@ r0136:= asinh(1/2*(1+2*x)^(1/2)*2^(1/2)) --R Type: Expression(Integer) --E 182 ---S 183 of 512 + + +-- +------+ +------+ +-- log(- \|2x + 1 \|2x + 3 + 2x + 2) +-- (90) - ---------------------------------- +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 183 of 512 ok to fail. seems there are 2 answers (see above) a0136:= integrate(t0136,x) --R --R @@ -2250,7 +2296,7 @@ a0136:= integrate(t0136,x) --R Type: Union(Expression(Integer),...) --E 183 ---S 184 of 512 +--S 184 of 512 ok to fail. due to 2 answers (see above) m0136:= a0136-r0136 --R --R @@ -2294,7 +2340,18 @@ r0137:= 1/3*6^(1/2)*atan(1/2*6^(1/2)*(-2+3*x)^(1/2)/(3+5*x)^(1/2)) --R Type: Expression(Integer) --E 187 ---S 188 of 512 + + +-- +-+ +-+ +------+ +------+ +-+ +-+ +-- +-+ +-+ 3192\|2 \|3 \|3x - 2 \|5x + 3 + (67x + 804)\|2 \|3 +-- \|2 \|3 atan(----------------------------------------------------) +-- +------+ +------+ +-- 804\|3x - 2 \|5x + 3 - 1596x - 19152 +-- (95) - ------------------------------------------------------------------ +-- 6 +-- Type: Union(Expression(Integer),...) + +--S 188 of 512 ok to fail. seems there are 2 answers (see above) a0137:= integrate(t0137,x) --R --R @@ -2308,7 +2365,7 @@ a0137:= integrate(t0137,x) --R Type: Union(Expression(Integer),...) --E 188 ---S 189 of 512 +--S 189 of 512 ok to fail. due to 2 answers (see above) m0137:= a0137-r0137 --R --R @@ -2363,7 +2420,20 @@ r0138:= -1/(-1+x)^(1/2)/(1+x)^(1/2)-2*atan((-1+x)^(1/2)/(1+x)^(1/2)) --R Type: Expression(Integer) --E 192 ---S 193 of 512 + + +-- (100) +-- +-----+ +-----+ +-- 2 416\|x - 1 \|x + 1 + 87 +-----+ +-----+ 2 +-- (24x - 24)atan(------------------------) - 24\|x - 1 \|x + 1 + 19x - 19 +-- +-----+ +-----+ +-- 87\|x - 1 \|x + 1 - 416 +-- -------------------------------------------------------------------------- +-- 2 +-- 24x - 24 +-- Type: Union(Expression(Integer),...) + +--S 193 of 512 ok to fail. seems there are 2 answers (see above) a0138:= integrate(t0138,x) --R --R @@ -2379,7 +2449,7 @@ a0138:= integrate(t0138,x) --R Type: Union(Expression(Integer),...) --E 193 ---S 194 of 512 +--S 194 of 512 ok to fail. due to 2 answers (see above) m0138:= a0138-r0138 --R --R @@ -2538,7 +2608,25 @@ r0141:= 1/2*x^2+(2+x)^(1/2)*(3+x)^(1/2)-5*asinh((2+x)^(1/2)) --R Type: Expression(Integer) --E 207 ---S 208 of 512 + + +-- (115) +-- +-----+ +-----+ 2 +-- ((- 640x - 1600)\|x + 2 \|x + 3 - 640x - 3200x - 3920) +-- * +-- +-----+ +-----+ +-- log(\|x + 3 + \|x + 2 ) +-- + +-- 3 2 +-----+ +-----+ 4 3 2 +-- (64x + 288x + 232x - 236)\|x + 2 \|x + 3 + 64x + 448x + 944x + 328x +-- + +-- - 579 +-- / +-- +-----+ +-----+ 2 +-- (128x + 320)\|x + 2 \|x + 3 + 128x + 640x + 784 +-- Type: Union(Expression(Integer),...) + +--S 208 of 512 ok to fail. seems there are 2 answers (see above) a0141:= integrate(t0141,x) --R --R @@ -2549,7 +2637,7 @@ a0141:= integrate(t0141,x) --R Type: Union(Expression(Integer),...) --E 208 ---S 209 of 512 +--S 209 of 512 ok to fail. due to 2 answers (see above) m0141:= a0141-r0141 --R --R @@ -10751,7 +10839,16 @@ r0184:= (1-x^2)^(1/2)-atanh((1-x^2)^(1/2))+log(x) --R Type: Expression(Integer) --E 422 ---S 423 of 512 + + +-- +-------+ +-----+ +-- - \|- x + 1 \|x + 1 - 1 +-------+ +-----+ +-- (291) - log(------------------------) + \|- x + 1 \|x + 1 +-- 2 +-- x +-- Type: Union(Expression(Integer),...) + +--S 423 of 512 ok to fail. seems there are 2 answers (see above) a0184:= integrate(t0184,x) --R --R @@ -10763,7 +10860,7 @@ a0184:= integrate(t0184,x) --R Type: Union(Expression(Integer),...) --E 423 ---S 424 of 512 +--S 424 of 512 ok to fail. due to 2 answers (see above) m0184:= a0184-r0184 --R --R @@ -10818,7 +10915,15 @@ r0185:= 1/2*x^2-1/2*(-1+x)^(1/2)*x*(1+x)^(1/2)+1/2*acosh(x) --R Type: Expression(Integer) --E 427 ---S 428 of 512 + + +-- +-----+ +-----+ +-----+ +-----+ 2 +-- - log(- \|x - 1 \|x + 1 + x) - x\|x - 1 \|x + 1 + x +-- (296) ------------------------------------------------------ +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 428 of 512 ok to fail. seems there are 2 answers (see above) a0185:= integrate(t0185,x) --R --R @@ -10829,7 +10934,7 @@ a0185:= integrate(t0185,x) --R Type: Union(Expression(Integer),...) --E 428 ---S 429 of 512 +--S 429 of 512 ok to fail. due to 2 answers (see above) m0185:= a0185-r0185 --R --R @@ -12523,7 +12628,17 @@ r0193:= -1/2*x-1/2*(-(-2+x)*x)^(1/2)+atanh((2-x)^(1/2)/x^(1/2))-1/2*log(1-x) --R Type: Expression(Integer) --E 467 ---S 468 of 512 + +-- +-------+ +-+ +-- - \|- x + 2 \|x - 1 +-------+ +-+ +-- log(--------------------) - \|- x + 2 \|x - x +-- 2 +-- x - 2x + 1 +-- (324) ---------------------------------------------- +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 468 of 512 ok to fail. seems there are 2 answers (see above) a0193:= integrate(t0193,x) --R --R @@ -12537,7 +12652,7 @@ a0193:= integrate(t0193,x) --R Type: Union(Expression(Integer),...) --E 468 ---S 469 of 512 +--S 469 of 512 ok to fail. due to 2 answers (see above) m0193:= a0193-r0193 --R --R diff --git a/src/input/richalgebraic400-461.input.pamphlet b/src/input/richalgebraic400-461.input.pamphlet index 27f16b7..df05911 100644 --- a/src/input/richalgebraic400-461.input.pamphlet +++ b/src/input/richalgebraic400-461.input.pamphlet @@ -204,7 +204,15 @@ r0403:= x^(1/2)*(1+x)^(1/2)-asinh(x^(1/2)) --R Type: Expression(Integer) --E 17 ---S 18 of 324 + + +-- +-+ +-----+ +-+ +-----+ +-- - log(- 2\|x \|x + 1 - 2x - 1) + 2\|x \|x + 1 +-- (18) ----------------------------------------------- +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 18 of 324 ok to fail due to sign difference (see above) a0403:= integrate(t0403,x) --R --R @@ -215,7 +223,15 @@ a0403:= integrate(t0403,x) --R Type: Union(Expression(Integer),...) --E 18 ---S 19 of 324 + + +-- +-+ +-----+ +-+ +-- - log(- 2\|x \|x + 1 - 2x - 1) + 2asinh(\|x ) +-- (19) ---------------------------------------------- +-- 2 +-- Type: Expression(Integer) + +--S 19 of 324 ok to fail due to sign difference (see above) m0403:= a0403-r0403 --R --R @@ -255,7 +271,15 @@ r0404:= (-1+x)^(1/2)*x^(1/2)-asinh((-1+x)^(1/2)) --R Type: Expression(Integer) --E 22 ---S 23 of 324 + + +-- +-----+ +-+ +-----+ +-+ +-- - log(2\|x - 1 \|x + 2x - 1) + 2\|x - 1 \|x +-- (23) --------------------------------------------- +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 23 of 324 ok to fail due to sign difference (see above) a0404:= integrate(t0404,x) --R --R @@ -266,7 +290,15 @@ a0404:= integrate(t0404,x) --R Type: Union(Expression(Integer),...) --E 23 ---S 24 of 324 + + +-- +-----+ +-+ +-----+ +-- - log(2\|x - 1 \|x + 2x - 1) + 2asinh(\|x - 1 ) +-- (24) ------------------------------------------------ +-- 2 +-- Type: Expression(Integer) + +--S 24 of 324 ok to fail due to sign difference (see above) m0404:= a0404-r0404 --R --R diff --git a/src/input/richhyper1000-1098.input.pamphlet b/src/input/richhyper1000-1098.input.pamphlet index c27c7f6..5e4c6ca 100644 --- a/src/input/richhyper1000-1098.input.pamphlet +++ b/src/input/richhyper1000-1098.input.pamphlet @@ -16,6 +16,7 @@ )spool richhyper1000-1098.output )set message auto off )clear all + --S 1 of 531 t1000:= sech(6*x)*sinh(x) @@ -558,11 +559,14 @@ d1000:= D(m1000,x) --R Type: Expression(Integer) --E 5 +)clear all + + --S 6 of 531 t1001:= csch(2*x)*sinh(x) --R --R ---R (6) csch(2x)sinh(x) +--R (1) csch(2x)sinh(x) --R Type: Expression(Integer) --E 6 @@ -571,7 +575,7 @@ r1001:= 1/2*atan(sinh(x)) --R --R --R atan(sinh(x)) ---R (7) ------------- +--R (2) ------------- --R 2 --R Type: Expression(Integer) --E 7 @@ -580,7 +584,7 @@ r1001:= 1/2*atan(sinh(x)) a1001:= integrate(t1001,x) --R --R ---R (8) atan(sinh(x) + cosh(x)) +--R (3) atan(sinh(x) + cosh(x)) --R Type: Union(Expression(Integer),...) --E 8 @@ -589,7 +593,7 @@ m1001:= a1001-r1001 --R --R --R 2atan(sinh(x) + cosh(x)) - atan(sinh(x)) ---R (9) ---------------------------------------- +--R (4) ---------------------------------------- --R 2 --R Type: Expression(Integer) --E 9 @@ -598,7 +602,7 @@ m1001:= a1001-r1001 d1001:= D(m1001,x) --R --R ---R (10) +--R (5) --R 3 2 2 3 --R 2sinh(x) + cosh(x)sinh(x) + (- 2cosh(x) + 2)sinh(x) - cosh(x) + cosh(x) --R / @@ -610,11 +614,14 @@ d1001:= D(m1001,x) --R Type: Expression(Integer) --E 10 +)clear all + + --S 11 of 531 t1002:= csch(3*x)*sinh(x) --R --R ---R (11) csch(3x)sinh(x) +--R (1) csch(3x)sinh(x) --R Type: Expression(Integer) --E 11 @@ -622,12 +629,12 @@ t1002:= csch(3*x)*sinh(x) r1002:= 1/3*atan(1/3*tanh(x)*3^(1/2))*3^(1/2) --R --R ---R +-+ ---R +-+ \|3 tanh(x) ---R \|3 atan(-----------) ---R 3 ---R (12) --------------------- ---R 3 +--R +-+ +--R +-+ \|3 tanh(x) +--R \|3 atan(-----------) +--R 3 +--R (2) --------------------- +--R 3 --R Type: Expression(Integer) --E 12 @@ -635,13 +642,13 @@ r1002:= 1/3*atan(1/3*tanh(x)*3^(1/2))*3^(1/2) a1002:= integrate(t1002,x) --R --R ---R +-+ +-+ ---R \|3 sinh(x) + 3\|3 cosh(x) ---R atan(--------------------------) ---R 3sinh(x) - 3cosh(x) ---R (13) - -------------------------------- ---R +-+ ---R \|3 +--R +-+ +-+ +--R \|3 sinh(x) + 3\|3 cosh(x) +--R atan(--------------------------) +--R 3sinh(x) - 3cosh(x) +--R (3) - -------------------------------- +--R +-+ +--R \|3 --R Type: Union(Expression(Integer),...) --E 13 @@ -649,13 +656,13 @@ a1002:= integrate(t1002,x) m1002:= a1002-r1002 --R --R ---R +-+ +-+ +-+ ---R \|3 tanh(x) \|3 sinh(x) + 3\|3 cosh(x) ---R - atan(-----------) - atan(--------------------------) ---R 3 3sinh(x) - 3cosh(x) ---R (14) ------------------------------------------------------ ---R +-+ ---R \|3 +--R +-+ +-+ +-+ +--R \|3 tanh(x) \|3 sinh(x) + 3\|3 cosh(x) +--R - atan(-----------) - atan(--------------------------) +--R 3 3sinh(x) - 3cosh(x) +--R (4) ------------------------------------------------------ +--R +-+ +--R \|3 --R Type: Expression(Integer) --E 14 @@ -663,19 +670,22 @@ m1002:= a1002-r1002 d1002:= D(m1002,x) --R --R ---R 2 2 2 ---R 4cosh(x) tanh(x) - 4sinh(x) ---R (15) ------------------------------------------------------ ---R 2 2 2 2 2 ---R (sinh(x) + 3cosh(x) )tanh(x) + 3sinh(x) + 9cosh(x) +--R 2 2 2 +--R 4cosh(x) tanh(x) - 4sinh(x) +--R (5) ------------------------------------------------------ +--R 2 2 2 2 2 +--R (sinh(x) + 3cosh(x) )tanh(x) + 3sinh(x) + 9cosh(x) --R Type: Expression(Integer) --E 15 +)clear all + + --S 16 of 531 t1003:= csch(4*x)*sinh(x) --R --R ---R (16) csch(4x)sinh(x) +--R (1) csch(4x)sinh(x) --R Type: Expression(Integer) --E 16 @@ -683,10 +693,10 @@ t1003:= csch(4*x)*sinh(x) r1003:= -1/4*atan(sinh(x))+1/4*atan(2^(1/2)*sinh(x))*2^(1/2) --R --R ---R +-+ +-+ ---R \|2 atan(\|2 sinh(x)) - atan(sinh(x)) ---R (17) ------------------------------------- ---R 4 +--R +-+ +-+ +--R \|2 atan(\|2 sinh(x)) - atan(sinh(x)) +--R (2) ------------------------------------- +--R 4 --R Type: Expression(Integer) --E 17 @@ -694,7 +704,7 @@ r1003:= -1/4*atan(sinh(x))+1/4*atan(2^(1/2)*sinh(x))*2^(1/2) a1003:= integrate(t1003,x) --R --R ---R (18) +--R (3) --R +-+ +-+ --R \|2 sinh(x) + \|2 cosh(x) +-+ --R atan(-------------------------) - \|2 atan(sinh(x) + cosh(x)) @@ -715,7 +725,7 @@ a1003:= integrate(t1003,x) m1003:= a1003-r1003 --R --R ---R (19) +--R (4) --R +-+ +-+ --R +-+ \|2 sinh(x) + \|2 cosh(x) --R - 2atan(\|2 sinh(x)) + 2atan(-------------------------) @@ -739,7 +749,7 @@ m1003:= a1003-r1003 d1003:= D(m1003,x) --R --R ---R (20) +--R (5) --R 11 10 2 9 --R - 12sinh(x) - 60cosh(x)sinh(x) + (- 108cosh(x) - 62)sinh(x) --R + @@ -805,11 +815,14 @@ d1003:= D(m1003,x) --R Type: Expression(Integer) --E 20 +)clear all + + --S 21 of 531 t1004:= csch(5*x)*sinh(x) --R --R ---R (21) csch(5x)sinh(x) +--R (1) csch(5x)sinh(x) --R Type: Expression(Integer) --E 21 @@ -818,7 +831,7 @@ r1004:= -1/10*(10+2*5^(1/2))^(1/2)*atan(1/5*(25-10*5^(1/2))^(1/2)*tanh(x))+_ 1/10*(10-2*5^(1/2))^(1/2)*atan(1/5*(25+10*5^(1/2))^(1/2)*tanh(x)) --R --R ---R (22) +--R (2) --R +-----------+ --R +------------+ | +-+ --R | +-+ tanh(x)\|10\|5 + 25 @@ -839,7 +852,7 @@ r1004:= -1/10*(10+2*5^(1/2))^(1/2)*atan(1/5*(25-10*5^(1/2))^(1/2)*tanh(x))+_ a1004:= integrate(t1004,x) --R --R ---R (23) +--R (3) --R - --R +--------+ --R | +-+ @@ -882,7 +895,7 @@ a1004:= integrate(t1004,x) m1004:= a1004-r1004 --R --R ---R (24) +--R (4) --R +-----------+ --R +------------+ | +-+ --R | +-+ tanh(x)\|10\|5 + 25 @@ -939,7 +952,7 @@ m1004:= a1004-r1004 d1004:= D(m1004,x) --R --R ---R (25) +--R (5) --R +-+ 8 +-+ 7 --R (- 2\|5 + 5)sinh(x) + (- 16\|5 + 40)cosh(x)sinh(x) --R + @@ -1265,11 +1278,14 @@ d1004:= D(m1004,x) --R Type: Expression(Integer) --E 25 +)clear all + + --S 26 of 531 t1005:= csch(6*x)*sinh(x) --R --R ---R (26) csch(6x)sinh(x) +--R (1) csch(6x)sinh(x) --R Type: Expression(Integer) --E 26 @@ -1278,12 +1294,12 @@ r1005:= 1/6*atan(sinh(x))+1/6*atan(2*sinh(x))-_ 1/6*atan(2/3*sinh(x)*3^(1/2))*3^(1/2) --R --R ---R +-+ ---R +-+ 2\|3 sinh(x) ---R - \|3 atan(------------) + atan(2sinh(x)) + atan(sinh(x)) ---R 3 ---R (27) --------------------------------------------------------- ---R 6 +--R +-+ +--R +-+ 2\|3 sinh(x) +--R - \|3 atan(------------) + atan(2sinh(x)) + atan(sinh(x)) +--R 3 +--R (2) --------------------------------------------------------- +--R 6 --R Type: Expression(Integer) --E 27 @@ -1291,7 +1307,7 @@ r1005:= 1/6*atan(sinh(x))+1/6*atan(2*sinh(x))-_ a1005:= integrate(t1005,x) --R --R ---R (28) +--R (3) --R +-+ +-+ --R \|3 sinh(x) + \|3 cosh(x) --R - 3atan(-------------------------) @@ -1320,7 +1336,7 @@ a1005:= integrate(t1005,x) m1005:= a1005-r1005 --R --R ---R (29) +--R (4) --R +-+ +-+ +-+ --R 2\|3 sinh(x) \|3 sinh(x) + \|3 cosh(x) --R 3atan(------------) - 3atan(-------------------------) @@ -1349,7 +1365,7 @@ m1005:= a1005-r1005 d1005:= D(m1005,x) --R --R ---R (30) +--R (5) --R 17 16 2 15 --R 32sinh(x) + 288cosh(x)sinh(x) + (1120cosh(x) + 192)sinh(x) --R + @@ -1562,12 +1578,15 @@ d1005:= D(m1005,x) --R Type: Expression(Integer) --E 30 +)clear all + + --S 31 of 531 t1006:= x*cosh(2*x)*sech(x)^2 --R --R ---R 2 ---R (31) x cosh(2x)sech(x) +--R 2 +--R (1) x cosh(2x)sech(x) --R Type: Expression(Integer) --E 31 @@ -1575,8 +1594,8 @@ t1006:= x*cosh(2*x)*sech(x)^2 r1006:= x^2+log(cosh(x))-x*tanh(x) --R --R ---R 2 ---R (32) log(cosh(x)) - x tanh(x) + x +--R 2 +--R (2) log(cosh(x)) - x tanh(x) + x --R Type: Expression(Integer) --E 32 @@ -1584,7 +1603,7 @@ r1006:= x^2+log(cosh(x))-x*tanh(x) a1006:= integrate(t1006,x) --R --R ---R (33) +--R (3) --R 2 2 2cosh(x) --R (sinh(x) + 2cosh(x)sinh(x) + cosh(x) + 1)log(- -----------------) --R sinh(x) - cosh(x) @@ -1601,7 +1620,7 @@ a1006:= integrate(t1006,x) m1006:= a1006-r1006 --R --R ---R (34) +--R (4) --R 2 2 --R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) - 1)log(cosh(x)) --R + @@ -1624,7 +1643,7 @@ m1006:= a1006-r1006 d1006:= D(m1006,x) --R --R ---R (35) +--R (5) --R 4 3 2 2 --R - x sinh(x) - 4x cosh(x)sinh(x) + (- 6x cosh(x) - 2x)sinh(x) --R + @@ -1659,12 +1678,15 @@ d1006:= D(m1006,x) --R Type: Expression(Integer) --E 35 +)clear all + + --S 36 of 531 t1007:= x*cosh(2*x)*sech(x)^3 --R --R ---R 3 ---R (36) x cosh(2x)sech(x) +--R 3 +--R (1) x cosh(2x)sech(x) --R Type: Expression(Integer) --E 36 @@ -1691,10 +1713,10 @@ r1007:= 3*x*atan(exp(x))-3/2*%i*polylog(2,-%i*exp(x))+_ a1007:= integrate(t1007,x) --R --R ---R x ---R ++ 3 ---I (37) | %Q cosh(2%Q)sech(%Q) d%Q ---R ++ +--R x +--R ++ 3 +--I (2) | %U cosh(2%U)sech(%U) d%U +--R ++ --R Type: Union(Expression(Integer),...) --E 38 @@ -1706,15 +1728,18 @@ a1007:= integrate(t1007,x) --d1007:= D(m1007,x) --E 40 +)clear all + + --S 41 of 531 t1008:= sinh(a+b*x)^(1/2)/cosh(a+b*x)^(1/2) --R --R ---R +-------------+ ---R \|sinh(b x + a) ---R (38) ---------------- ---R +-------------+ ---R \|cosh(b x + a) +--R +-------------+ +--R \|sinh(b x + a) +--R (1) ---------------- +--R +-------------+ +--R \|cosh(b x + a) --R Type: Expression(Integer) --E 41 @@ -1723,13 +1748,13 @@ r1008:= -(atan(sinh(a+b*x)^(1/2)/cosh(a+b*x)^(1/2))-_ atanh(sinh(a+b*x)^(1/2)/cosh(a+b*x)^(1/2)))/b --R --R ---R +-------------+ +-------------+ ---R \|sinh(b x + a) \|sinh(b x + a) ---R atanh(----------------) - atan(----------------) ---R +-------------+ +-------------+ ---R \|cosh(b x + a) \|cosh(b x + a) ---R (39) ------------------------------------------------ ---R b +--R +-------------+ +-------------+ +--R \|sinh(b x + a) \|sinh(b x + a) +--R atanh(----------------) - atan(----------------) +--R +-------------+ +-------------+ +--R \|cosh(b x + a) \|cosh(b x + a) +--R (2) ------------------------------------------------ +--R b --R Type: Expression(Integer) --E 42 @@ -1752,15 +1777,18 @@ a1008:= integrate(t1008,x) --d1008:= D(m1008,x) --E 45 +)clear all + + --S 46 of 531 t1009:= cosh(a+b*x)^(1/2)/sinh(a+b*x)^(1/2) --R --R ---R +-------------+ ---R \|cosh(b x + a) ---R (40) ---------------- ---R +-------------+ ---R \|sinh(b x + a) +--R +-------------+ +--R \|cosh(b x + a) +--R (1) ---------------- +--R +-------------+ +--R \|sinh(b x + a) --R Type: Expression(Integer) --E 46 @@ -1769,13 +1797,13 @@ r1009:= -(atan(cosh(a+b*x)^(1/2)/sinh(a+b*x)^(1/2))-_ atanh(cosh(a+b*x)^(1/2)/sinh(a+b*x)^(1/2)))/b --R --R ---R +-------------+ +-------------+ ---R \|cosh(b x + a) \|cosh(b x + a) ---R atanh(----------------) - atan(----------------) ---R +-------------+ +-------------+ ---R \|sinh(b x + a) \|sinh(b x + a) ---R (41) ------------------------------------------------ ---R b +--R +-------------+ +-------------+ +--R \|cosh(b x + a) \|cosh(b x + a) +--R atanh(----------------) - atan(----------------) +--R +-------------+ +-------------+ +--R \|sinh(b x + a) \|sinh(b x + a) +--R (2) ------------------------------------------------ +--R b --R Type: Expression(Integer) --E 47 @@ -1798,15 +1826,18 @@ a1009:= integrate(t1009,x) --d1009:= D(m1009,x) --E 50 +)clear all + + --S 51 of 531 t1010:= sinh(a+b*x)^(1/3)/cosh(a+b*x)^(1/3) --R --R ---R 3+-------------+ ---R \|sinh(b x + a) ---R (42) ---------------- ---R 3+-------------+ ---R \|cosh(b x + a) +--R 3+-------------+ +--R \|sinh(b x + a) +--R (1) ---------------- +--R 3+-------------+ +--R \|cosh(b x + a) --R Type: Expression(Integer) --E 51 @@ -1817,7 +1848,7 @@ r1010:= -1/2*3^(1/2)*atan(1/3*(1+2*sinh(a+b*x)^(2/3)/cosh(a+b*x)^(2/3))*_ sinh(a+b*x)^(4/3)/cosh(a+b*x)^(4/3))/b --R --R ---R (43) +--R (2) --R log --R 3+-------------+2 --R cosh(b x + a)\|sinh(b x + a) @@ -1866,15 +1897,18 @@ a1010:= integrate(t1010,x) --d1010:= D(m1010,x) --E 55 +)clear all + + --S 56 of 531 t1011:= cosh(a+b*x)^(1/3)/sinh(a+b*x)^(1/3) --R --R ---R 3+-------------+ ---R \|cosh(b x + a) ---R (44) ---------------- ---R 3+-------------+ ---R \|sinh(b x + a) +--R 3+-------------+ +--R \|cosh(b x + a) +--R (1) ---------------- +--R 3+-------------+ +--R \|sinh(b x + a) --R Type: Expression(Integer) --E 56 @@ -1885,7 +1919,7 @@ r1011:= -1/2*3^(1/2)*atan(1/3*(1+2*cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))*_ cosh(a+b*x)^(2/3)/sinh(a+b*x)^(2/3))/b --R --R ---R (45) +--R (2) --R log --R 3+-------------+2 --R sinh(b x + a)\|sinh(b x + a) @@ -1934,15 +1968,18 @@ a1011:= integrate(t1011,x) --d1011:= D(m1011,x) --E 60 +)clear all + + --S 61 of 531 t1012:= cosh(x)^(2/3)/sinh(x)^(8/3) --R --R ---R 3+-------+2 ---R \|cosh(x) ---R (46) ------------------- ---R 2 3+-------+2 ---R sinh(x) \|sinh(x) +--R 3+-------+2 +--R \|cosh(x) +--R (1) ------------------- +--R 2 3+-------+2 +--R sinh(x) \|sinh(x) --R Type: Expression(Integer) --E 61 @@ -1950,84 +1987,124 @@ t1012:= cosh(x)^(2/3)/sinh(x)^(8/3) r1012:= -3/5*cosh(x)^(5/3)/sinh(x)^(5/3) --R --R ---R 3+-------+2 ---R 3cosh(x)\|cosh(x) ---R (47) - ------------------- ---R 3+-------+2 ---R 5sinh(x)\|sinh(x) +--R 3+-------+2 +--R 3cosh(x)\|cosh(x) +--R (2) - ------------------- +--R 3+-------+2 +--R 5sinh(x)\|sinh(x) --R Type: Expression(Integer) --E 62 ---S 63 of 531 + +-- +-- (3) +-- 3 2 +-- - 31914sinh(x) - 95742cosh(x)sinh(x) +-- + +-- 2 3 +-- (- 95742cosh(x) - 31914)sinh(x) - 31914cosh(x) - 31914cosh(x) +-- * +-- 3+-------+2 3+-------+ +-- \|cosh(x) \|sinh(x) +-- + +-- 4 3 2 2 +-- 61805sinh(x) + 247220cosh(x)sinh(x) + (370830cosh(x) - 123610)sinh(x) +-- + +-- 3 4 2 +-- (247220cosh(x) - 247220cosh(x))sinh(x) + 61805cosh(x) - 123610cosh(x) +-- + +-- 61805 +-- / +-- 4 3 2 2 +-- 26595sinh(x) + 106380cosh(x)sinh(x) + (159570cosh(x) - 53190)sinh(x) +-- + +-- 3 4 2 +-- (106380cosh(x) - 106380cosh(x))sinh(x) + 26595cosh(x) - 53190cosh(x) +-- + +-- 26595 +-- Type: Union(Expression(Integer),...) + +--S 63 of 531 ok to fail. seems there are 2 answers (see above) a1012:= integrate(t1012,x) --R --R ---R (48) ---R 3 2 ---R - 9234sinh(x) - 27702cosh(x)sinh(x) +--R (3) +--R 3 2 +--R - 30294sinh(x) - 90882cosh(x)sinh(x) --R + ---R 2 3 ---R (- 27702cosh(x) - 9234)sinh(x) - 9234cosh(x) - 9234cosh(x) +--R 2 3 +--R (- 90882cosh(x) - 30294)sinh(x) - 30294cosh(x) - 30294cosh(x) --R * --R 3+-------+2 3+-------+ --R \|cosh(x) \|sinh(x) --R + ---R 4 3 2 2 ---R 1745sinh(x) + 6980cosh(x)sinh(x) + (10470cosh(x) - 3490)sinh(x) +--R 4 3 2 2 +--R 30605sinh(x) + 122420cosh(x)sinh(x) + (183630cosh(x) - 61210)sinh(x) +--R + +--R 3 4 2 +--R (122420cosh(x) - 122420cosh(x))sinh(x) + 30605cosh(x) - 61210cosh(x) --R + ---R 3 4 2 ---R (6980cosh(x) - 6980cosh(x))sinh(x) + 1745cosh(x) - 3490cosh(x) + 1745 +--R 30605 --R / ---R 4 3 2 2 ---R 7695sinh(x) + 30780cosh(x)sinh(x) + (46170cosh(x) - 15390)sinh(x) +--R 4 3 2 2 +--R 25245sinh(x) + 100980cosh(x)sinh(x) + (151470cosh(x) - 50490)sinh(x) --R + ---R 3 4 2 ---R (30780cosh(x) - 30780cosh(x))sinh(x) + 7695cosh(x) - 15390cosh(x) + 7695 +--R 3 4 2 +--R (100980cosh(x) - 100980cosh(x))sinh(x) + 25245cosh(x) - 50490cosh(x) +--R + +--R 25245 --R Type: Union(Expression(Integer),...) --E 63 ---S 64 of 531 +--S 64 of 531 ok to fail. due to 2 answers (see above) m1012:= a1012-r1012 --R --R ---R (49) ---R 5 4 2 3 ---R 1745sinh(x) + 6980cosh(x)sinh(x) + (10470cosh(x) - 3490)sinh(x) +--R (4) +--R 5 4 +--R 30605sinh(x) + 122420cosh(x)sinh(x) --R + ---R 3 2 ---R (6980cosh(x) - 6980cosh(x))sinh(x) +--R 2 3 +--R (183630cosh(x) - 61210)sinh(x) --R + ---R 4 2 ---R (1745cosh(x) - 3490cosh(x) + 1745)sinh(x) +--R 3 2 +--R (122420cosh(x) - 122420cosh(x))sinh(x) +--R + +--R 4 2 +--R (30605cosh(x) - 61210cosh(x) + 30605)sinh(x) --R * --R 3+-------+2 --R \|sinh(x) --R + ---R 5 4 ---R - 9234sinh(x) - 23085cosh(x)sinh(x) +--R 5 4 +--R - 30294sinh(x) - 75735cosh(x)sinh(x) --R + ---R 2 3 ---R (- 9234cosh(x) - 9234)sinh(x) +--R 2 3 +--R (- 30294cosh(x) - 30294)sinh(x) --R + --R 3 2 ---R (18468cosh(x) - 18468cosh(x))sinh(x) +--R (60588cosh(x) - 60588cosh(x))sinh(x) --R + ---R 4 2 5 3 ---R (18468cosh(x) - 18468cosh(x) )sinh(x) + 4617cosh(x) - 9234cosh(x) +--R 4 2 5 +--R (60588cosh(x) - 60588cosh(x) )sinh(x) + 15147cosh(x) --R + ---R 4617cosh(x) +--R 3 +--R - 30294cosh(x) + 15147cosh(x) --R * --R 3+-------+2 --R \|cosh(x) --R / ---R 5 4 2 3 ---R 7695sinh(x) + 30780cosh(x)sinh(x) + (46170cosh(x) - 15390)sinh(x) +--R 5 4 +--R 25245sinh(x) + 100980cosh(x)sinh(x) --R + ---R 3 2 ---R (30780cosh(x) - 30780cosh(x))sinh(x) +--R 2 3 +--R (151470cosh(x) - 50490)sinh(x) --R + ---R 4 2 ---R (7695cosh(x) - 15390cosh(x) + 7695)sinh(x) +--R 3 2 +--R (100980cosh(x) - 100980cosh(x))sinh(x) +--R + +--R 4 2 +--R (25245cosh(x) - 50490cosh(x) + 25245)sinh(x) --R * --R 3+-------+2 --R \|sinh(x) @@ -2038,7 +2115,7 @@ m1012:= a1012-r1012 d1012:= D(m1012,x) --R --R ---R (50) +--R (5) --R 9 8 2 7 --R - 4sinh(x) - 9cosh(x)sinh(x) + 18cosh(x) sinh(x) --R + @@ -2080,15 +2157,18 @@ d1012:= D(m1012,x) --R Type: Expression(Integer) --E 65 +)clear all + + --S 66 of 531 t1013:= sinh(x)^(2/3)/cosh(x)^(8/3) --R --R ---R 3+-------+2 ---R \|sinh(x) ---R (51) ------------------- ---R 2 3+-------+2 ---R cosh(x) \|cosh(x) +--R 3+-------+2 +--R \|sinh(x) +--R (1) ------------------- +--R 2 3+-------+2 +--R cosh(x) \|cosh(x) --R Type: Expression(Integer) --E 66 @@ -2096,51 +2176,75 @@ t1013:= sinh(x)^(2/3)/cosh(x)^(8/3) r1013:= 3/5*sinh(x)^(5/3)/cosh(x)^(5/3) --R --R ---R 3+-------+2 ---R 3sinh(x)\|sinh(x) ---R (52) ------------------- ---R 3+-------+2 ---R 5cosh(x)\|cosh(x) +--R 3+-------+2 +--R 3sinh(x)\|sinh(x) +--R (2) ------------------- +--R 3+-------+2 +--R 5cosh(x)\|cosh(x) --R Type: Expression(Integer) --E 67 ---S 68 of 531 + +-- (3) +-- 3 2 2 +-- 14250sinh(x) + 42750cosh(x)sinh(x) + (42750cosh(x) - 14250)sinh(x) +-- + +-- 3 +-- 14250cosh(x) - 14250cosh(x) +-- * +-- 3+-------+3+-------+2 +-- \|cosh(x) \|sinh(x) +-- + +-- 4 3 2 2 +-- - 5869sinh(x) - 23476cosh(x)sinh(x) + (- 35214cosh(x) - 11738)sinh(x) +-- + +-- 3 4 2 +-- (- 23476cosh(x) - 23476cosh(x))sinh(x) - 5869cosh(x) - 11738cosh(x) +-- + +-- - 5869 +-- / +-- 4 3 2 2 +-- 11875sinh(x) + 47500cosh(x)sinh(x) + (71250cosh(x) + 23750)sinh(x) +-- + +-- 3 4 2 +-- (47500cosh(x) + 47500cosh(x))sinh(x) + 11875cosh(x) + 23750cosh(x) +-- + +-- 11875 +-- Type: Union(Expression(Integer),...) + +--S 68 of 531 ok to fail. seems there are 2 answers (see above) a1013:= integrate(t1013,x) --R --R ---R (53) ---R 3 2 2 ---R 14250sinh(x) + 42750cosh(x)sinh(x) + (42750cosh(x) - 14250)sinh(x) +--R (3) +--R 3 2 2 +--R 150sinh(x) + 450cosh(x)sinh(x) + (450cosh(x) - 150)sinh(x) --R + ---R 3 ---R 14250cosh(x) - 14250cosh(x) +--R 3 +--R 150cosh(x) - 150cosh(x) --R * --R 3+-------+3+-------+2 --R \|cosh(x) \|sinh(x) --R + ---R 4 3 2 2 ---R - 5869sinh(x) - 23476cosh(x)sinh(x) + (- 35214cosh(x) - 11738)sinh(x) ---R + ---R 3 4 2 ---R (- 23476cosh(x) - 23476cosh(x))sinh(x) - 5869cosh(x) - 11738cosh(x) +--R 4 3 2 2 +--R 67sinh(x) + 268cosh(x)sinh(x) + (402cosh(x) + 134)sinh(x) --R + ---R - 5869 +--R 3 4 2 +--R (268cosh(x) + 268cosh(x))sinh(x) + 67cosh(x) + 134cosh(x) + 67 --R / ---R 4 3 2 2 ---R 11875sinh(x) + 47500cosh(x)sinh(x) + (71250cosh(x) + 23750)sinh(x) +--R 4 3 2 2 +--R 125sinh(x) + 500cosh(x)sinh(x) + (750cosh(x) + 250)sinh(x) --R + ---R 3 4 2 ---R (47500cosh(x) + 47500cosh(x))sinh(x) + 11875cosh(x) + 23750cosh(x) ---R + ---R 11875 +--R 3 4 2 +--R (500cosh(x) + 500cosh(x))sinh(x) + 125cosh(x) + 250cosh(x) + 125 --R Type: Union(Expression(Integer),...) --E 68 ---S 69 of 531 +--S 69 of 531 ok to fail. due to 2 answers (see above) m1013:= a1013-r1013 --R --R ---R (54) +--R (4) --R 5 4 2 3 --R - 75sinh(x) - 300cosh(x)sinh(x) + (- 300cosh(x) - 150)sinh(x) --R + @@ -2153,16 +2257,16 @@ m1013:= a1013-r1013 --R 3+-------+2 --R \|sinh(x) --R + ---R 4 2 3 ---R - 32cosh(x)sinh(x) - 128cosh(x) sinh(x) +--R 4 2 3 +--R 67cosh(x)sinh(x) + 268cosh(x) sinh(x) --R + ---R 3 2 ---R (- 192cosh(x) - 64cosh(x))sinh(x) +--R 3 2 +--R (402cosh(x) + 134cosh(x))sinh(x) --R + ---R 4 2 5 3 ---R (- 128cosh(x) - 128cosh(x) )sinh(x) - 32cosh(x) - 64cosh(x) +--R 4 2 5 3 +--R (268cosh(x) + 268cosh(x) )sinh(x) + 67cosh(x) + 134cosh(x) --R + ---R - 32cosh(x) +--R 67cosh(x) --R * --R 3+-------+2 --R \|cosh(x) @@ -2185,7 +2289,7 @@ m1013:= a1013-r1013 d1013:= D(m1013,x) --R --R ---R (55) +--R (5) --R 9 8 2 7 --R 5sinh(x) + 30cosh(x)sinh(x) + (72cosh(x) + 15)sinh(x) --R + @@ -2230,12 +2334,15 @@ d1013:= D(m1013,x) --R Type: Expression(Integer) --E 70 +)clear all + + --S 71 of 531 t1014:= cosh(x)*csch(x)^(7/3) --R --R ---R 2 3+-------+ ---R (56) cosh(x)csch(x) \|csch(x) +--R 2 3+-------+ +--R (1) cosh(x)csch(x) \|csch(x) --R Type: Expression(Integer) --E 71 @@ -2243,10 +2350,10 @@ t1014:= cosh(x)*csch(x)^(7/3) r1014:= -3/4*csch(x)^(4/3) --R --R ---R 3+-------+ ---R 3csch(x)\|csch(x) ---R (57) - ------------------ ---R 4 +--R 3+-------+ +--R 3csch(x)\|csch(x) +--R (2) - ------------------ +--R 4 --R Type: Expression(Integer) --E 72 @@ -2254,7 +2361,7 @@ r1014:= -3/4*csch(x)^(4/3) a1014:= integrate(t1014,x) --R --R ---R (58) +--R (3) --R +-----------------------------------------+ --R | 2sinh(x) + 2cosh(x) --R (- 3sinh(x) - 3cosh(x)) |----------------------------------------- @@ -2279,7 +2386,7 @@ a1014:= integrate(t1014,x) m1014:= a1014-r1014 --R --R ---R (59) +--R (4) --R 6 5 --R 3csch(x)sinh(x) + 18cosh(x)csch(x)sinh(x) --R + @@ -2325,7 +2432,7 @@ m1014:= a1014-r1014 d1014:= D(m1014,x) --R --R ---R (60) +--R (5) --R 4 3 2 2 --R 16sinh(x) + 64cosh(x)sinh(x) + (96cosh(x) + 4)sinh(x) --R + @@ -2421,12 +2528,15 @@ d1014:= D(m1014,x) --R Type: Expression(Integer) --E 75 +)clear all + + --S 76 of 531 t1015:= (1+coth(x))^(1/2)*sech(x)^2 --R --R ---R 2 +-----------+ ---R (61) sech(x) \|coth(x) + 1 +--R 2 +-----------+ +--R (1) sech(x) \|coth(x) + 1 --R Type: Expression(Integer) --E 76 @@ -2434,8 +2544,8 @@ t1015:= (1+coth(x))^(1/2)*sech(x)^2 r1015:= atanh((1+coth(x))^(1/2))+(1+coth(x))^(1/2)*tanh(x) --R --R ---R +-----------+ +-----------+ ---R (62) atanh(\|coth(x) + 1 ) + tanh(x)\|coth(x) + 1 +--R +-----------+ +-----------+ +--R (2) atanh(\|coth(x) + 1 ) + tanh(x)\|coth(x) + 1 --R Type: Expression(Integer) --E 77 @@ -2443,7 +2553,7 @@ r1015:= atanh((1+coth(x))^(1/2))+(1+coth(x))^(1/2)*tanh(x) a1015:= integrate(t1015,x) --R --R ---R (63) +--R (3) --R 12 11 2 10 --R sinh(x) + 12cosh(x)sinh(x) + (66cosh(x) + 8)sinh(x) --R + @@ -2733,7 +2843,7 @@ a1015:= integrate(t1015,x) m1015:= a1015-r1015 --R --R ---R (64) +--R (4) --R 12 11 2 10 --R sinh(x) + 12cosh(x)sinh(x) + (66cosh(x) + 8)sinh(x) --R + @@ -3133,13 +3243,16 @@ m1015:= a1015-r1015 --d1015:= D(m1015,x) --E 80 +)clear all + + --S 81 of 531 t1016:= sinh(x)/(a*cosh(x)+b*sinh(x)) --R --R ---R sinh(x) ---R (65) --------------------- ---R b sinh(x) + a cosh(x) +--R sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 81 @@ -3147,10 +3260,10 @@ t1016:= sinh(x)/(a*cosh(x)+b*sinh(x)) r1016:= (-b*x+a*log(a*cosh(x)+b*sinh(x)))/(a^2-b^2) --R --R ---R - a log(b sinh(x) + a cosh(x)) + b x ---R (66) ------------------------------------ ---R 2 2 ---R b - a +--R - a log(b sinh(x) + a cosh(x)) + b x +--R (2) ------------------------------------ +--R 2 2 +--R b - a --R Type: Expression(Integer) --E 82 @@ -3158,12 +3271,12 @@ r1016:= (-b*x+a*log(a*cosh(x)+b*sinh(x)))/(a^2-b^2) a1016:= integrate(t1016,x) --R --R ---R - 2b sinh(x) - 2a cosh(x) ---R - a log(-------------------------) + (b + a)x ---R sinh(x) - cosh(x) ---R (67) --------------------------------------------- ---R 2 2 ---R b - a +--R - 2b sinh(x) - 2a cosh(x) +--R - a log(-------------------------) + (b + a)x +--R sinh(x) - cosh(x) +--R (3) --------------------------------------------- +--R 2 2 +--R b - a --R Type: Union(Expression(Integer),...) --E 83 @@ -3171,12 +3284,12 @@ a1016:= integrate(t1016,x) m1016:= a1016-r1016 --R --R ---R - 2b sinh(x) - 2a cosh(x) ---R a log(b sinh(x) + a cosh(x)) - a log(-------------------------) + a x ---R sinh(x) - cosh(x) ---R (68) --------------------------------------------------------------------- ---R 2 2 ---R b - a +--R - 2b sinh(x) - 2a cosh(x) +--R a log(b sinh(x) + a cosh(x)) - a log(-------------------------) + a x +--R sinh(x) - cosh(x) +--R (4) --------------------------------------------------------------------- +--R 2 2 +--R b - a --R Type: Expression(Integer) --E 84 @@ -3184,18 +3297,21 @@ m1016:= a1016-r1016 d1016:= D(m1016,x) --R --R ---R (69) 0 +--R (5) 0 --R Type: Expression(Integer) --E 85 +)clear all + + --S 86 of 531 t1017:= sinh(x)^2/(a*cosh(x)+b*sinh(x)) --R --R ---R 2 ---R sinh(x) ---R (70) --------------------- ---R b sinh(x) + a cosh(x) +--R 2 +--R sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 86 @@ -3204,16 +3320,16 @@ r1017:= -a^2*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ b*cosh(x)/(a^2-b^2)+a*sinh(x)/(a^2-b^2) --R --R ---R +---------+ ---R 2 a sinh(x) + b cosh(x) | 2 2 ---R a atan(---------------------) + (- a sinh(x) + b cosh(x))\|- b + a ---R +---------+ ---R | 2 2 ---R \|- b + a ---R (71) --------------------------------------------------------------------- ---R +---------+ ---R 2 2 | 2 2 ---R (b - a )\|- b + a +--R +---------+ +--R 2 a sinh(x) + b cosh(x) | 2 2 +--R a atan(---------------------) + (- a sinh(x) + b cosh(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) --------------------------------------------------------------------- +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a --R Type: Expression(Integer) --E 87 @@ -3221,7 +3337,7 @@ r1017:= -a^2*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ a1017:= integrate(t1017,x) --R --R ---R (72) +--R (3) --R [ --R 2 2 --R (2a sinh(x) + 2a cosh(x)) @@ -3281,7 +3397,7 @@ a1017:= integrate(t1017,x) m1017a:= a1017.1-r1017 --R --R ---R (73) +--R (4) --R +---------+ --R 2 2 | 2 2 --R (2a sinh(x) + 2a cosh(x))\|- b + a @@ -3325,7 +3441,7 @@ m1017a:= a1017.1-r1017 d1017a:= D(m1017a,x) --R --R ---R (74) +--R (5) --R 2 2 3 4 6 --R (- a b - 2a b - a )sinh(x) --R + @@ -3426,7 +3542,7 @@ d1017a:= D(m1017a,x) m1017b:= a1017.2-r1017 --R --R ---R (75) +--R (6) --R +---------+ --R | 2 2 --R 2 2 (sinh(x) + cosh(x))\|- b + a @@ -3453,7 +3569,7 @@ m1017b:= a1017.2-r1017 d1017b:= D(m1017b,x) --R --R ---R (76) +--R (7) --R 2 2 3 4 6 --R (- a b - 2a b - a )sinh(x) --R + @@ -3550,14 +3666,17 @@ d1017b:= D(m1017b,x) --R Type: Expression(Integer) --E 92 +)clear all + + --S 93 of 531 t1018:= sinh(x)^3/(a*cosh(x)+b*sinh(x)) --R --R ---R 3 ---R sinh(x) ---R (77) --------------------- ---R b sinh(x) + a cosh(x) +--R 3 +--R sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 93 @@ -3567,7 +3686,7 @@ r1018:= -1/2*(-3*a^2*b*x+b^3*x+2*a^3*log(a*cosh(x)+_ a^3-cosh(x)^2*a^3-b^2*a+cosh(x)^2*b^2*a)/(a^2-b^2)^2 --R --R ---R (78) +--R (2) --R 3 3 2 --R - 2a log(b sinh(x) + a cosh(x)) + (b - a b)cosh(x)sinh(x) --R + @@ -3583,7 +3702,7 @@ r1018:= -1/2*(-3*a^2*b*x+b^3*x+2*a^3*log(a*cosh(x)+_ a1018:= integrate(t1018,x) --R --R ---R (79) +--R (3) --R 3 2 3 3 2 --R (- 8a sinh(x) - 16a cosh(x)sinh(x) - 8a cosh(x) ) --R * @@ -3623,7 +3742,7 @@ a1018:= integrate(t1018,x) m1018:= a1018-r1018 --R --R ---R (80) +--R (4) --R 3 2 3 3 2 --R (8a sinh(x) + 16a cosh(x)sinh(x) + 8a cosh(x) ) --R * @@ -3663,22 +3782,25 @@ m1018:= a1018-r1018 d1018:= D(m1018,x) --R --R ---R 4 2 2 4 ---R - sinh(x) + 2cosh(x) sinh(x) - cosh(x) + 1 ---R (81) --------------------------------------------------------------- ---R 2 2 ---R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R 4 2 2 4 +--R - sinh(x) + 2cosh(x) sinh(x) - cosh(x) + 1 +--R (5) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) --R Type: Expression(Integer) --E 97 +)clear all + + --S 98 of 531 t1019:= sinh(x)/(a*cosh(x)+b*sinh(x))^2 --R --R ---R sinh(x) ---R (82) --------------------------------------------- ---R 2 2 2 2 ---R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) +--R sinh(x) +--R (1) --------------------------------------------- +--R 2 2 2 2 +--R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 98 @@ -3687,16 +3809,16 @@ r1019:= -b*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ a/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) --R --R ---R +---------+ ---R 2 a sinh(x) + b cosh(x) | 2 2 ---R (b sinh(x) + a b cosh(x))atan(---------------------) + a\|- b + a ---R +---------+ ---R | 2 2 ---R \|- b + a ---R (83) -------------------------------------------------------------------- ---R +---------+ ---R 3 2 2 3 | 2 2 ---R ((b - a b)sinh(x) + (a b - a )cosh(x))\|- b + a +--R +---------+ +--R 2 a sinh(x) + b cosh(x) | 2 2 +--R (b sinh(x) + a b cosh(x))atan(---------------------) + a\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) -------------------------------------------------------------------- +--R +---------+ +--R 3 2 2 3 | 2 2 +--R ((b - a b)sinh(x) + (a b - a )cosh(x))\|- b + a --R Type: Expression(Integer) --E 99 @@ -3704,7 +3826,7 @@ r1019:= -b*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ a1019:= integrate(t1019,x) --R --R ---R (84) +--R (3) --R [ --R 2 2 2 --R (b + a b)sinh(x) + (2b + 2a b)cosh(x)sinh(x) @@ -3785,7 +3907,7 @@ a1019:= integrate(t1019,x) m1019a:= a1019.1-r1019 --R --R ---R (85) +--R (4) --R 3 2 3 3 2 2 2 --R (b + a b )sinh(x) + (2b + 3a b + a b)cosh(x)sinh(x) --R + @@ -3865,7 +3987,7 @@ m1019a:= a1019.1-r1019 d1019a:= D(m1019a,x) --R --R ---R (86) +--R (5) --R 4 3 3 4 7 --R (- b - 2a b - 2a b - a )sinh(x) --R + @@ -4023,7 +4145,7 @@ d1019a:= D(m1019a,x) m1019b:= a1019.2-r1019 --R --R ---R (87) +--R (6) --R 3 2 3 3 2 2 2 --R (- 2b - 2a b )sinh(x) + (- 4b - 6a b - 2a b)cosh(x)sinh(x) --R + @@ -4082,7 +4204,7 @@ m1019b:= a1019.2-r1019 d1019b:= D(m1019b,x) --R --R ---R (88) +--R (7) --R 4 3 3 4 7 --R (- b - 2a b - 2a b - a )sinh(x) --R + @@ -4236,15 +4358,18 @@ d1019b:= D(m1019b,x) --R Type: Expression(Integer) --E 104 +)clear all + + --S 105 of 531 t1020:= sinh(x)^2/(a*cosh(x)+b*sinh(x))^2 --R --R ---R 2 ---R sinh(x) ---R (89) --------------------------------------------- ---R 2 2 2 2 ---R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) +--R 2 +--R sinh(x) +--R (1) --------------------------------------------- +--R 2 2 2 2 +--R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 105 @@ -4253,7 +4378,7 @@ r1020:= (a^2+b^2)*x/(a^2-b^2)^2-a/(a^2-b^2)/(b+a*coth(x))-_ 2*a*b*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2 --R --R ---R (90) +--R (2) --R 2 2 2 3 --R (- 2a b coth(x) - 2a b )log(b sinh(x) + a cosh(x)) + (a b + a )x coth(x) --R + @@ -4269,7 +4394,7 @@ r1020:= (a^2+b^2)*x/(a^2-b^2)^2-a/(a^2-b^2)/(b+a*coth(x))-_ a1020:= integrate(t1020,x) --R --R ---R (91) +--R (3) --R 2 2 2 2 2 --R (- 2a b - 2a b)sinh(x) + (- 4a b - 4a b)cosh(x)sinh(x) --R + @@ -4307,7 +4432,7 @@ a1020:= integrate(t1020,x) m1020:= a1020-r1020 --R --R ---R (92) +--R (4) --R 2 2 3 3 2 2 2 --R ((2a b + 2a b)coth(x) + 2a b + 2a b )sinh(x) --R + @@ -4398,7 +4523,7 @@ m1020:= a1020-r1020 d1020:= D(m1020,x) --R --R ---R (93) +--R (5) --R 2 2 3 4 2 2 2 3 4 4 --R ((- a b - 2a b - a )coth(x) + a b + 2a b + a )sinh(x) --R + @@ -4528,14 +4653,17 @@ d1020:= D(m1020,x) --R Type: Expression(Integer) --E 109 +)clear all + + --S 110 of 531 t1021:= sinh(x)/(a*cosh(x)+b*sinh(x))^3 --R --R ---R sinh(x) ---R (94) --------------------------------------------------------------------- ---R 3 3 2 2 2 2 3 3 ---R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R sinh(x) +--R (1) --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 110 @@ -4544,7 +4672,7 @@ r1021:= -1/2*a/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^2-_ b*sinh(x)/a/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) --R --R ---R (95) +--R (2) --R 2 2 2 --R 2b sinh(x) + 2a b cosh(x)sinh(x) + a --R / @@ -4560,7 +4688,7 @@ r1021:= -1/2*a/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^2-_ a1021:= integrate(t1021,x) --R --R ---R (96) +--R (3) --R (- 4b - 2a)sinh(x) - 2a cosh(x) --R / --R 4 3 2 2 3 4 3 @@ -4589,7 +4717,7 @@ a1021:= integrate(t1021,x) m1021:= a1021-r1021 --R --R ---R (97) +--R (4) --R 5 4 2 3 3 2 5 --R (- 2b - 6a b - 6a b - 2a b )sinh(x) --R + @@ -4675,7 +4803,7 @@ m1021:= a1021-r1021 d1021:= D(m1021,x) --R --R ---R (98) +--R (5) --R 6 5 2 4 3 3 4 2 9 --R (b + 4a b + 6a b + 4a b + a b )sinh(x) --R + @@ -4968,15 +5096,18 @@ d1021:= D(m1021,x) --R Type: Expression(Integer) --E 114 +)clear all + + --S 115 of 531 t1022:= sinh(x)^3/(a*cosh(x)+b*sinh(x))^3 --R --R ---R 3 ---R sinh(x) ---R (99) --------------------------------------------------------------------- ---R 3 3 2 2 2 2 3 3 ---R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R 3 +--R sinh(x) +--R (1) --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 115 @@ -4986,7 +5117,7 @@ r1022:= -b*(3*a^2+b^2)*x/(a^2-b^2)^3-1/2*a/(a^2-b^2)/(b+a*coth(x))^2+_ log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^3 --R --R ---R (100) +--R (2) --R 3 2 5 2 2 3 4 4 3 2 --R ((- 6a b - 2a )coth(x) + (- 12a b - 4a b)coth(x) - 6a b - 2a b ) --R * @@ -5010,7 +5141,7 @@ r1022:= -b*(3*a^2+b^2)*x/(a^2-b^2)^3-1/2*a/(a^2-b^2)/(b+a*coth(x))^2+_ a1022:= integrate(t1022,x) --R --R ---R (101) +--R (3) --R 4 2 3 3 2 4 5 4 --R (- 3a b - 6a b - 4a b - 2a b - a )sinh(x) --R + @@ -5134,7 +5265,7 @@ a1022:= integrate(t1022,x) m1022:= a1022-r1022 --R --R ---R (102) +--R (4) --R 3 4 4 3 5 2 6 7 2 --R (6a b + 12a b + 8a b + 4a b + 2a )coth(x) --R + @@ -5717,13 +5848,16 @@ m1022:= a1022-r1022 --d1022:= D(m1022,x) --E 119 +)clear all + + --S 120 of 531 t1023:= cosh(x)/(a*cosh(x)+b*sinh(x)) --R --R ---R cosh(x) ---R (103) --------------------- ---R b sinh(x) + a cosh(x) +--R cosh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 120 @@ -5731,10 +5865,10 @@ t1023:= cosh(x)/(a*cosh(x)+b*sinh(x)) r1023:= -(-a*x+b*log(a*cosh(x)+b*sinh(x)))/(a^2-b^2) --R --R ---R b log(b sinh(x) + a cosh(x)) - a x ---R (104) ---------------------------------- ---R 2 2 ---R b - a +--R b log(b sinh(x) + a cosh(x)) - a x +--R (2) ---------------------------------- +--R 2 2 +--R b - a --R Type: Expression(Integer) --E 121 @@ -5742,12 +5876,12 @@ r1023:= -(-a*x+b*log(a*cosh(x)+b*sinh(x)))/(a^2-b^2) a1023:= integrate(t1023,x) --R --R ---R - 2b sinh(x) - 2a cosh(x) ---R b log(-------------------------) + (- b - a)x ---R sinh(x) - cosh(x) ---R (105) --------------------------------------------- ---R 2 2 ---R b - a +--R - 2b sinh(x) - 2a cosh(x) +--R b log(-------------------------) + (- b - a)x +--R sinh(x) - cosh(x) +--R (3) --------------------------------------------- +--R 2 2 +--R b - a --R Type: Union(Expression(Integer),...) --E 122 @@ -5755,7 +5889,7 @@ a1023:= integrate(t1023,x) m1023:= a1023-r1023 --R --R ---R (106) +--R (4) --R - 2b sinh(x) - 2a cosh(x) --R - b log(b sinh(x) + a cosh(x)) + b log(-------------------------) - b x --R sinh(x) - cosh(x) @@ -5769,18 +5903,21 @@ m1023:= a1023-r1023 d1023:= D(m1023,x) --R --R ---R (107) 0 +--R (5) 0 --R Type: Expression(Integer) --E 124 +)clear all + + --S 125 of 531 t1024:= cosh(x)^2/(a*cosh(x)+b*sinh(x)) --R --R ---R 2 ---R cosh(x) ---R (108) --------------------- ---R b sinh(x) + a cosh(x) +--R 2 +--R cosh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 125 @@ -5789,17 +5926,16 @@ r1024:= -b^2*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ b*cosh(x)/(a^2-b^2)+a*sinh(x)/(a^2-b^2) --R --R ---R (109) ---R +---------+ ---R 2 a sinh(x) + b cosh(x) | 2 2 ---R b atan(---------------------) + (- a sinh(x) + b cosh(x))\|- b + a ---R +---------+ ---R | 2 2 ---R \|- b + a ---R --------------------------------------------------------------------- ---R +---------+ ---R 2 2 | 2 2 ---R (b - a )\|- b + a +--R +---------+ +--R 2 a sinh(x) + b cosh(x) | 2 2 +--R b atan(---------------------) + (- a sinh(x) + b cosh(x))\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) --------------------------------------------------------------------- +--R +---------+ +--R 2 2 | 2 2 +--R (b - a )\|- b + a --R Type: Expression(Integer) --E 126 @@ -5807,7 +5943,7 @@ r1024:= -b^2*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)-_ a1024:= integrate(t1024,x) --R --R ---R (110) +--R (3) --R [ --R 2 2 --R (2b sinh(x) + 2b cosh(x)) @@ -5867,7 +6003,7 @@ a1024:= integrate(t1024,x) m1024a:= a1024.1-r1024 --R --R ---R (111) +--R (4) --R +---------+ --R 2 2 | 2 2 --R (2b sinh(x) + 2b cosh(x))\|- b + a @@ -5911,7 +6047,7 @@ m1024a:= a1024.1-r1024 d1024a:= D(m1024a,x) --R --R ---R (112) +--R (5) --R 2 2 3 4 6 --R (- a b - 2a b - a )sinh(x) --R + @@ -6006,7 +6142,7 @@ d1024a:= D(m1024a,x) m1024b:= a1024.2-r1024 --R --R ---R (113) +--R (6) --R +---------+ --R | 2 2 --R 2 2 (sinh(x) + cosh(x))\|- b + a @@ -6033,7 +6169,7 @@ m1024b:= a1024.2-r1024 d1024b:= D(m1024b,x) --R --R ---R (114) +--R (7) --R 2 2 3 4 6 --R (- a b - 2a b - a )sinh(x) --R + @@ -6124,14 +6260,17 @@ d1024b:= D(m1024b,x) --R Type: Expression(Integer) --E 131 +)clear all + + --S 132 of 531 t1025:= cosh(x)^3/(a*cosh(x)+b*sinh(x)) --R --R ---R 3 ---R cosh(x) ---R (115) --------------------- ---R b sinh(x) + a cosh(x) +--R 3 +--R cosh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 132 @@ -6141,7 +6280,7 @@ r1025:= 1/2/(a^2-b^2)^2*(-3*a*b^2*x+a^3*x+2*log(a*cosh(x)+_ a^2*b*cosh(x)^2-b^3+cosh(x)^2*b^3) --R --R ---R (116) +--R (2) --R 3 2 3 --R 2b log(b sinh(x) + a cosh(x)) + (- a b + a )cosh(x)sinh(x) --R + @@ -6157,7 +6296,7 @@ r1025:= 1/2/(a^2-b^2)^2*(-3*a*b^2*x+a^3*x+2*log(a*cosh(x)+_ a1025:= integrate(t1025,x) --R --R ---R (117) +--R (3) --R 3 2 3 3 2 --R (8b sinh(x) + 16b cosh(x)sinh(x) + 8b cosh(x) ) --R * @@ -6197,7 +6336,7 @@ a1025:= integrate(t1025,x) m1025:= a1025-r1025 --R --R ---R (118) +--R (4) --R 3 2 3 3 2 --R (- 8b sinh(x) - 16b cosh(x)sinh(x) - 8b cosh(x) ) --R * @@ -6237,22 +6376,25 @@ m1025:= a1025-r1025 d1025:= D(m1025,x) --R --R ---R 4 2 2 4 ---R sinh(x) - 2cosh(x) sinh(x) + cosh(x) - 1 ---R (119) --------------------------------------------------------------- ---R 2 2 ---R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R 4 2 2 4 +--R sinh(x) - 2cosh(x) sinh(x) + cosh(x) - 1 +--R (5) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) --R Type: Expression(Integer) --E 136 +)clear all + + --S 137 of 531 t1026:= cosh(x)/(a*cosh(x)+b*sinh(x))^2 --R --R ---R cosh(x) ---R (120) --------------------------------------------- ---R 2 2 2 2 ---R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) +--R cosh(x) +--R (1) --------------------------------------------- +--R 2 2 2 2 +--R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 137 @@ -6261,17 +6403,16 @@ r1026:= a*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)+_ b/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) --R --R ---R (121) ---R +---------+ ---R 2 a sinh(x) + b cosh(x) | 2 2 ---R (- a b sinh(x) - a cosh(x))atan(---------------------) - b\|- b + a ---R +---------+ ---R | 2 2 ---R \|- b + a ---R ---------------------------------------------------------------------- ---R +---------+ ---R 3 2 2 3 | 2 2 ---R ((b - a b)sinh(x) + (a b - a )cosh(x))\|- b + a +--R +---------+ +--R 2 a sinh(x) + b cosh(x) | 2 2 +--R (- a b sinh(x) - a cosh(x))atan(---------------------) - b\|- b + a +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) ---------------------------------------------------------------------- +--R +---------+ +--R 3 2 2 3 | 2 2 +--R ((b - a b)sinh(x) + (a b - a )cosh(x))\|- b + a --R Type: Expression(Integer) --E 138 @@ -6279,7 +6420,7 @@ r1026:= a*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)+_ a1026:= integrate(t1026,x) --R --R ---R (122) +--R (3) --R [ --R 2 2 2 --R (a b + a )sinh(x) + (2a b + 2a )cosh(x)sinh(x) @@ -6360,7 +6501,7 @@ a1026:= integrate(t1026,x) m1026a:= a1026.1-r1026 --R --R ---R (123) +--R (4) --R 2 2 3 2 2 3 2 --R (a b + a b)sinh(x) + (2a b + 3a b + a )cosh(x)sinh(x) --R + @@ -6440,7 +6581,7 @@ m1026a:= a1026.1-r1026 d1026a:= D(m1026a,x) --R --R ---R (124) +--R (5) --R 3 2 2 3 7 3 2 2 3 6 --R (a b + 4a b + a b)sinh(x) + (8a b + 14a b + 8a b)cosh(x)sinh(x) --R + @@ -6595,7 +6736,7 @@ d1026a:= D(m1026a,x) m1026b:= a1026.2-r1026 --R --R ---R (125) +--R (6) --R 2 2 3 2 2 3 2 --R (2a b + 2a b)sinh(x) + (4a b + 6a b + 2a )cosh(x)sinh(x) --R + @@ -6654,7 +6795,7 @@ m1026b:= a1026.2-r1026 d1026b:= D(m1026b,x) --R --R ---R (126) +--R (7) --R 3 2 2 3 7 3 2 2 3 6 --R (a b + 4a b + a b)sinh(x) + (8a b + 14a b + 8a b)cosh(x)sinh(x) --R + @@ -6805,15 +6946,18 @@ d1026b:= D(m1026b,x) --R Type: Expression(Integer) --E 143 +)clear all + + --S 144 of 531 t1027:= cosh(x)^2/(a*cosh(x)+b*sinh(x))^2 --R --R ---R 2 ---R cosh(x) ---R (127) --------------------------------------------- ---R 2 2 2 2 ---R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) +--R 2 +--R cosh(x) +--R (1) --------------------------------------------- +--R 2 2 2 2 +--R b sinh(x) + 2a b cosh(x)sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 144 @@ -6822,7 +6966,7 @@ r1027:= (a^2+b^2)*x/(a^2-b^2)^2-2*a*b*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2+_ b/(a^2-b^2)/(a+b*tanh(x)) --R --R ---R (128) +--R (2) --R 2 2 3 2 --R (- 2a b tanh(x) - 2a b)log(b sinh(x) + a cosh(x)) + (b + a b)x tanh(x) --R + @@ -6838,7 +6982,7 @@ r1027:= (a^2+b^2)*x/(a^2-b^2)^2-2*a*b*log(a*cosh(x)+b*sinh(x))/(a^2-b^2)^2+_ a1027:= integrate(t1027,x) --R --R ---R (129) +--R (3) --R 2 2 2 2 2 --R (- 2a b - 2a b)sinh(x) + (- 4a b - 4a b)cosh(x)sinh(x) --R + @@ -6879,7 +7023,7 @@ a1027:= integrate(t1027,x) m1027:= a1027-r1027 --R --R ---R (130) +--R (4) --R 3 2 2 2 3 2 2 --R (2a b + 2a b )sinh(x) + (4a b + 4a b )cosh(x)sinh(x) --R + @@ -6966,7 +7110,7 @@ m1027:= a1027-r1027 d1027:= D(m1027,x) --R --R ---R (131) +--R (5) --R 4 3 2 2 4 4 3 2 2 3 --R (b + 2a b + a b )sinh(x) + (4b + 8a b + 4a b )cosh(x)sinh(x) --R + @@ -7076,15 +7220,17 @@ d1027:= D(m1027,x) --R Type: Expression(Integer) --E 148 +)clear all + + --S 149 of 531 t1028:= cosh(x)/(a*cosh(x)+b*sinh(x))^3 --R --R ---R (132) ---R cosh(x) ---R --------------------------------------------------------------------- ---R 3 3 2 2 2 2 3 3 ---R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R cosh(x) +--R (1) --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 149 @@ -7093,7 +7239,7 @@ r1028:= 1/2*b/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^2+_ sinh(x)/(a^2-b^2)/(a*cosh(x)+b*sinh(x)) --R --R ---R (133) +--R (2) --R 2 --R - 2b sinh(x) - 2a cosh(x)sinh(x) - b --R ---------------------------------------------------------------------------- @@ -7106,7 +7252,7 @@ r1028:= 1/2*b/(a^2-b^2)/(a*cosh(x)+b*sinh(x))^2+_ a1028:= integrate(t1028,x) --R --R ---R (134) +--R (3) --R - 2b sinh(x) + (- 2b - 4a)cosh(x) --R / --R 4 3 2 2 3 4 3 @@ -7135,7 +7281,7 @@ a1028:= integrate(t1028,x) m1028:= a1028-r1028 --R --R ---R (135) +--R (4) --R 4 3 2 2 3 5 --R (2b + 6a b + 6a b + 2a b)sinh(x) --R + @@ -7224,7 +7370,7 @@ m1028:= a1028-r1028 d1028:= D(m1028,x) --R --R ---R (136) +--R (5) --R 5 2 4 3 3 4 2 5 9 --R (- a b - 4a b - 6a b - 4a b - a b)sinh(x) --R + @@ -7517,16 +7663,18 @@ d1028:= D(m1028,x) --R Type: Expression(Integer) --E 153 +)clear all + + --S 154 of 531 t1029:= cosh(x)^3/(a*cosh(x)+b*sinh(x))^3 --R --R ---R (137) ---R 3 ---R cosh(x) ---R --------------------------------------------------------------------- ---R 3 3 2 2 2 2 3 3 ---R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) +--R 3 +--R cosh(x) +--R (1) --------------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sinh(x) + 3a b cosh(x)sinh(x) + 3a b cosh(x) sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 154 @@ -7536,7 +7684,7 @@ r1029:= a*(a^2+3*b^2)*x/(a^2-b^2)^3-b*(3*a^2+b^2)*log(a*cosh(x)+_ 2*a*b/(a^2-b^2)^2/(a+b*tanh(x)) --R --R ---R (138) +--R (2) --R 5 2 3 2 4 3 2 2 3 4 --R ((2b + 6a b )tanh(x) + (4a b + 12a b )tanh(x) + 2a b + 6a b) --R * @@ -7560,7 +7708,7 @@ r1029:= a*(a^2+3*b^2)*x/(a^2-b^2)^3-b*(3*a^2+b^2)*log(a*cosh(x)+_ a1029:= integrate(t1029,x) --R --R ---R (139) +--R (3) --R 5 4 2 3 3 2 4 4 --R (b + 2a b + 4a b + 6a b + 3a b)sinh(x) --R + @@ -7684,7 +7832,7 @@ a1029:= integrate(t1029,x) m1029:= a1029-r1029 --R --R ---R (140) +--R (4) --R 7 6 2 5 3 4 4 3 4 --R (- 2b - 4a b - 8a b - 12a b - 6a b )sinh(x) --R + @@ -8246,7 +8394,7 @@ m1029:= a1029-r1029 d1029:= D(m1029,x) --R --R ---R (141) +--R (5) --R 6 2 5 3 4 4 3 6 --R (- 2a b - 6a b - 6a b - 2a b )sinh(x) --R + @@ -8969,13 +9117,16 @@ d1029:= D(m1029,x) --R Type: Expression(Integer) --E 158 +)clear all + + --S 159 of 531 t1030:= cosh(x)*sinh(x)/(a*cosh(x)+b*sinh(x)) --R --R ---R cosh(x)sinh(x) ---R (142) --------------------- ---R b sinh(x) + a cosh(x) +--R cosh(x)sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 159 @@ -8984,7 +9135,7 @@ r1030:= a*b*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)+_ a*cosh(x)/(a^2-b^2)-b*sinh(x)/(a^2-b^2) --R --R ---R (143) +--R (2) --R +---------+ --R a sinh(x) + b cosh(x) | 2 2 --R - a b atan(---------------------) + (b sinh(x) - a cosh(x))\|- b + a @@ -9002,7 +9153,7 @@ r1030:= a*b*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(3/2)+_ a1030:= integrate(t1030,x) --R --R ---R (144) +--R (3) --R [ --R (2a b sinh(x) + 2a b cosh(x)) --R * @@ -9061,7 +9212,7 @@ a1030:= integrate(t1030,x) m1030a:= a1030.1-r1030 --R --R ---R (145) +--R (4) --R +---------+ --R | 2 2 --R (2a b sinh(x) + 2a b cosh(x))\|- b + a @@ -9105,7 +9256,7 @@ m1030a:= a1030.1-r1030 d1030a:= D(m1030a,x) --R --R ---R (146) +--R (5) --R 2 2 3 4 6 3 2 2 3 4 5 --R (a b + 2a b + a )sinh(x) + (2a b + 6a b + 6a b + 2a )cosh(x)sinh(x) --R + @@ -9194,7 +9345,7 @@ d1030a:= D(m1030a,x) m1030b:= a1030.2-r1030 --R --R ---R (147) +--R (6) --R +---------+ --R | 2 2 --R (sinh(x) + cosh(x))\|- b + a @@ -9221,7 +9372,7 @@ m1030b:= a1030.2-r1030 d1030b:= D(m1030b,x) --R --R ---R (148) +--R (7) --R 2 2 3 4 6 3 2 2 3 4 5 --R (a b + 2a b + a )sinh(x) + (2a b + 6a b + 6a b + 2a )cosh(x)sinh(x) --R + @@ -9306,14 +9457,17 @@ d1030b:= D(m1030b,x) --R Type: Expression(Integer) --E 165 +)clear all + + --S 166 of 531 t1031:= cosh(x)*sinh(x)^2/(a*cosh(x)+b*sinh(x)) --R --R ---R 2 ---R cosh(x)sinh(x) ---R (149) --------------------- ---R b sinh(x) + a cosh(x) +--R 2 +--R cosh(x)sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 166 @@ -9323,7 +9477,7 @@ r1031:= 1/2/(a^2-b^2)^2*(-a^3*x-a*b^2*x+2*a^2*b*log(a*cosh(x)+b*sinh(x))+_ a^2*b*cosh(x)^2-b^3+cosh(x)^2*b^3) --R --R ---R (150) +--R (2) --R 2 2 3 --R 2a b log(b sinh(x) + a cosh(x)) + (- a b + a )cosh(x)sinh(x) --R + @@ -9339,7 +9493,7 @@ r1031:= 1/2/(a^2-b^2)^2*(-a^3*x-a*b^2*x+2*a^2*b*log(a*cosh(x)+b*sinh(x))+_ a1031:= integrate(t1031,x) --R --R ---R (151) +--R (3) --R 2 2 2 2 2 --R (8a b sinh(x) + 16a b cosh(x)sinh(x) + 8a b cosh(x) ) --R * @@ -9379,7 +9533,7 @@ a1031:= integrate(t1031,x) m1031:= a1031-r1031 --R --R ---R (152) +--R (4) --R 2 2 2 2 2 --R (- 8a b sinh(x) - 16a b cosh(x)sinh(x) - 8a b cosh(x) ) --R * @@ -9419,22 +9573,25 @@ m1031:= a1031-r1031 d1031:= D(m1031,x) --R --R ---R 4 2 2 4 ---R sinh(x) - 2cosh(x) sinh(x) + cosh(x) - 1 ---R (153) --------------------------------------------------------------- ---R 2 2 ---R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R 4 2 2 4 +--R sinh(x) - 2cosh(x) sinh(x) + cosh(x) - 1 +--R (5) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) --R Type: Expression(Integer) --E 170 +)clear all + + --S 171 of 531 t1032:= cosh(x)*sinh(x)^3/(a*cosh(x)+b*sinh(x)) --R --R ---R 3 ---R cosh(x)sinh(x) ---R (154) --------------------- ---R b sinh(x) + a cosh(x) +--R 3 +--R cosh(x)sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 171 @@ -9445,7 +9602,7 @@ r1032:= -a^3*b*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)-_ b*sinh(x)^3/(3*a^2-3*b^2) --R --R ---R (155) +--R (2) --R 3 a sinh(x) + b cosh(x) --R - 3a b atan(---------------------) --R +---------+ @@ -9472,7 +9629,7 @@ r1032:= -a^3*b*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)-_ a1032:= integrate(t1032,x) --R --R ---R (156) +--R (3) --R [ --R 3 3 3 2 3 2 --R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) @@ -9665,7 +9822,7 @@ a1032:= integrate(t1032,x) m1032a:= a1032.1-r1032 --R --R ---R (157) +--R (4) --R 3 3 3 2 3 2 --R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) --R + @@ -9780,7 +9937,7 @@ m1032a:= a1032.1-r1032 d1032a:= D(m1032a,x) --R --R ---R (158) +--R (5) --R 2 4 4 2 6 10 --R (a b - 2a b + a )sinh(x) --R + @@ -10038,7 +10195,7 @@ d1032a:= D(m1032a,x) m1032b:= a1032.2-r1032 --R --R ---R (159) +--R (6) --R 3 3 3 2 3 2 --R 48a b sinh(x) + 144a b cosh(x)sinh(x) + 144a b cosh(x) sinh(x) --R + @@ -10136,7 +10293,7 @@ m1032b:= a1032.2-r1032 d1032b:= D(m1032b,x) --R --R ---R (160) +--R (7) --R 2 4 4 2 6 10 --R (a b - 2a b + a )sinh(x) --R + @@ -10390,14 +10547,17 @@ d1032b:= D(m1032b,x) --R Type: Expression(Integer) --E 177 +)clear all + + --S 178 of 531 t1033:= sinh(x)*cosh(x)^2/(a*cosh(x)+b*sinh(x)) --R --R ---R 2 ---R cosh(x) sinh(x) ---R (161) --------------------- ---R b sinh(x) + a cosh(x) +--R 2 +--R cosh(x) sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 178 @@ -10407,7 +10567,7 @@ r1033:= -1/2*(-b^3*x-a^2*b*x+2*a*b^2*log(a*cosh(x)+b*sinh(x))+_ b^2*a+cosh(x)^2*b^2*a)/(a^2-b^2)^2 --R --R ---R (162) +--R (2) --R 2 3 2 --R - 2a b log(b sinh(x) + a cosh(x)) + (b - a b)cosh(x)sinh(x) --R + @@ -10423,7 +10583,7 @@ r1033:= -1/2*(-b^3*x-a^2*b*x+2*a*b^2*log(a*cosh(x)+b*sinh(x))+_ a1033:= integrate(t1033,x) --R --R ---R (163) +--R (3) --R 2 2 2 2 2 --R (- 8a b sinh(x) - 16a b cosh(x)sinh(x) - 8a b cosh(x) ) --R * @@ -10463,7 +10623,7 @@ a1033:= integrate(t1033,x) m1033:= a1033-r1033 --R --R ---R (164) +--R (4) --R 2 2 2 2 2 --R (8a b sinh(x) + 16a b cosh(x)sinh(x) + 8a b cosh(x) ) --R * @@ -10503,22 +10663,25 @@ m1033:= a1033-r1033 d1033:= D(m1033,x) --R --R ---R 4 2 2 4 ---R - sinh(x) + 2cosh(x) sinh(x) - cosh(x) + 1 ---R (165) --------------------------------------------------------------- ---R 2 2 ---R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) +--R 4 2 2 4 +--R - sinh(x) + 2cosh(x) sinh(x) - cosh(x) + 1 +--R (5) --------------------------------------------------------------- +--R 2 2 +--R (4b - 4a)sinh(x) + (8b - 8a)cosh(x)sinh(x) + (4b - 4a)cosh(x) --R Type: Expression(Integer) --E 182 +)clear all + + --S 183 of 531 t1034:= sinh(x)*cosh(x)^3/(a*cosh(x)+b*sinh(x)) --R --R ---R 3 ---R cosh(x) sinh(x) ---R (166) --------------------- ---R b sinh(x) + a cosh(x) +--R 3 +--R cosh(x) sinh(x) +--R (1) --------------------- +--R b sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 183 @@ -10528,7 +10691,7 @@ r1034:= -a*b^3*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)-_ a^2*b*sinh(x)/(a^2-b^2)^2-b*sinh(x)/(a^2-b^2)-b*sinh(x)^3/(3*a^2-3*b^2) --R --R ---R (167) +--R (2) --R 3 a sinh(x) + b cosh(x) --R - 3a b atan(---------------------) --R +---------+ @@ -10555,7 +10718,7 @@ r1034:= -a*b^3*atan((b*cosh(x)+a*sinh(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(5/2)-_ a1034:= integrate(t1034,x) --R --R ---R (168) +--R (3) --R [ --R 3 3 3 2 3 2 --R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) @@ -10748,7 +10911,7 @@ a1034:= integrate(t1034,x) m1034a:= a1034.1-r1034 --R --R ---R (169) +--R (4) --R 3 3 3 2 3 2 --R 24a b sinh(x) + 72a b cosh(x)sinh(x) + 72a b cosh(x) sinh(x) --R + @@ -10863,7 +11026,7 @@ m1034a:= a1034.1-r1034 d1034a:= D(m1034a,x) --R --R ---R (170) +--R (5) --R 2 4 4 2 6 10 --R (a b - 2a b + a )sinh(x) --R + @@ -11121,7 +11284,7 @@ d1034a:= D(m1034a,x) m1034b:= a1034.2-r1034 --R --R ---R (171) +--R (6) --R 3 3 3 2 3 2 --R 48a b sinh(x) + 144a b cosh(x)sinh(x) + 144a b cosh(x) sinh(x) --R + @@ -11219,7 +11382,7 @@ m1034b:= a1034.2-r1034 d1034b:= D(m1034b,x) --R --R ---R (172) +--R (7) --R 2 4 4 2 6 10 --R (a b - 2a b + a )sinh(x) --R + @@ -11473,13 +11636,16 @@ d1034b:= D(m1034b,x) --R Type: Expression(Integer) --E 189 +)clear all + + --S 190 of 531 t1035:= (A+C*sinh(x))/(a+b*cosh(x)+c*sinh(x)) --R --R ---R C sinh(x) + A ---R (173) ------------------------- ---R c sinh(x) + b cosh(x) + a +--R C sinh(x) + A +--R (1) ------------------------- +--R c sinh(x) + b cosh(x) + a --R Type: Expression(Integer) --E 190 @@ -11489,7 +11655,7 @@ r1035:= -c*C*x/(b^2-c^2)-2*(A+a*c*C/(b^2-c^2))*_ (a^2-b^2+c^2)^(1/2)+b*C*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2) --R --R ---R (174) +--R (2) --R +------------+ --R | 2 2 2 --R - C b\|c - b + a log(c sinh(x) + b cosh(x) + a) @@ -11512,7 +11678,7 @@ r1035:= -c*C*x/(b^2-c^2)-2*(A+a*c*C/(b^2-c^2))*_ a1035:= integrate(t1035,x) --R --R ---R (175) +--R (3) --R [ --R 2 2 --R (- A c + C a c + A b ) @@ -11593,7 +11759,7 @@ a1035:= integrate(t1035,x) m1035a:= a1035.1-r1035 --R --R ---R (176) +--R (4) --R 2 2 --R (- A c + C a c + A b ) --R * @@ -11656,7 +11822,7 @@ m1035a:= a1035.1-r1035 d1035a:= D(m1035a,x) --R --R ---R (177) +--R (5) --R 3 2 2 3 2 --R (A c + (A b - C a)c + (- A b - C a b)c - A b )sinh(x) --R + @@ -11778,7 +11944,7 @@ d1035a:= D(m1035a,x) m1035b:= a1035.2-r1035 --R --R ---R (178) +--R (6) --R +--------------+ +------------+ --R | 2 2 2 | 2 2 2 --R C b\|- c + b - a \|c - b + a log(c sinh(x) + b cosh(x) + a) @@ -11821,7 +11987,7 @@ m1035b:= a1035.2-r1035 d1035b:= D(m1035b,x) --R --R ---R (179) +--R (7) --R 3 2 2 3 2 --R (A c + (A b - C a)c + (- A b - C a b)c - A b )sinh(x) --R + @@ -11939,11 +12105,14 @@ d1035b:= D(m1035b,x) --R Type: Expression(Integer) --E 196 +)clear all + + --S 197 of 531 t1036:= (A+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^2 --R --R ---R (180) +--R (1) --R C sinh(x) + A --R -------------------------------------------------------------------------- --R 2 2 2 2 2 @@ -11957,7 +12126,7 @@ r1036:= -2*(a*A+c*C)*atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ (a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x)) --R --R ---R (181) +--R (2) --R 2 --R (- 2C c - 2A a c)sinh(x) + (- 2C b c - 2A a b)cosh(x) - 2C a c --R + @@ -11992,7 +12161,7 @@ r1036:= -2*(a*A+c*C)*atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ a1036:= integrate(t1036,x) --R --R ---R (182) +--R (3) --R [ --R 3 2 2 2 2 --R (C c + (2C b + A a)c + (C b + 2A a b)c + A a b )sinh(x) @@ -12163,7 +12332,7 @@ a1036:= integrate(t1036,x) m1036a:= a1036.1-r1036 --R --R ---R (183) +--R (4) --R 4 3 2 2 2 3 --R (C c + (2C b + A a)c + (C b + 2A a b)c + A a b c)sinh(x) --R + @@ -12444,7 +12613,7 @@ m1036a:= a1036.1-r1036 m1036b:= a1036.2-r1036 --R --R ---R (184) +--R (5) --R 4 3 2 2 2 3 --R (2C c + (4C b + 2A a)c + (2C b + 4A a b)c + 2A a b c)sinh(x) --R + @@ -12715,11 +12884,14 @@ m1036b:= a1036.2-r1036 --d1036b:= D(m1036b,x) --E 203 +)clear all + + --S 204 of 531 t1037:= (A+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^3 --R --R ---R (185) +--R (1) --R C sinh(x) + A --R / --R 3 3 2 2 2 @@ -12741,7 +12913,7 @@ r1037:= -(2*a^2*A+A*b^2-c*(A*c-3*a*C))*atanh((c-(a-b)*tanh(1/2*x))/_ sinh(x))/(a^2-b^2+c^2)^2/(a+b*cosh(x)+c*sinh(x)) --R --R ---R (186) +--R (2) --R 4 3 2 2 2 2 --R (2A c - 6C a c + (- 2A b - 4A a )c )sinh(x) --R + @@ -12824,7 +12996,7 @@ r1037:= -(2*a^2*A+A*b^2-c*(A*c-3*a*C))*atanh((c-(a-b)*tanh(1/2*x))/_ a1037:= integrate(t1037,x) --R --R ---R (187) +--R (3) --R [ --R 5 4 2 2 3 --R A c + (3A b - 3C a)c + (2A b - 9C a b - 2A a )c @@ -13728,13 +13900,16 @@ a1037:= integrate(t1037,x) --d1037b:= D(m1037b,x) --E 210 +)clear all + + --S 211 of 531 t1038:= (A+B*cosh(x))/(a+b*cosh(x)+c*sinh(x)) --R --R ---R B cosh(x) + A ---R (188) ------------------------- ---R c sinh(x) + b cosh(x) + a +--R B cosh(x) + A +--R (1) ------------------------- +--R c sinh(x) + b cosh(x) + a --R Type: Expression(Integer) --E 211 @@ -13744,7 +13919,7 @@ r1038:= b*B*x/(b^2-c^2)-2*(A-a*b*B/(b^2-c^2))*_ (a^2-b^2+c^2)^(1/2)-B*c*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2) --R --R ---R (189) +--R (2) --R +------------+ --R | 2 2 2 --R B c\|c - b + a log(c sinh(x) + b cosh(x) + a) @@ -13767,7 +13942,7 @@ r1038:= b*B*x/(b^2-c^2)-2*(A-a*b*B/(b^2-c^2))*_ a1038:= integrate(t1038,x) --R --R ---R (190) +--R (3) --R [ --R 2 2 --R (A c - A b + B a b) @@ -13848,7 +14023,7 @@ a1038:= integrate(t1038,x) m1038a:= a1038.1-r1038 --R --R ---R (191) +--R (4) --R 2 2 --R (A c - A b + B a b) --R * @@ -13911,7 +14086,7 @@ m1038a:= a1038.1-r1038 d1038a:= D(m1038a,x) --R --R ---R (192) +--R (5) --R 3 2 2 3 2 2 --R (A c + A b c + (- A b + B a b)c - A b + B a b )sinh(x) --R + @@ -14036,7 +14211,7 @@ d1038a:= D(m1038a,x) m1038b:= a1038.2-r1038 --R --R ---R (193) +--R (6) --R +--------------+ +------------+ --R | 2 2 2 | 2 2 2 --R - B c\|- c + b - a \|c - b + a log(c sinh(x) + b cosh(x) + a) @@ -14079,7 +14254,7 @@ m1038b:= a1038.2-r1038 d1038b:= D(m1038b,x) --R --R ---R (194) +--R (7) --R 3 2 2 3 2 2 --R (A c + A b c + (- A b + B a b)c - A b + B a b )sinh(x) --R + @@ -14200,11 +14375,14 @@ d1038b:= D(m1038b,x) --R Type: Expression(Integer) --E 217 +)clear all + + --S 218 of 531 t1039:= (A+B*cosh(x))/(a+b*cosh(x)+c*sinh(x))^2 --R --R ---R (195) +--R (1) --R B cosh(x) + A --R -------------------------------------------------------------------------- --R 2 2 2 2 2 @@ -14218,7 +14396,7 @@ r1039:= -2*(a*A-b*B)*atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ (a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x)) --R --R ---R (196) +--R (2) --R 2 2 --R ((2B b - 2A a)c sinh(x) + (2B b - 2A a b)cosh(x) + 2B a b - 2A a ) --R * @@ -14250,7 +14428,7 @@ r1039:= -2*(a*A-b*B)*atanh((c-(a-b)*tanh(1/2*x))/(a^2-b^2+c^2)^(1/2))/_ a1039:= integrate(t1039,x) --R --R ---R (197) +--R (3) --R [ --R 2 2 3 2 2 --R ((B b - A a)c + (2B b - 2A a b)c + B b - A a b )sinh(x) @@ -14413,7 +14591,7 @@ a1039:= integrate(t1039,x) m1039a:= a1039.1-r1039 --R --R ---R (198) +--R (4) --R 3 2 2 3 2 3 --R ((B b - A a)c + (2B b - 2A a b)c + (B b - A a b )c)sinh(x) --R + @@ -14700,7 +14878,7 @@ m1039a:= a1039.1-r1039 m1039b:= a1039.2-r1039 --R --R ---R (199) +--R (5) --R 3 2 2 3 2 --R ((- 2B b + 2A a)c + (- 4B b + 4A a b)c + (- 2B b + 2A a b )c) --R * @@ -14968,11 +15146,14 @@ m1039b:= a1039.2-r1039 --d1039b:= D(m1039b,x) --E 224 +)clear all + + --S 225 of 531 t1040:= (A+B*cosh(x))/(a+b*cosh(x)+c*sinh(x))^3 --R --R ---R (200) +--R (1) --R B cosh(x) + A --R / --R 3 3 2 2 2 @@ -14994,7 +15175,7 @@ r1040:= -(2*a^2*A+b*(A*b-3*a*B)-A*c^2)*atanh((c-(a-b)*tanh(1/2*x))/_ sinh(x))/(a^2-b^2+c^2)^2/(a+b*cosh(x)+c*sinh(x)) --R --R ---R (201) +--R (2) --R 4 2 2 2 2 --R (2A c + (- 2A b + 6B a b - 4A a )c )sinh(x) --R + @@ -15074,7 +15255,7 @@ r1040:= -(2*a^2*A+b*(A*b-3*a*B)-A*c^2)*atanh((c-(a-b)*tanh(1/2*x))/_ a1040:= integrate(t1040,x) --R --R ---R (202) +--R (3) --R [ --R 5 4 2 2 3 --R A c + 3A b c + (2A b + 3B a b - 2A a )c @@ -16008,13 +16189,16 @@ a1040:= integrate(t1040,x) --d1040b:= D(m1040b,x) --E 231 +)clear all + + --S 232 of 531 t1041:= (A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x)) --R --R ---R C sinh(x) + B cosh(x) + A ---R (203) ------------------------- ---R c sinh(x) + b cosh(x) + a +--R C sinh(x) + B cosh(x) + A +--R (1) ------------------------- +--R c sinh(x) + b cosh(x) + a --R Type: Expression(Integer) --E 232 @@ -16024,7 +16208,7 @@ r1041:= (b*B-c*C)*x/(b^2-c^2)-2*(A-a*(b*B-c*C)/(b^2-c^2))*_ (a^2-b^2+c^2)^(1/2)-(B*c-b*C)*log(a+b*cosh(x)+c*sinh(x))/(b^2-c^2) --R --R ---R (204) +--R (2) --R +------------+ --R | 2 2 2 --R (B c - C b)\|c - b + a log(c sinh(x) + b cosh(x) + a) @@ -16051,7 +16235,7 @@ r1041:= (b*B-c*C)*x/(b^2-c^2)-2*(A-a*(b*B-c*C)/(b^2-c^2))*_ a1041:= integrate(t1041,x) --R --R ---R (205) +--R (3) --R [ --R 2 2 --R (- A c + C a c + A b - B a b) @@ -16132,7 +16316,7 @@ a1041:= integrate(t1041,x) m1041a:= a1041.1-r1041 --R --R ---R (206) +--R (4) --R 2 2 --R (- A c + C a c + A b - B a b) --R * @@ -16199,7 +16383,7 @@ m1041a:= a1041.1-r1041 d1041a:= D(m1041a,x) --R --R ---R (207) +--R (5) --R 3 2 2 3 2 --R (A c + (A b - C a)c + (- A b + (- C + B)a b)c - A b + B a b ) --R * @@ -16340,7 +16524,7 @@ d1041a:= D(m1041a,x) m1041b:= a1041.2-r1041 --R --R ---R (208) +--R (6) --R +--------------+ +------------+ --R | 2 2 2 | 2 2 2 --R (- B c + C b)\|- c + b - a \|c - b + a @@ -16392,7 +16576,7 @@ m1041b:= a1041.2-r1041 d1041b:= D(m1041b,x) --R --R ---R (209) +--R (7) --R 3 2 2 3 2 --R (A c + (A b - C a)c + (- A b + (- C + B)a b)c - A b + B a b ) --R * @@ -16529,11 +16713,14 @@ d1041b:= D(m1041b,x) --R Type: Expression(Integer) --E 238 +)clear all + + --S 239 of 531 t1042:= (A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^2 --R --R ---R (210) +--R (1) --R C sinh(x) + B cosh(x) + A --R -------------------------------------------------------------------------- --R 2 2 2 2 2 @@ -16547,7 +16734,7 @@ r1042:= -2*(a*A-b*B+c*C)*atanh((c-(a-b)*tanh(1/2*x))/_ cosh(x)+(A*b-a*B)*sinh(x))/(a^2-b^2+c^2)/(a+b*cosh(x)+c*sinh(x)) --R --R ---R (211) +--R (2) --R 2 --R (- 2C c + (2B b - 2A a)c)sinh(x) --R + @@ -16582,7 +16769,7 @@ r1042:= -2*(a*A-b*B+c*C)*atanh((c-(a-b)*tanh(1/2*x))/_ a1042:= integrate(t1042,x) --R --R ---R (212) +--R (3) --R [ --R 3 2 2 3 --R C c + ((2C - B)b + A a)c + ((C - 2B)b + 2A a b)c - B b @@ -16787,7 +16974,7 @@ a1042:= integrate(t1042,x) m1042a:= a1042.1-r1042 --R --R ---R (213) +--R (4) --R 4 3 2 2 --R C c + ((2C - B)b + A a)c + ((C - 2B)b + 2A a b)c --R + @@ -17133,7 +17320,7 @@ m1042a:= a1042.1-r1042 m1042b:= a1042.2-r1042 --R --R ---R (214) +--R (5) --R 4 3 2 2 --R 2C c + ((4C - 2B)b + 2A a)c + ((2C - 4B)b + 4A a b)c --R + @@ -17463,11 +17650,14 @@ m1042b:= a1042.2-r1042 --d1042b:= D(m1042b,x) --E 245 +)clear all + + --S 246 of 531 t1043:= (A+B*cosh(x)+C*sinh(x))/(a+b*cosh(x)+c*sinh(x))^3 --R --R ---R (215) +--R (1) --R C sinh(x) + B cosh(x) + A --R / --R 3 3 2 2 2 @@ -17491,7 +17681,7 @@ r1043:= -(2*a^2*A+b*(A*b-3*a*B)-c*(A*c-3*a*C))*_ (a+b*cosh(x)+c*sinh(x)) --R --R ---R (216) +--R (2) --R 4 3 2 2 2 2 --R (2A c - 6C a c + (- 2A b + 6B a b - 4A a )c )sinh(x) --R + @@ -17579,7 +17769,7 @@ r1043:= -(2*a^2*A+b*(A*b-3*a*B)-c*(A*c-3*a*C))*_ a1043:= integrate(t1043,x) --R --R ---R (217) +--R (3) --R [ --R 5 4 2 2 3 --R A c + (3A b - 3C a)c + (2A b + (- 9C + 3B)a b - 2A a )c @@ -18612,7 +18802,7 @@ a1043:= integrate(t1043,x) m1043a:= a1043.1-r1043 --R --R ---R (218) +--R (4) --R 7 6 2 2 5 --R A c + (3A b - 3C a)c + (2A b + (- 9C + 3B)a b - 2A a )c --R + @@ -21184,7 +21374,7 @@ m1043a:= a1043.1-r1043 m1043b:= a1043.2-r1043 --R --R ---R (219) +--R (5) --R 7 6 2 2 5 --R - 2A c + (- 6A b + 6C a)c + (- 4A b + (18C - 6B)a b + 4A a )c --R + @@ -23749,14 +23939,17 @@ m1043b:= a1043.2-r1043 --d1043b:= D(m1043b,x) --E 252 +)clear all + + --S 253 of 531 t1044:= 1/(a+b*sinh(x)+c*sinh(x)^2) --R --R ---R 1 ---R (220) -------------------------- ---R 2 ---R c sinh(x) + b sinh(x) + a +--R 1 +--R (1) -------------------------- +--R 2 +--R c sinh(x) + b sinh(x) + a --R Type: Expression(Integer) --E 253 @@ -23769,7 +23962,7 @@ r1044:= -4*c*atanh((2*c-(b-(b^2-4*a*c)^(1/2))*tanh(1/2*x))/_ (4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2) --R --R ---R (221) +--R (2) --R - --R +-----------------------------------+ --R | +-----------+ @@ -23818,7 +24011,7 @@ r1044:= -4*c*atanh((2*c-(b-(b^2-4*a*c)^(1/2))*tanh(1/2*x))/_ a1044:= integrate(t1044,x) --R --R ---R (222) +--R (3) --R ROOT --R 3 2 2 2 2 3 4 2 2 --R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) @@ -24224,7 +24417,7 @@ a1044:= integrate(t1044,x) m1044:= a1044-r1044 --R --R ---R (223) +--R (4) --R +-------------------------------------+ --R +-----------+ | +-----------+ --R | 2 | | 2 2 2 @@ -24716,7 +24909,7 @@ m1044:= a1044-r1044 d1044:= D(m1044,x) --R --R ---R (224) +--R (5) --R 4 3 --R - c sinh(x) + (- 4c cosh(x) - 2b)sinh(x) --R + @@ -24864,14 +25057,17 @@ d1044:= D(m1044,x) --R Type: Expression(Integer) --E 257 +)clear all + + --S 258 of 531 t1045:= sinh(x)/(a+b*sinh(x)+c*sinh(x)^2) --R --R ---R sinh(x) ---R (225) -------------------------- ---R 2 ---R c sinh(x) + b sinh(x) + a +--R sinh(x) +--R (1) -------------------------- +--R 2 +--R c sinh(x) + b sinh(x) + a --R Type: Expression(Integer) --E 258 @@ -24883,7 +25079,7 @@ r1045:= -2*(1-b/(b^2-4*a*c)^(1/2))*atanh((2*c-(b-(b^2-4*a*c)^(1/2))*_ (b+(b^2-4*a*c)^(1/2))^2)^(1/2))/(4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2) --R --R ---R (226) +--R (2) --R +-----------------------------------+ --R +-----------+ | +-----------+ --R | 2 | | 2 2 2 @@ -24930,7 +25126,7 @@ r1045:= -2*(1-b/(b^2-4*a*c)^(1/2))*atanh((2*c-(b-(b^2-4*a*c)^(1/2))*_ a1045:= integrate(t1045,x) --R --R ---R (227) +--R (3) --R ROOT --R 3 2 2 2 2 3 4 2 2 --R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) @@ -25336,7 +25532,7 @@ a1045:= integrate(t1045,x) m1045:= a1045-r1045 --R --R ---R (228) +--R (4) --R +-------------------------------------+ --R +-----------+ | +-----------+ --R | 2 | | 2 2 2 @@ -25828,7 +26024,7 @@ m1045:= a1045-r1045 d1045:= D(m1045,x) --R --R ---R (229) +--R (5) --R 3 2 2 --R 2a sinh(x) + 6a cosh(x)sinh(x) + (6a cosh(x) - 2a)sinh(x) --R + @@ -25984,15 +26180,18 @@ d1045:= D(m1045,x) --R Type: Expression(Integer) --E 262 +)clear all + + --S 263 of 531 t1046:= sinh(x)^2/(a+b*sinh(x)+c*sinh(x)^2) --R --R ---R 2 ---R sinh(x) ---R (230) -------------------------- ---R 2 ---R c sinh(x) + b sinh(x) + a +--R 2 +--R sinh(x) +--R (1) -------------------------- +--R 2 +--R c sinh(x) + b sinh(x) + a --R Type: Expression(Integer) --E 263 @@ -26006,7 +26205,7 @@ r1046:= x/c+2*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ (4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2) --R --R ---R (231) +--R (2) --R +-----------------------------------+ --R +-----------+ | +-----------+ --R | 2 2 | | 2 2 2 @@ -26067,7 +26266,7 @@ r1046:= x/c+2*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ a1046:= integrate(t1046,x) --R --R ---R (232) +--R (3) --R - --R c --R * @@ -26506,7 +26705,7 @@ a1046:= integrate(t1046,x) m1046:= a1046-r1046 --R --R ---R (233) +--R (4) --R - --R +-------------------------------------+ --R +-----------+ | +-----------+ @@ -27021,7 +27220,7 @@ m1046:= a1046-r1046 d1046:= D(m1046,x) --R --R ---R (234) +--R (5) --R 4 3 2 2 --R a sinh(x) + 4a cosh(x)sinh(x) + (6a cosh(x) - 2a)sinh(x) --R + @@ -27172,15 +27371,18 @@ d1046:= D(m1046,x) --R Type: Expression(Integer) --E 267 +)clear all + + --S 268 of 531 t1047:= sinh(x)^3/(a+b*sinh(x)+c*sinh(x)^2) --R --R ---R 3 ---R sinh(x) ---R (235) -------------------------- ---R 2 ---R c sinh(x) + b sinh(x) + a +--R 3 +--R sinh(x) +--R (1) -------------------------- +--R 2 +--R c sinh(x) + b sinh(x) + a --R Type: Expression(Integer) --E 268 @@ -27194,7 +27396,7 @@ r1047:= -b*x/c^2-2*(b^2-a*c-b*(b^2-3*a*c)/(b^2-4*a*c)^(1/2))*_ (4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2)+cosh(x)/c --R --R ---R (236) +--R (2) --R +-----------+ --R 2 | 2 3 --R ((2a c - 2b )\|- 4a c + b - 6a b c + 2b ) @@ -27259,7 +27461,7 @@ r1047:= -b*x/c^2-2*(b^2-a*c-b*(b^2-3*a*c)/(b^2-4*a*c)^(1/2))*_ a1047:= integrate(t1047,x) --R --R ---R (237) +--R (3) --R 2 2 --R (- c sinh(x) - c cosh(x)) --R * @@ -27816,7 +28018,7 @@ a1047:= integrate(t1047,x) m1047:= a1047-r1047 --R --R ---R (238) +--R (4) --R +-----------+ --R 2 2 | 2 --R (- c sinh(x) - c cosh(x))\|- 4a c + b @@ -28483,7 +28685,7 @@ m1047:= a1047-r1047 d1047:= D(m1047,x) --R --R ---R (239) +--R (5) --R 6 5 --R - a c sinh(x) + (- 4a c cosh(x) - 4a b)sinh(x) --R + @@ -28856,14 +29058,17 @@ d1047:= D(m1047,x) --R Type: Expression(Integer) --E 272 +)clear all + + --S 273 of 531 t1048:= (a+b*sinh(x))/(b^2-2*a*b*sinh(x)+a^2*sinh(x)^2) --R --R ---R b sinh(x) + a ---R (240) ------------------------------ ---R 2 2 2 ---R a sinh(x) - 2a b sinh(x) + b +--R b sinh(x) + a +--R (1) ------------------------------ +--R 2 2 2 +--R a sinh(x) - 2a b sinh(x) + b --R Type: Expression(Integer) --E 273 @@ -28871,9 +29076,9 @@ t1048:= (a+b*sinh(x))/(b^2-2*a*b*sinh(x)+a^2*sinh(x)^2) r1048:= cosh(x)/(b-a*sinh(x)) --R --R ---R cosh(x) ---R (241) - ------------- ---R a sinh(x) - b +--R cosh(x) +--R (2) - ------------- +--R a sinh(x) - b --R Type: Expression(Integer) --E 274 @@ -28881,7 +29086,7 @@ r1048:= cosh(x)/(b-a*sinh(x)) a1048:= integrate(t1048,x) --R --R ---R (242) +--R (3) --R - 2b sinh(x) - 2b cosh(x) - 2a --R ------------------------------------------------------------------------ --R 2 2 2 2 2 2 @@ -28893,7 +29098,7 @@ a1048:= integrate(t1048,x) m1048:= a1048-r1048 --R --R ---R (243) +--R (4) --R 2 2 --R (a cosh(x) - 2a b)sinh(x) --R + @@ -28918,7 +29123,7 @@ m1048:= a1048-r1048 d1048:= D(m1048,x) --R --R ---R (244) +--R (5) --R 3 6 3 2 5 --R a sinh(x) + (4a cosh(x) - 3a b)sinh(x) --R + @@ -28985,14 +29190,17 @@ d1048:= D(m1048,x) --R Type: Expression(Integer) --E 277 +)clear all + + --S 278 of 531 t1049:= (d+e*sinh(x))/(a+b*sinh(x)+c*sinh(x)^2) --R --R ---R e sinh(x) + d ---R (245) -------------------------- ---R 2 ---R c sinh(x) + b sinh(x) + a +--R e sinh(x) + d +--R (1) -------------------------- +--R 2 +--R c sinh(x) + b sinh(x) + a --R Type: Expression(Integer) --E 278 @@ -29006,7 +29214,7 @@ r1049:= -2*(e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ (4*c^2+(b+(b^2-4*a*c)^(1/2))^2)^(1/2) --R --R ---R (246) +--R (2) --R +-----------+ --R | 2 --R (- 2e\|- 4a c + b + 2b e - 4c d) @@ -29061,7 +29269,7 @@ r1049:= -2*(e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ a1049:= integrate(t1049,x) --R --R ---R (247) +--R (3) --R ROOT --R 3 2 2 2 2 3 4 2 2 --R (8a c + (- 2b - 16a )c + (12a b + 8a )c - 2b - 2a b ) @@ -29785,7 +29993,7 @@ a1049:= integrate(t1049,x) m1049:= a1049-r1049 --R --R ---R (248) +--R (4) --R +-------------------------------------+ --R +-----------+ | +-----------+ --R | 2 | | 2 2 2 @@ -30591,7 +30799,7 @@ m1049:= a1049-r1049 d1049:= D(m1049,x) --R --R ---R (249) +--R (5) --R 4 3 --R - c d sinh(x) + (- 4c d cosh(x) + 2a e - 2b d)sinh(x) --R + @@ -30782,14 +30990,17 @@ d1049:= D(m1049,x) --R Type: Expression(Integer) --E 282 +)clear all + + --S 283 of 531 t1050:= 1/(a+b*cosh(x)+c*cosh(x)^2) --R --R ---R 1 ---R (250) -------------------------- ---R 2 ---R c cosh(x) + b cosh(x) + a +--R 1 +--R (1) -------------------------- +--R 2 +--R c cosh(x) + b cosh(x) + a --R Type: Expression(Integer) --E 283 @@ -30802,7 +31013,7 @@ r1050:= -2*2^(1/2)*c*atan(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*_ (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) --R --R ---R (251) +--R (2) --R +---------------------------------+ --R | +-----------+ --R | | 2 2 2 @@ -30849,7 +31060,7 @@ r1050:= -2*2^(1/2)*c*atan(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*_ a1050:= integrate(t1050,x) --R --R ---R (252) +--R (3) --R - --R ROOT --R 3 2 2 2 2 3 4 @@ -31255,7 +31466,7 @@ a1050:= integrate(t1050,x) m1050:= a1050-r1050 --R --R ---R (253) +--R (4) --R - --R +-------------------------------------+ --R +-----------+ | +-----------+ @@ -31749,7 +31960,7 @@ m1050:= a1050-r1050 d1050:= D(m1050,x) --R --R ---R (254) +--R (5) --R 4 3 --R - c sinh(x) + (- 4c cosh(x) - 2b)sinh(x) --R + @@ -31893,14 +32104,17 @@ d1050:= D(m1050,x) --R Type: Expression(Integer) --E 287 +)clear all + + --S 288 of 531 t1051:= cosh(x)/(a+b*cosh(x)+c*cosh(x)^2) --R --R ---R cosh(x) ---R (255) -------------------------- ---R 2 ---R c cosh(x) + b cosh(x) + a +--R cosh(x) +--R (1) -------------------------- +--R 2 +--R c cosh(x) + b cosh(x) + a --R Type: Expression(Integer) --E 288 @@ -31914,7 +32128,7 @@ r1051:= -2^(1/2)*(1-b/(b^2-4*a*c)^(1/2))*_ (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) --R --R ---R (256) +--R (2) --R +---------------------------------+ --R +-----------+ | +-----------+ --R | 2 | | 2 2 2 @@ -31961,7 +32175,7 @@ r1051:= -2^(1/2)*(1-b/(b^2-4*a*c)^(1/2))*_ a1051:= integrate(t1051,x) --R --R ---R (257) +--R (3) --R ROOT --R 3 2 2 2 2 3 4 2 2 --R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) @@ -32367,7 +32581,7 @@ a1051:= integrate(t1051,x) m1051:= a1051-r1051 --R --R ---R (258) +--R (4) --R +-------------------------------------+ --R +-----------+ | +-----------+ --R | 2 | | 2 2 2 @@ -32863,7 +33077,7 @@ m1051:= a1051-r1051 d1051:= D(m1051,x) --R --R ---R (259) +--R (5) --R 4 3 --R c sinh(x) + (4c cosh(x) + 2c + 2a)sinh(x) --R + @@ -33007,15 +33221,18 @@ d1051:= D(m1051,x) --R Type: Expression(Integer) --E 292 +)clear all + + --S 293 of 531 t1052:= cosh(x)^2/(a+b*cosh(x)+c*cosh(x)^2) --R --R ---R 2 ---R cosh(x) ---R (260) -------------------------- ---R 2 ---R c cosh(x) + b cosh(x) + a +--R 2 +--R cosh(x) +--R (1) -------------------------- +--R 2 +--R c cosh(x) + b cosh(x) + a --R Type: Expression(Integer) --E 293 @@ -33029,7 +33246,7 @@ r1052:= x/c+2^(1/2)*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) --R --R ---R (261) +--R (2) --R +---------------------------------+ --R +-----------+ | +-----------+ --R | 2 2 | | 2 2 2 @@ -33090,7 +33307,7 @@ r1052:= x/c+2^(1/2)*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ a1052:= integrate(t1052,x) --R --R ---R (262) +--R (3) --R - --R c --R * @@ -33529,7 +33746,7 @@ a1052:= integrate(t1052,x) m1052:= a1052-r1052 --R --R ---R (263) +--R (4) --R - --R +-------------------------------------+ --R +-----------+ | +-----------+ @@ -34048,7 +34265,7 @@ m1052:= a1052-r1052 d1052:= D(m1052,x) --R --R ---R (264) +--R (5) --R 4 3 --R (- b + a)sinh(x) + ((- 4b + 4a)cosh(x) - 2b)sinh(x) --R + @@ -34194,15 +34411,18 @@ d1052:= D(m1052,x) --R Type: Expression(Integer) --E 297 +)clear all + + --S 298 of 531 t1053:= cosh(x)^3/(a+b*cosh(x)+c*cosh(x)^2) --R --R ---R 3 ---R cosh(x) ---R (265) -------------------------- ---R 2 ---R c cosh(x) + b cosh(x) + a +--R 3 +--R cosh(x) +--R (1) -------------------------- +--R 2 +--R c cosh(x) + b cosh(x) + a --R Type: Expression(Integer) --E 298 @@ -34216,7 +34436,7 @@ r1053:= -b*x/c^2-2^(1/2)*(b^2-a*c-b*(b^2-3*a*c)/(b^2-4*a*c)^(1/2))*_ (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2)+sinh(x)/c --R --R ---R (266) +--R (2) --R +-----------+ --R 2 | 2 3 --R ((2a c - 2b )\|- 4a c + b + 6a b c - 2b ) @@ -34281,7 +34501,7 @@ r1053:= -b*x/c^2-2^(1/2)*(b^2-a*c-b*(b^2-3*a*c)/(b^2-4*a*c)^(1/2))*_ a1053:= integrate(t1053,x) --R --R ---R (267) +--R (3) --R 2 2 --R (- c sinh(x) - c cosh(x)) --R * @@ -34838,7 +35058,7 @@ a1053:= integrate(t1053,x) m1053:= a1053-r1053 --R --R ---R (268) +--R (4) --R +-----------+ --R 2 2 | 2 --R (- c sinh(x) - c cosh(x))\|- 4a c + b @@ -35505,7 +35725,7 @@ m1053:= a1053-r1053 d1053:= D(m1053,x) --R --R ---R (269) +--R (5) --R 2 6 --R (c + (- b + a)c)sinh(x) --R + @@ -35860,14 +36080,17 @@ d1053:= D(m1053,x) --R Type: Expression(Integer) --E 302 +)clear all + + --S 303 of 531 t1054:= (d+e*cosh(x))/(a+b*cosh(x)+c*cosh(x)^2) --R --R ---R e cosh(x) + d ---R (270) -------------------------- ---R 2 ---R c cosh(x) + b cosh(x) + a +--R e cosh(x) + d +--R (1) -------------------------- +--R 2 +--R c cosh(x) + b cosh(x) + a --R Type: Expression(Integer) --E 303 @@ -35881,7 +36104,7 @@ r1054:= -2^(1/2)*(e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) --R --R ---R (271) +--R (2) --R +---------------------------------+ --R +-----------+ | +-----------+ --R | 2 | | 2 2 2 @@ -35932,7 +36155,7 @@ r1054:= -2^(1/2)*(e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ a1054:= integrate(t1054,x) --R --R ---R (272) +--R (3) --R ROOT --R 3 2 2 2 2 3 4 2 2 --R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) @@ -36644,7 +36867,7 @@ a1054:= integrate(t1054,x) m1054:= a1054-r1054 --R --R ---R (273) +--R (4) --R +-------------------------------------+ --R +-----------+ | +-----------+ --R | 2 | | 2 2 2 @@ -37438,7 +37661,7 @@ m1054:= a1054-r1054 d1054:= D(m1054,x) --R --R ---R (274) +--R (5) --R 4 --R (c e - c d)sinh(x) --R + @@ -37622,15 +37845,18 @@ d1054:= D(m1054,x) --R Type: Expression(Integer) --E 307 +)clear all + + --S 308 of 531 t1055:= sinh(x)^2/(a*cosh(x)^2+b*sinh(x)^2) --R --R ---R 2 ---R sinh(x) ---R (275) ----------------------- ---R 2 2 ---R b sinh(x) + a cosh(x) +--R 2 +--R sinh(x) +--R (1) ----------------------- +--R 2 2 +--R b sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 308 @@ -37638,14 +37864,14 @@ t1055:= sinh(x)^2/(a*cosh(x)^2+b*sinh(x)^2) r1055:= x/(a+b)+a^(1/2)*atan(a^(1/2)*coth(x)/b^(1/2))/b^(1/2)/(a+b) --R --R ---R +-+ ---R +-+ coth(x)\|a +-+ ---R \|a atan(-----------) + x\|b ---R +-+ ---R \|b ---R (276) ----------------------------- ---R +-+ ---R (b + a)\|b +--R +-+ +--R +-+ coth(x)\|a +-+ +--R \|a atan(-----------) + x\|b +--R +-+ +--R \|b +--R (2) ----------------------------- +--R +-+ +--R (b + a)\|b --R Type: Expression(Integer) --E 309 @@ -37653,7 +37879,7 @@ r1055:= x/(a+b)+a^(1/2)*atan(a^(1/2)*coth(x)/b^(1/2))/b^(1/2)/(a+b) a1055:= integrate(t1055,x) --R --R ---R (277) +--R (3) --R [ --R +---+ --R | a @@ -37731,7 +37957,7 @@ a1055:= integrate(t1055,x) m1055a:= a1055.1-r1055 --R --R ---R (278) +--R (4) --R +---+ --R | a +-+ --R |- - \|b @@ -37788,7 +38014,7 @@ m1055a:= a1055.1-r1055 d1055a:= D(m1055a,x) --R --R ---R (279) +--R (5) --R 2 4 2 3 --R (a coth(x) - a)sinh(x) + (4a cosh(x)coth(x) - 4a cosh(x))sinh(x) --R + @@ -37836,7 +38062,7 @@ d1055a:= D(m1055a,x) m1055b:= a1055.2-r1055 --R --R ---R (280) +--R (6) --R +-+ --R |a +-+ --R |- \|b @@ -37865,7 +38091,7 @@ m1055b:= a1055.2-r1055 d1055b:= D(m1055b,x) --R --R ---R (281) +--R (7) --R 2 4 2 3 --R (a coth(x) - a)sinh(x) + (4a cosh(x)coth(x) - 4a cosh(x))sinh(x) --R + @@ -37909,15 +38135,18 @@ d1055b:= D(m1055b,x) --R Type: Expression(Integer) --E 314 +)clear all + + --S 315 of 531 t1056:= cosh(x)^2/(a*cosh(x)^2+b*sinh(x)^2) --R --R ---R 2 ---R cosh(x) ---R (282) ----------------------- ---R 2 2 ---R b sinh(x) + a cosh(x) +--R 2 +--R cosh(x) +--R (1) ----------------------- +--R 2 2 +--R b sinh(x) + a cosh(x) --R Type: Expression(Integer) --E 315 @@ -37925,14 +38154,14 @@ t1056:= cosh(x)^2/(a*cosh(x)^2+b*sinh(x)^2) r1056:= x/(a+b)+b^(1/2)*atan(b^(1/2)*tanh(x)/a^(1/2))/a^(1/2)/(a+b) --R --R ---R +-+ ---R +-+ tanh(x)\|b +-+ ---R \|b atan(-----------) + x\|a ---R +-+ ---R \|a ---R (283) ----------------------------- ---R +-+ ---R (b + a)\|a +--R +-+ +--R +-+ tanh(x)\|b +-+ +--R \|b atan(-----------) + x\|a +--R +-+ +--R \|a +--R (2) ----------------------------- +--R +-+ +--R (b + a)\|a --R Type: Expression(Integer) --E 316 @@ -37940,7 +38169,7 @@ r1056:= x/(a+b)+b^(1/2)*atan(b^(1/2)*tanh(x)/a^(1/2))/a^(1/2)/(a+b) a1056:= integrate(t1056,x) --R --R ---R (284) +--R (3) --R [ --R +---+ --R | b @@ -38019,7 +38248,7 @@ a1056:= integrate(t1056,x) m1056a:= a1056.1-r1056 --R --R ---R (285) +--R (4) --R +---+ --R | b +-+ --R |- - \|a @@ -38076,7 +38305,7 @@ m1056a:= a1056.1-r1056 d1056a:= D(m1056a,x) --R --R ---R (286) +--R (5) --R 4 3 2 2 --R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) --R + @@ -38125,7 +38354,7 @@ d1056a:= D(m1056a,x) m1056b:= a1056.2-r1056 --R --R ---R (287) +--R (6) --R +-+ --R +-+ tanh(x)\|b --R - \|b atan(-----------) @@ -38158,7 +38387,7 @@ m1056b:= a1056.2-r1056 d1056b:= D(m1056b,x) --R --R ---R (288) +--R (7) --R 4 3 2 2 --R b sinh(x) + 4b cosh(x)sinh(x) + (6b cosh(x) + 2b)sinh(x) --R + @@ -38203,15 +38432,18 @@ d1056b:= D(m1056b,x) --R Type: Expression(Integer) --E 321 +)clear all + + --S 322 of 531 t1057:= sinh(x)^3/(cosh(x)^3+sinh(x)^3) --R --R ---R 3 ---R sinh(x) ---R (289) ------------------- ---R 3 3 ---R sinh(x) + cosh(x) +--R 3 +--R sinh(x) +--R (1) ------------------- +--R 3 3 +--R sinh(x) + cosh(x) --R Type: Expression(Integer) --E 322 @@ -38219,13 +38451,12 @@ t1057:= sinh(x)^3/(cosh(x)^3+sinh(x)^3) r1057:= 1/2*x-2/9*atan(1/3*(1-2*coth(x))*3^(1/2))*3^(1/2)-1/(6+6*coth(x)) --R --R ---R (290) ---R +-+ +-+ ---R +-+ +-+ 2\|3 coth(x) - \|3 ---R (4\|3 coth(x) + 4\|3 )atan(-------------------) + 9x coth(x) + 9x - 3 ---R 3 ---R --------------------------------------------------------------------- ---R 18coth(x) + 18 +--R +-+ +-+ +--R +-+ +-+ 2\|3 coth(x) - \|3 +--R (4\|3 coth(x) + 4\|3 )atan(-------------------) + 9x coth(x) + 9x - 3 +--R 3 +--R (2) --------------------------------------------------------------------- +--R 18coth(x) + 18 --R Type: Expression(Integer) --E 323 @@ -38233,7 +38464,7 @@ r1057:= 1/2*x-2/9*atan(1/3*(1-2*coth(x))*3^(1/2))*3^(1/2)-1/(6+6*coth(x)) a1057:= integrate(t1057,x) --R --R ---R (291) +--R (3) --R +-+ +-+ --R 2 2 \|3 sinh(x) + \|3 cosh(x) --R (8sinh(x) + 16cosh(x)sinh(x) + 8cosh(x) )atan(-------------------------) @@ -38251,7 +38482,7 @@ a1057:= integrate(t1057,x) m1057:= a1057-r1057 --R --R ---R (292) +--R (4) --R 2 --R (- 8coth(x) - 8)sinh(x) + (- 16cosh(x)coth(x) - 16cosh(x))sinh(x) --R + @@ -38292,7 +38523,7 @@ m1057:= a1057-r1057 d1057:= D(m1057,x) --R --R ---R (293) +--R (5) --R 3 4 3 3 --R (5coth(x) - 1)sinh(x) + (7cosh(x)coth(x) + cosh(x))sinh(x) --R + @@ -38313,15 +38544,18 @@ d1057:= D(m1057,x) --R Type: Expression(Integer) --E 326 +)clear all + + --S 327 of 531 t1058:= cosh(x)^3/(cosh(x)^3+sinh(x)^3) --R --R ---R 3 ---R cosh(x) ---R (294) ------------------- ---R 3 3 ---R sinh(x) + cosh(x) +--R 3 +--R cosh(x) +--R (1) ------------------- +--R 3 3 +--R sinh(x) + cosh(x) --R Type: Expression(Integer) --E 327 @@ -38329,13 +38563,12 @@ t1058:= cosh(x)^3/(cosh(x)^3+sinh(x)^3) r1058:= 1/2*x-2/9*atan(1/3*(1-2*tanh(x))*3^(1/2))*3^(1/2)-1/(6+6*tanh(x)) --R --R ---R (295) ---R +-+ +-+ ---R +-+ +-+ 2\|3 tanh(x) - \|3 ---R (4\|3 tanh(x) + 4\|3 )atan(-------------------) + 9x tanh(x) + 9x - 3 ---R 3 ---R --------------------------------------------------------------------- ---R 18tanh(x) + 18 +--R +-+ +-+ +--R +-+ +-+ 2\|3 tanh(x) - \|3 +--R (4\|3 tanh(x) + 4\|3 )atan(-------------------) + 9x tanh(x) + 9x - 3 +--R 3 +--R (2) --------------------------------------------------------------------- +--R 18tanh(x) + 18 --R Type: Expression(Integer) --E 328 @@ -38343,7 +38576,7 @@ r1058:= 1/2*x-2/9*atan(1/3*(1-2*tanh(x))*3^(1/2))*3^(1/2)-1/(6+6*tanh(x)) a1058:= integrate(t1058,x) --R --R ---R (296) +--R (3) --R 2 2 --R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) ) --R * @@ -38364,7 +38597,7 @@ a1058:= integrate(t1058,x) m1058:= a1058-r1058 --R --R ---R (297) +--R (4) --R 2 2 2 --R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) )tanh(x) - 8sinh(x) --R + @@ -38402,7 +38635,7 @@ m1058:= a1058-r1058 d1058:= D(m1058,x) --R --R ---R (298) +--R (5) --R 4 3 2 3 --R sinh(x) - cosh(x)sinh(x) + sinh(x) + (7cosh(x) - cosh(x))sinh(x) --R + @@ -38426,12 +38659,15 @@ d1058:= D(m1058,x) --R Type: Expression(Integer) --E 331 +)clear all + + --S 332 of 531 t1059:= exp(1)^(a+b*x)*sinh(a+b*x) --R --R ---R b x + a ---R (299) %e sinh(b x + a) +--R b x + a +--R (1) %e sinh(b x + a) --R Type: Expression(Integer) --E 332 @@ -38439,10 +38675,10 @@ t1059:= exp(1)^(a+b*x)*sinh(a+b*x) r1059:= 1/4*(exp(2*a+2*b*x)-2*b*x)/b --R --R ---R 2b x + 2a ---R %e - 2b x ---R (300) ------------------ ---R 4b +--R 2b x + 2a +--R %e - 2b x +--R (2) ------------------ +--R 4b --R Type: Expression(Integer) --E 333 @@ -38450,9 +38686,9 @@ r1059:= 1/4*(exp(2*a+2*b*x)-2*b*x)/b a1059:= integrate(t1059,x) --R --R ---R (- 2b x - 1)sinh(b x + a) + (2b x - 1)cosh(b x + a) ---R (301) --------------------------------------------------- ---R 4b sinh(b x + a) - 4b cosh(b x + a) +--R (- 2b x - 1)sinh(b x + a) + (2b x - 1)cosh(b x + a) +--R (3) --------------------------------------------------- +--R 4b sinh(b x + a) - 4b cosh(b x + a) --R Type: Union(Expression(Integer),...) --E 334 @@ -38460,7 +38696,7 @@ a1059:= integrate(t1059,x) m1059:= a1059-r1059 --R --R ---R (302) +--R (4) --R 2b x + 2a 2b x + 2a --R (- %e - 1)sinh(b x + a) + cosh(b x + a)%e - cosh(b x + a) --R --------------------------------------------------------------------------- @@ -38472,7 +38708,7 @@ m1059:= a1059-r1059 d1059:= D(m1059,x) --R --R ---R (303) +--R (5) --R 2b x + 2a 2b x + 2a --R (- %e - 1)sinh(b x + a) + cosh(b x + a)%e - cosh(b x + a) --R --------------------------------------------------------------------------- @@ -38480,12 +38716,15 @@ d1059:= D(m1059,x) --R Type: Expression(Integer) --E 336 +)clear all + + --S 337 of 531 t1060:= exp(1)^(a+b*x)*sinh(a+b*x)^3 --R --R ---R b x + a 3 ---R (304) %e sinh(b x + a) +--R b x + a 3 +--R (1) %e sinh(b x + a) --R Type: Expression(Integer) --E 337 @@ -38493,10 +38732,10 @@ t1060:= exp(1)^(a+b*x)*sinh(a+b*x)^3 r1060:= 1/32*(2*exp(-2*a-2*b*x)-6*exp(2*a+2*b*x)+exp(4*a+4*b*x)+12*b*x)/b --R --R ---R 4b x + 4a 2b x + 2a - 2b x - 2a ---R %e - 6%e + 2%e + 12b x ---R (305) --------------------------------------------------- ---R 32b +--R 4b x + 4a 2b x + 2a - 2b x - 2a +--R %e - 6%e + 2%e + 12b x +--R (2) --------------------------------------------------- +--R 32b --R Type: Expression(Integer) --E 338 @@ -38504,7 +38743,7 @@ r1060:= 1/32*(2*exp(-2*a-2*b*x)-6*exp(2*a+2*b*x)+exp(4*a+4*b*x)+12*b*x)/b a1060:= integrate(t1060,x) --R --R ---R (306) +--R (3) --R 3 2 --R sinh(b x + a) - 9cosh(b x + a)sinh(b x + a) --R + @@ -38521,7 +38760,7 @@ a1060:= integrate(t1060,x) m1060:= a1060-r1060 --R --R ---R (307) +--R (4) --R 3 2 --R sinh(b x + a) - 9cosh(b x + a)sinh(b x + a) --R + @@ -38544,7 +38783,7 @@ m1060:= a1060-r1060 d1060:= D(m1060,x) --R --R ---R (308) +--R (5) --R 3 --R - 2sinh(b x + a) --R + @@ -38563,16 +38802,19 @@ d1060:= D(m1060,x) --R Type: Expression(Integer) --E 341 +)clear all + + --S 342 of 531 t1061:= exp(1)^(a+b*x)*sinh(c+d*x)^(3/2)-3*d^2/(4*b^2-9*d^2)*_ exp(1)^(a+b*x)/sinh(c+d*x)^(1/2) --R --R ---R 2 2 b x + a 2 2 b x + a ---R (9d - 4b )%e sinh(d x + c) + 3d %e ---R (309) ------------------------------------------------- ---R 2 2 +-------------+ ---R (9d - 4b )\|sinh(d x + c) +--R 2 2 b x + a 2 2 b x + a +--R (9d - 4b )%e sinh(d x + c) + 3d %e +--R (1) ------------------------------------------------- +--R 2 2 +-------------+ +--R (9d - 4b )\|sinh(d x + c) --R Type: Expression(Integer) --E 342 @@ -38581,7 +38823,7 @@ r1061:= -2*exp(a+b*x)*sinh(c+d*x)^(1/2)*(3*d*cosh(c+d*x)-_ 2*b*sinh(c+d*x))/(4*b^2-9*d^2) --R --R ---R (310) +--R (2) --R b x + a b x + a +-------------+ --R (- 4b %e sinh(d x + c) + 6d cosh(d x + c)%e )\|sinh(d x + c) --R ------------------------------------------------------------------------- @@ -38609,12 +38851,15 @@ a1061:= integrate(t1061,x) --d1061:= D(m1061,x) --E 346 +)clear all + + --S 347 of 531 t1062:= exp(1)^(a+b*x)*cosh(a+b*x) --R --R ---R b x + a ---R (311) cosh(b x + a)%e +--R b x + a +--R (1) cosh(b x + a)%e --R Type: Expression(Integer) --E 347 @@ -38622,10 +38867,10 @@ t1062:= exp(1)^(a+b*x)*cosh(a+b*x) r1062:= 1/4*(exp(2*a+2*b*x)+2*b*x)/b --R --R ---R 2b x + 2a ---R %e + 2b x ---R (312) ------------------ ---R 4b +--R 2b x + 2a +--R %e + 2b x +--R (2) ------------------ +--R 4b --R Type: Expression(Integer) --E 348 @@ -38633,9 +38878,9 @@ r1062:= 1/4*(exp(2*a+2*b*x)+2*b*x)/b a1062:= integrate(t1062,x) --R --R ---R (2b x - 1)sinh(b x + a) + (- 2b x - 1)cosh(b x + a) ---R (313) --------------------------------------------------- ---R 4b sinh(b x + a) - 4b cosh(b x + a) +--R (2b x - 1)sinh(b x + a) + (- 2b x - 1)cosh(b x + a) +--R (3) --------------------------------------------------- +--R 4b sinh(b x + a) - 4b cosh(b x + a) --R Type: Union(Expression(Integer),...) --E 349 @@ -38643,7 +38888,7 @@ a1062:= integrate(t1062,x) m1062:= a1062-r1062 --R --R ---R (314) +--R (4) --R 2b x + 2a 2b x + 2a --R (- %e - 1)sinh(b x + a) + cosh(b x + a)%e - cosh(b x + a) --R --------------------------------------------------------------------------- @@ -38655,7 +38900,7 @@ m1062:= a1062-r1062 d1062:= D(m1062,x) --R --R ---R (315) +--R (5) --R 2b x + 2a 2b x + 2a --R (- %e - 1)sinh(b x + a) + cosh(b x + a)%e - cosh(b x + a) --R --------------------------------------------------------------------------- @@ -38663,12 +38908,15 @@ d1062:= D(m1062,x) --R Type: Expression(Integer) --E 351 +)clear all + + --S 352 of 531 t1063:= exp(1)^(a+b*x)*cosh(a+b*x)^3 --R --R ---R 3 b x + a ---R (316) cosh(b x + a) %e +--R 3 b x + a +--R (1) cosh(b x + a) %e --R Type: Expression(Integer) --E 352 @@ -38676,10 +38924,10 @@ t1063:= exp(1)^(a+b*x)*cosh(a+b*x)^3 r1063:= 1/32*(-2*exp(-2*a-2*b*x)+6*exp(2*a+2*b*x)+exp(4*a+4*b*x)+12*b*x)/b --R --R ---R 4b x + 4a 2b x + 2a - 2b x - 2a ---R %e + 6%e - 2%e + 12b x ---R (317) --------------------------------------------------- ---R 32b +--R 4b x + 4a 2b x + 2a - 2b x - 2a +--R %e + 6%e - 2%e + 12b x +--R (2) --------------------------------------------------- +--R 32b --R Type: Expression(Integer) --E 353 @@ -38687,7 +38935,7 @@ r1063:= 1/32*(-2*exp(-2*a-2*b*x)+6*exp(2*a+2*b*x)+exp(4*a+4*b*x)+12*b*x)/b a1063:= integrate(t1063,x) --R --R ---R (318) +--R (3) --R 3 2 --R - 3sinh(b x + a) + 3cosh(b x + a)sinh(b x + a) --R + @@ -38704,7 +38952,7 @@ a1063:= integrate(t1063,x) m1063:= a1063-r1063 --R --R ---R (319) +--R (4) --R 3 2 --R - 3sinh(b x + a) + 3cosh(b x + a)sinh(b x + a) --R + @@ -38727,7 +38975,7 @@ m1063:= a1063-r1063 d1063:= D(m1063,x) --R --R ---R (320) +--R (5) --R 2 --R - 6cosh(b x + a)sinh(b x + a) --R + @@ -38744,14 +38992,17 @@ d1063:= D(m1063,x) --R Type: Expression(Integer) --E 356 +)clear all + + --S 357 of 531 t1064:= sech(x)^2/(a+b*tanh(x)) --R --R ---R 2 ---R sech(x) ---R (321) ------------- ---R b tanh(x) + a +--R 2 +--R sech(x) +--R (1) ------------- +--R b tanh(x) + a --R Type: Expression(Integer) --E 357 @@ -38759,9 +39010,9 @@ t1064:= sech(x)^2/(a+b*tanh(x)) r1064:= log(a+b*tanh(x))/b --R --R ---R log(b tanh(x) + a) ---R (322) ------------------ ---R b +--R log(b tanh(x) + a) +--R (2) ------------------ +--R b --R Type: Expression(Integer) --E 358 @@ -38769,11 +39020,11 @@ r1064:= log(a+b*tanh(x))/b a1064:= integrate(t1064,x) --R --R ---R 2cosh(x) - 2b sinh(x) - 2a cosh(x) ---R - log(- -----------------) + log(-------------------------) ---R sinh(x) - cosh(x) sinh(x) - cosh(x) ---R (323) ----------------------------------------------------------- ---R b +--R 2cosh(x) - 2b sinh(x) - 2a cosh(x) +--R - log(- -----------------) + log(-------------------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R (3) ----------------------------------------------------------- +--R b --R Type: Union(Expression(Integer),...) --E 359 @@ -38781,7 +39032,7 @@ a1064:= integrate(t1064,x) m1064:= a1064-r1064 --R --R ---R (324) +--R (4) --R 2cosh(x) --R - log(b tanh(x) + a) - log(- -----------------) --R sinh(x) - cosh(x) @@ -38798,7 +39049,7 @@ m1064:= a1064-r1064 d1064:= D(m1064,x) --R --R ---R (325) +--R (5) --R 2 2 --R (b cosh(x)sinh(x) + a cosh(x) )tanh(x) --R + @@ -38810,12 +39061,15 @@ d1064:= D(m1064,x) --R Type: Expression(Integer) --E 361 +)clear all + + --S 362 of 531 t1065:= sech(x)^2*(a+b*tanh(x))^n --R --R ---R 2 n ---R (326) sech(x) (b tanh(x) + a) +--R 2 n +--R (1) sech(x) (b tanh(x) + a) --R Type: Expression(Integer) --E 362 @@ -38823,10 +39077,10 @@ t1065:= sech(x)^2*(a+b*tanh(x))^n r1065:= (a+b*tanh(x))^(1+n)/b/(1+n) --R --R ---R n + 1 ---R (b tanh(x) + a) ---R (327) -------------------- ---R b n + b +--R n + 1 +--R (b tanh(x) + a) +--R (2) -------------------- +--R b n + b --R Type: Expression(Integer) --E 363 @@ -38834,7 +39088,7 @@ r1065:= (a+b*tanh(x))^(1+n)/b/(1+n) a1065:= integrate(t1065,x) --R --R ---R (328) +--R (3) --R b sinh(x) + a cosh(x) --R (b sinh(x) + a cosh(x))sinh(n log(---------------------)) --R cosh(x) @@ -38851,7 +39105,7 @@ a1065:= integrate(t1065,x) m1065:= a1065-r1065 --R --R ---R (329) +--R (4) --R b sinh(x) + a cosh(x) --R (b sinh(x) + a cosh(x))sinh(n log(---------------------)) --R cosh(x) @@ -38871,7 +39125,7 @@ m1065:= a1065-r1065 d1065:= D(m1065,x) --R --R ---R (330) +--R (5) --R 2 2 b sinh(x) + a cosh(x) --R (- sinh(x) + cosh(x) )sinh(n log(---------------------)) --R cosh(x) @@ -38888,15 +39142,18 @@ d1065:= D(m1065,x) --R Type: Expression(Integer) --E 366 +)clear all + + --S 367 of 531 t1066:= sech(x)^2*(1+1/(1-tanh(x)^2)) --R --R ---R 2 2 2 ---R sech(x) tanh(x) - 2sech(x) ---R (331) ---------------------------- ---R 2 ---R tanh(x) - 1 +--R 2 2 2 +--R sech(x) tanh(x) - 2sech(x) +--R (1) ---------------------------- +--R 2 +--R tanh(x) - 1 --R Type: Expression(Integer) --E 367 @@ -38904,7 +39161,7 @@ t1066:= sech(x)^2*(1+1/(1-tanh(x)^2)) r1066:= x+tanh(x) --R --R ---R (332) tanh(x) + x +--R (2) tanh(x) + x --R Type: Expression(Integer) --E 368 @@ -38912,9 +39169,9 @@ r1066:= x+tanh(x) a1066:= integrate(t1066,x) --R --R ---R sinh(x) + (x - 1)cosh(x) ---R (333) ------------------------ ---R cosh(x) +--R sinh(x) + (x - 1)cosh(x) +--R (3) ------------------------ +--R cosh(x) --R Type: Union(Expression(Integer),...) --E 369 @@ -38922,9 +39179,9 @@ a1066:= integrate(t1066,x) m1066:= a1066-r1066 --R --R ---R - cosh(x)tanh(x) + sinh(x) - cosh(x) ---R (334) ------------------------------------ ---R cosh(x) +--R - cosh(x)tanh(x) + sinh(x) - cosh(x) +--R (4) ------------------------------------ +--R cosh(x) --R Type: Expression(Integer) --E 370 @@ -38932,23 +39189,26 @@ m1066:= a1066-r1066 d1066:= D(m1066,x) --R --R ---R 2 2 2 ---R cosh(x) tanh(x) - sinh(x) ---R (335) --------------------------- ---R 2 ---R cosh(x) +--R 2 2 2 +--R cosh(x) tanh(x) - sinh(x) +--R (5) --------------------------- +--R 2 +--R cosh(x) --R Type: Expression(Integer) --E 371 +)clear all + + --S 372 of 531 t1067:= sech(x)^2*(2-tanh(x)^2)/(1-tanh(x)^2) --R --R ---R 2 2 2 ---R sech(x) tanh(x) - 2sech(x) ---R (336) ---------------------------- ---R 2 ---R tanh(x) - 1 +--R 2 2 2 +--R sech(x) tanh(x) - 2sech(x) +--R (1) ---------------------------- +--R 2 +--R tanh(x) - 1 --R Type: Expression(Integer) --E 372 @@ -38956,7 +39216,7 @@ t1067:= sech(x)^2*(2-tanh(x)^2)/(1-tanh(x)^2) r1067:= x+tanh(x) --R --R ---R (337) tanh(x) + x +--R (2) tanh(x) + x --R Type: Expression(Integer) --E 373 @@ -38964,9 +39224,9 @@ r1067:= x+tanh(x) a1067:= integrate(t1067,x) --R --R ---R sinh(x) + (x - 1)cosh(x) ---R (338) ------------------------ ---R cosh(x) +--R sinh(x) + (x - 1)cosh(x) +--R (3) ------------------------ +--R cosh(x) --R Type: Union(Expression(Integer),...) --E 374 @@ -38974,9 +39234,9 @@ a1067:= integrate(t1067,x) m1067:= a1067-r1067 --R --R ---R - cosh(x)tanh(x) + sinh(x) - cosh(x) ---R (339) ------------------------------------ ---R cosh(x) +--R - cosh(x)tanh(x) + sinh(x) - cosh(x) +--R (4) ------------------------------------ +--R cosh(x) --R Type: Expression(Integer) --E 375 @@ -38984,23 +39244,26 @@ m1067:= a1067-r1067 d1067:= D(m1067,x) --R --R ---R 2 2 2 ---R cosh(x) tanh(x) - sinh(x) ---R (340) --------------------------- ---R 2 ---R cosh(x) +--R 2 2 2 +--R cosh(x) tanh(x) - sinh(x) +--R (5) --------------------------- +--R 2 +--R cosh(x) --R Type: Expression(Integer) --E 376 +)clear all + + --S 377 of 531 t1068:= sech(x)^2/(1+tanh(x)^2) --R --R ---R 2 ---R sech(x) ---R (341) ------------ --R 2 ---R tanh(x) + 1 +--R sech(x) +--R (1) ------------ +--R 2 +--R tanh(x) + 1 --R Type: Expression(Integer) --E 377 @@ -39008,7 +39271,7 @@ t1068:= sech(x)^2/(1+tanh(x)^2) r1068:= atan(tanh(x)) --R --R ---R (342) atan(tanh(x)) +--R (2) atan(tanh(x)) --R Type: Expression(Integer) --E 378 @@ -39016,9 +39279,9 @@ r1068:= atan(tanh(x)) a1068:= integrate(t1068,x) --R --R ---R sinh(x) + cosh(x) ---R (343) - atan(-----------------) ---R sinh(x) - cosh(x) +--R sinh(x) + cosh(x) +--R (3) - atan(-----------------) +--R sinh(x) - cosh(x) --R Type: Union(Expression(Integer),...) --E 379 @@ -39026,9 +39289,9 @@ a1068:= integrate(t1068,x) m1068:= a1068-r1068 --R --R ---R sinh(x) + cosh(x) ---R (344) - atan(tanh(x)) - atan(-----------------) ---R sinh(x) - cosh(x) +--R sinh(x) + cosh(x) +--R (4) - atan(tanh(x)) - atan(-----------------) +--R sinh(x) - cosh(x) --R Type: Expression(Integer) --E 380 @@ -39036,23 +39299,26 @@ m1068:= a1068-r1068 d1068:= D(m1068,x) --R --R ---R 2 2 2 ---R 2cosh(x) tanh(x) - 2sinh(x) ---R (345) --------------------------------------------------- ---R 2 2 2 2 2 ---R (sinh(x) + cosh(x) )tanh(x) + sinh(x) + cosh(x) +--R 2 2 2 +--R 2cosh(x) tanh(x) - 2sinh(x) +--R (5) --------------------------------------------------- +--R 2 2 2 2 2 +--R (sinh(x) + cosh(x) )tanh(x) + sinh(x) + cosh(x) --R Type: Expression(Integer) --E 381 +)clear all + + --S 382 of 531 t1069:= sech(x)^2/(9+tanh(x)^2) --R --R ---R 2 ---R sech(x) ---R (346) ------------ --R 2 ---R tanh(x) + 9 +--R sech(x) +--R (1) ------------ +--R 2 +--R tanh(x) + 9 --R Type: Expression(Integer) --E 382 @@ -39060,11 +39326,11 @@ t1069:= sech(x)^2/(9+tanh(x)^2) r1069:= 1/3*atan(1/3*tanh(x)) --R --R ---R tanh(x) ---R atan(-------) ---R 3 ---R (347) ------------- +--R tanh(x) +--R atan(-------) --R 3 +--R (2) ------------- +--R 3 --R Type: Expression(Integer) --E 383 @@ -39072,11 +39338,11 @@ r1069:= 1/3*atan(1/3*tanh(x)) a1069:= integrate(t1069,x) --R --R ---R sinh(x) + 9cosh(x) ---R atan(-------------------) ---R 3sinh(x) - 3cosh(x) ---R (348) - ------------------------- ---R 3 +--R sinh(x) + 9cosh(x) +--R atan(-------------------) +--R 3sinh(x) - 3cosh(x) +--R (3) - ------------------------- +--R 3 --R Type: Union(Expression(Integer),...) --E 384 @@ -39084,11 +39350,11 @@ a1069:= integrate(t1069,x) m1069:= a1069-r1069 --R --R ---R tanh(x) sinh(x) + 9cosh(x) ---R - atan(-------) - atan(-------------------) ---R 3 3sinh(x) - 3cosh(x) ---R (349) ------------------------------------------- ---R 3 +--R tanh(x) sinh(x) + 9cosh(x) +--R - atan(-------) - atan(-------------------) +--R 3 3sinh(x) - 3cosh(x) +--R (4) ------------------------------------------- +--R 3 --R Type: Expression(Integer) --E 385 @@ -39096,24 +39362,27 @@ m1069:= a1069-r1069 d1069:= D(m1069,x) --R --R ---R 2 2 2 ---R 10cosh(x) tanh(x) - 10sinh(x) ---R (350) ------------------------------------------------------- ---R 2 2 2 2 2 ---R (sinh(x) + 9cosh(x) )tanh(x) + 9sinh(x) + 81cosh(x) +--R 2 2 2 +--R 10cosh(x) tanh(x) - 10sinh(x) +--R (5) ------------------------------------------------------- +--R 2 2 2 2 2 +--R (sinh(x) + 9cosh(x) )tanh(x) + 9sinh(x) + 81cosh(x) --R Type: Expression(Integer) --E 386 +)clear all + + --S 387 of 531 t1070:= sech(x)^2/(4-sech(x)^2)^(1/2) --R --R ---R 2 ---R sech(x) ---R (351) ----------------- ---R +--------------+ ---R | 2 ---R \|- sech(x) + 4 +--R 2 +--R sech(x) +--R (1) ----------------- +--R +--------------+ +--R | 2 +--R \|- sech(x) + 4 --R Type: Expression(Integer) --E 387 @@ -39121,10 +39390,10 @@ t1070:= sech(x)^2/(4-sech(x)^2)^(1/2) r1070:= asinh(1/3*tanh(x)*3^(1/2)) --R --R ---R +-+ ---R \|3 tanh(x) ---R (352) asinh(-----------) ---R 3 +--R +-+ +--R \|3 tanh(x) +--R (2) asinh(-----------) +--R 3 --R Type: Expression(Integer) --E 388 @@ -39132,7 +39401,7 @@ r1070:= asinh(1/3*tanh(x)*3^(1/2)) a1070:= integrate(t1070,x) --R --R ---R (353) +--R (3) --R - --R log --R +-------------------------------------+ @@ -39162,7 +39431,7 @@ a1070:= integrate(t1070,x) m1070:= a1070-r1070 --R --R ---R (354) +--R (4) --R - --R log --R +-------------------------------------+ @@ -39197,7 +39466,7 @@ m1070:= a1070-r1070 d1070:= D(m1070,x) --R --R ---R (355) +--R (5) --R 4 2 2 --R - 4sinh(x) + (8cosh(x) - 2)sinh(x) + 4cosh(x)sinh(x) --R + @@ -39319,16 +39588,19 @@ d1070:= D(m1070,x) --R Type: Expression(Integer) --E 391 +)clear all + + --S 392 of 531 t1071:= sech(x)^2/(1-4*tanh(x)^2)^(1/2) --R --R ---R 2 ---R sech(x) ---R (356) ------------------ ---R +---------------+ ---R | 2 ---R \|- 4tanh(x) + 1 +--R 2 +--R sech(x) +--R (1) ------------------ +--R +---------------+ +--R | 2 +--R \|- 4tanh(x) + 1 --R Type: Expression(Integer) --E 392 @@ -39336,9 +39608,9 @@ t1071:= sech(x)^2/(1-4*tanh(x)^2)^(1/2) r1071:= 1/2*asin(2*tanh(x)) --R --R ---R asin(2tanh(x)) ---R (357) -------------- ---R 2 +--R asin(2tanh(x)) +--R (2) -------------- +--R 2 --R Type: Expression(Integer) --E 393 @@ -39346,17 +39618,17 @@ r1071:= 1/2*asin(2*tanh(x)) a1071:= integrate(t1071,x) --R --R ---R +-------------------------------------+ ---R | 2 2 ---R | - 6sinh(x) - 6cosh(x) + 10 ---R |------------------------------------- ---R | 2 2 ---R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) ---R atan(-------------------------------------------) ---R 2 2 ---R 2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 2 ---R (358) - ------------------------------------------------- ---R 2 +--R +-------------------------------------+ +--R | 2 2 +--R | - 6sinh(x) - 6cosh(x) + 10 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R atan(-------------------------------------------) +--R 2 2 +--R 2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 2 +--R (3) - ------------------------------------------------- +--R 2 --R Type: Union(Expression(Integer),...) --E 394 @@ -39364,17 +39636,17 @@ a1071:= integrate(t1071,x) m1071:= a1071-r1071 --R --R ---R +-------------------------------------+ ---R | 2 2 ---R | - 6sinh(x) - 6cosh(x) + 10 ---R |------------------------------------- ---R | 2 2 ---R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) ---R - atan(-------------------------------------------) - asin(2tanh(x)) ---R 2 2 ---R 2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 2 ---R (359) -------------------------------------------------------------------- ---R 2 +--R +-------------------------------------+ +--R | 2 2 +--R | - 6sinh(x) - 6cosh(x) + 10 +--R |------------------------------------- +--R | 2 2 +--R \|sinh(x) - 2cosh(x)sinh(x) + cosh(x) +--R - atan(-------------------------------------------) - asin(2tanh(x)) +--R 2 2 +--R 2sinh(x) + 4cosh(x)sinh(x) + 2cosh(x) - 2 +--R (4) -------------------------------------------------------------------- +--R 2 --R Type: Expression(Integer) --E 395 @@ -39382,7 +39654,7 @@ m1071:= a1071-r1071 d1071:= D(m1071,x) --R --R ---R (360) +--R (5) --R 6 5 2 4 --R 2sinh(x) + 4cosh(x)sinh(x) + (- 2cosh(x) - 4)sinh(x) --R + @@ -39441,16 +39713,19 @@ d1071:= D(m1071,x) --R Type: Expression(Integer) --E 396 +)clear all + + --S 397 of 531 t1072:= sech(x)^2/(-4+tanh(x)^2)^(1/2) --R --R ---R 2 ---R sech(x) ---R (361) --------------- ---R +------------+ ---R | 2 ---R \|tanh(x) - 4 +--R 2 +--R sech(x) +--R (1) --------------- +--R +------------+ +--R | 2 +--R \|tanh(x) - 4 --R Type: Expression(Integer) --E 397 @@ -39458,9 +39733,9 @@ t1072:= sech(x)^2/(-4+tanh(x)^2)^(1/2) r1072:= atanh(coth(x)*(-4+tanh(x)^2)^(1/2)) --R --R ---R +------------+ ---R | 2 ---R (362) atanh(coth(x)\|tanh(x) - 4 ) +--R +------------+ +--R | 2 +--R (2) atanh(coth(x)\|tanh(x) - 4 ) --R Type: Expression(Integer) --E 398 @@ -39468,7 +39743,7 @@ r1072:= atanh(coth(x)*(-4+tanh(x)^2)^(1/2)) a1072:= integrate(t1072,x) --R --R ---R (363) 0 +--R (3) 0 --R Type: Union(Expression(Integer),...) --E 399 @@ -39476,9 +39751,9 @@ a1072:= integrate(t1072,x) m1072:= a1072-r1072 --R --R ---R +------------+ ---R | 2 ---R (364) - atanh(coth(x)\|tanh(x) - 4 ) +--R +------------+ +--R | 2 +--R (4) - atanh(coth(x)\|tanh(x) - 4 ) --R Type: Expression(Integer) --E 400 @@ -39486,7 +39761,7 @@ m1072:= a1072-r1072 d1072:= D(m1072,x) --R --R ---R (365) +--R (5) --R 3 2 2 2 --R - coth(x)tanh(x) + (- coth(x) + 1)tanh(x) + coth(x)tanh(x) + 4coth(x) - 4 --R ----------------------------------------------------------------------------- @@ -39496,13 +39771,16 @@ d1072:= D(m1072,x) --R Type: Expression(Integer) --E 401 +)clear all + + --S 402 of 531 t1073:= sech(x)^2*(1+coth(x)^2)^(1/2) --R --R ---R +------------+ ---R 2 | 2 ---R (366) sech(x) \|coth(x) + 1 +--R +------------+ +--R 2 | 2 +--R (1) sech(x) \|coth(x) + 1 --R Type: Expression(Integer) --E 402 @@ -39510,9 +39788,9 @@ t1073:= sech(x)^2*(1+coth(x)^2)^(1/2) r1073:= -acsch(tanh(x))+(1+coth(x)^2)^(1/2)*tanh(x) --R --R ---R +------------+ ---R | 2 ---R (367) tanh(x)\|coth(x) + 1 - acsch(tanh(x)) +--R +------------+ +--R | 2 +--R (2) tanh(x)\|coth(x) + 1 - acsch(tanh(x)) --R Type: Expression(Integer) --E 403 @@ -39520,7 +39798,7 @@ r1073:= -acsch(tanh(x))+(1+coth(x)^2)^(1/2)*tanh(x) a1073:= integrate(t1073,x) --R --R ---R (368) +--R (3) --R +-+ 2 +-+ +-+ 2 +-+ --R (- \|2 sinh(x) - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) - \|2 ) --R * @@ -39610,7 +39888,7 @@ a1073:= integrate(t1073,x) m1073:= a1073-r1073 --R --R ---R (369) +--R (4) --R +-+ 2 +-+ +-+ 2 +-+ --R (- \|2 sinh(x) - 2\|2 cosh(x)sinh(x) - \|2 cosh(x) - \|2 ) --R * @@ -39725,13 +40003,16 @@ m1073:= a1073-r1073 --d1073:= D(m1073,x) --E 406 +)clear all + + --S 407 of 531 t1074:= sech(x)^2*(1+tanh(x)^2)^(1/2) --R --R ---R +------------+ ---R 2 | 2 ---R (370) sech(x) \|tanh(x) + 1 +--R +------------+ +--R 2 | 2 +--R (1) sech(x) \|tanh(x) + 1 --R Type: Expression(Integer) --E 407 @@ -39739,11 +40020,11 @@ t1074:= sech(x)^2*(1+tanh(x)^2)^(1/2) r1074:= 1/2*asinh(tanh(x))+1/2*tanh(x)*(1+tanh(x)^2)^(1/2) --R --R ---R +------------+ ---R | 2 ---R tanh(x)\|tanh(x) + 1 + asinh(tanh(x)) ---R (371) --------------------------------------- ---R 2 +--R +------------+ +--R | 2 +--R tanh(x)\|tanh(x) + 1 + asinh(tanh(x)) +--R (2) --------------------------------------- +--R 2 --R Type: Expression(Integer) --E 408 @@ -39751,7 +40032,7 @@ r1074:= 1/2*asinh(tanh(x))+1/2*tanh(x)*(1+tanh(x)^2)^(1/2) a1074:= integrate(t1074,x) --R --R ---R (372) +--R (3) --R +-+ 4 +-+ 3 --R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) --R + @@ -39949,7 +40230,7 @@ a1074:= integrate(t1074,x) m1074:= a1074-r1074 --R --R ---R (373) +--R (4) --R +-+ 4 +-+ 3 --R \|2 sinh(x) + 4\|2 cosh(x)sinh(x) --R + @@ -40230,15 +40511,18 @@ m1074:= a1074-r1074 --d1074:= D(m1074,x) --E 411 +)clear all + + --S 412 of 531 t1075:= sech(x)^2/(tanh(x)^2+tanh(x)^3) --R --R ---R 2 ---R sech(x) ---R (374) ------------------- ---R 3 2 ---R tanh(x) + tanh(x) +--R 2 +--R sech(x) +--R (1) ------------------- +--R 3 2 +--R tanh(x) + tanh(x) --R Type: Expression(Integer) --E 412 @@ -40246,7 +40530,7 @@ t1075:= sech(x)^2/(tanh(x)^2+tanh(x)^3) r1075:= -coth(x)+log(1+coth(x)) --R --R ---R (375) log(coth(x) + 1) - coth(x) +--R (2) log(coth(x) + 1) - coth(x) --R Type: Expression(Integer) --E 413 @@ -40254,7 +40538,7 @@ r1075:= -coth(x)+log(1+coth(x)) a1075:= integrate(t1075,x) --R --R ---R (376) +--R (3) --R 2 2 2sinh(x) --R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(- -----------------) --R sinh(x) - cosh(x) @@ -40271,7 +40555,7 @@ a1075:= integrate(t1075,x) m1075:= a1075-r1075 --R --R ---R (377) +--R (4) --R 2 2 --R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(coth(x) + 1) --R + @@ -40294,7 +40578,7 @@ m1075:= a1075-r1075 d1075:= D(m1075,x) --R --R ---R (378) +--R (5) --R 2 5 --R (- coth(x) + coth(x) + 1)sinh(x) --R + @@ -40335,15 +40619,18 @@ d1075:= D(m1075,x) --R Type: Expression(Integer) --E 416 +)clear all + + --S 417 of 531 t1076:= sech(x)^2/(-tanh(x)^2+tanh(x)^3) --R --R ---R 2 ---R sech(x) ---R (379) ------------------- ---R 3 2 ---R tanh(x) - tanh(x) +--R 2 +--R sech(x) +--R (1) ------------------- +--R 3 2 +--R tanh(x) - tanh(x) --R Type: Expression(Integer) --E 417 @@ -40351,7 +40638,7 @@ t1076:= sech(x)^2/(-tanh(x)^2+tanh(x)^3) r1076:= coth(x)+log(1-coth(x)) --R --R ---R (380) log(- coth(x) + 1) + coth(x) +--R (2) log(- coth(x) + 1) + coth(x) --R Type: Expression(Integer) --E 418 @@ -40359,7 +40646,7 @@ r1076:= coth(x)+log(1-coth(x)) a1076:= integrate(t1076,x) --R --R ---R (381) +--R (3) --R 2 2 2sinh(x) --R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(- -----------------) + 2 --R sinh(x) - cosh(x) @@ -40373,7 +40660,7 @@ a1076:= integrate(t1076,x) m1076:= a1076-r1076 --R --R ---R (382) +--R (4) --R 2 2 2sinh(x) --R (- sinh(x) - 2cosh(x)sinh(x) - cosh(x) + 1)log(- -----------------) --R sinh(x) - cosh(x) @@ -40393,7 +40680,7 @@ m1076:= a1076-r1076 d1076:= D(m1076,x) --R --R ---R (383) +--R (5) --R 2 5 --R (coth(x) + coth(x) - 1)sinh(x) --R + @@ -40434,15 +40721,18 @@ d1076:= D(m1076,x) --R Type: Expression(Integer) --E 421 +)clear all + + --S 422 of 531 t1077:= sech(x)^2/(2+2*tanh(x)+tanh(x)^2) --R --R ---R 2 ---R sech(x) ---R (384) ----------------------- ---R 2 ---R tanh(x) + 2tanh(x) + 2 +--R 2 +--R sech(x) +--R (1) ----------------------- +--R 2 +--R tanh(x) + 2tanh(x) + 2 --R Type: Expression(Integer) --E 422 @@ -40450,7 +40740,7 @@ t1077:= sech(x)^2/(2+2*tanh(x)+tanh(x)^2) r1077:= atan(1+tanh(x)) --R --R ---R (385) atan(tanh(x) + 1) +--R (2) atan(tanh(x) + 1) --R Type: Expression(Integer) --E 423 @@ -40458,9 +40748,9 @@ r1077:= atan(1+tanh(x)) a1077:= integrate(t1077,x) --R --R ---R 2sinh(x) + 3cosh(x) ---R (386) - atan(-------------------) ---R sinh(x) - cosh(x) +--R 2sinh(x) + 3cosh(x) +--R (3) - atan(-------------------) +--R sinh(x) - cosh(x) --R Type: Union(Expression(Integer),...) --E 424 @@ -40468,9 +40758,9 @@ a1077:= integrate(t1077,x) m1077:= a1077-r1077 --R --R ---R 2sinh(x) + 3cosh(x) ---R (387) - atan(tanh(x) + 1) - atan(-------------------) ---R sinh(x) - cosh(x) +--R 2sinh(x) + 3cosh(x) +--R (4) - atan(tanh(x) + 1) - atan(-------------------) +--R sinh(x) - cosh(x) --R Type: Expression(Integer) --E 425 @@ -40478,7 +40768,7 @@ m1077:= a1077-r1077 d1077:= D(m1077,x) --R --R ---R (388) +--R (5) --R 2 2 2 2 --R (2cosh(x)sinh(x) + 3cosh(x) )tanh(x) + (- 2sinh(x) + 2cosh(x) )tanh(x) --R + @@ -40496,15 +40786,18 @@ d1077:= D(m1077,x) --R Type: Expression(Integer) --E 426 +)clear all + + --S 427 of 531 t1078:= sech(x)^2/(3-4*tanh(x)^3) --R --R ---R 2 ---R sech(x) ---R (389) - ------------- ---R 3 ---R 4tanh(x) - 3 +--R 2 +--R sech(x) +--R (1) - ------------- +--R 3 +--R 4tanh(x) - 3 --R Type: Expression(Integer) --E 427 @@ -40514,7 +40807,7 @@ r1078:= 1/18*atan(1/6*(6^(1/3)+4*tanh(x))*2^(2/3)*3^(1/6))*2^(1/3)*3^(5/6)-_ 2*6^(1/3)*tanh(x)+4*tanh(x)^2)*6^(1/3) --R --R ---R (390) +--R (2) --R 3+-+ 2 3+-+ 3+-+2 3+-+ 3+-+ --R \|6 log(4tanh(x) + 2\|6 tanh(x) + \|6 ) - 2\|6 log(- 2tanh(x) + \|6 ) --R + @@ -40531,7 +40824,7 @@ r1078:= 1/18*atan(1/6*(6^(1/3)+4*tanh(x))*2^(2/3)*3^(1/6))*2^(1/3)*3^(5/6)-_ a1078:= integrate(t1078,x) --R --R ---R (391) +--R (3) --R - --R 3+---+ +-+ --R \|- 1 \|3 @@ -40590,7 +40883,7 @@ a1078:= integrate(t1078,x) m1078:= a1078-r1078 --R --R ---R (392) +--R (4) --R +-+3+-+3+--+ 2 3+-+ 3+-+2 --R - \|3 \|6 \|36 log(4tanh(x) + 2\|6 tanh(x) + \|6 ) --R + @@ -40660,15 +40953,18 @@ m1078:= a1078-r1078 --d1078:= D(m1078,x) --E 431 +)clear all + + --S 432 of 531 t1079:= sech(x)^2/(11-5*tanh(x)+5*tanh(x)^2) --R --R ---R 2 ---R sech(x) ---R (393) ------------------------- ---R 2 ---R 5tanh(x) - 5tanh(x) + 11 +--R 2 +--R sech(x) +--R (1) ------------------------- +--R 2 +--R 5tanh(x) - 5tanh(x) + 11 --R Type: Expression(Integer) --E 432 @@ -40676,12 +40972,12 @@ t1079:= sech(x)^2/(11-5*tanh(x)+5*tanh(x)^2) r1079:= -2/195*atan(1/39*195^(1/2)*(1-2*tanh(x)))*195^(1/2) --R --R ---R +---+ +---+ ---R +---+ 2\|195 tanh(x) - \|195 ---R 2\|195 atan(-----------------------) ---R 39 ---R (394) ------------------------------------ ---R 195 +--R +---+ +---+ +--R +---+ 2\|195 tanh(x) - \|195 +--R 2\|195 atan(-----------------------) +--R 39 +--R (2) ------------------------------------ +--R 195 --R Type: Expression(Integer) --E 433 @@ -40689,13 +40985,13 @@ r1079:= -2/195*atan(1/39*195^(1/2)*(1-2*tanh(x)))*195^(1/2) a1079:= integrate(t1079,x) --R --R ---R +---+ +---+ ---R 5\|195 sinh(x) + 17\|195 cosh(x) ---R 2atan(--------------------------------) ---R 195sinh(x) - 195cosh(x) ---R (395) - --------------------------------------- ---R +---+ ---R \|195 +--R +---+ +---+ +--R 5\|195 sinh(x) + 17\|195 cosh(x) +--R 2atan(--------------------------------) +--R 195sinh(x) - 195cosh(x) +--R (3) - --------------------------------------- +--R +---+ +--R \|195 --R Type: Union(Expression(Integer),...) --E 434 @@ -40703,7 +40999,7 @@ a1079:= integrate(t1079,x) m1079:= a1079-r1079 --R --R ---R (396) +--R (4) --R +---+ +---+ +---+ +---+ --R 2\|195 tanh(x) - \|195 5\|195 sinh(x) + 17\|195 cosh(x) --R - 2atan(-----------------------) - 2atan(--------------------------------) @@ -40718,7 +41014,7 @@ m1079:= a1079-r1079 d1079:= D(m1079,x) --R --R ---R (397) +--R (5) --R 2 2 2 2 --R (- 5cosh(x)sinh(x) + 16cosh(x) )tanh(x) + (5sinh(x) - 5cosh(x) )tanh(x) --R + @@ -40736,15 +41032,18 @@ d1079:= D(m1079,x) --R Type: Expression(Integer) --E 436 +)clear all + + --S 437 of 531 t1080:= sech(x)^2/(1+sech(x)^2-3*tanh(x)) --R --R ---R 2 ---R sech(x) ---R (398) - ----------------------- ---R 2 ---R 3tanh(x) - sech(x) - 1 +--R 2 +--R sech(x) +--R (1) - ----------------------- +--R 2 +--R 3tanh(x) - sech(x) - 1 --R Type: Expression(Integer) --E 437 @@ -40752,12 +41051,12 @@ t1080:= sech(x)^2/(1+sech(x)^2-3*tanh(x)) r1080:= 2/17*atanh(1/17*(3+2*tanh(x))*17^(1/2))*17^(1/2) --R --R ---R +--+ +--+ ---R +--+ 2\|17 tanh(x) + 3\|17 ---R 2\|17 atanh(----------------------) ---R 17 ---R (399) ----------------------------------- ---R 17 +--R +--+ +--+ +--R +--+ 2\|17 tanh(x) + 3\|17 +--R 2\|17 atanh(----------------------) +--R 17 +--R (2) ----------------------------------- +--R 17 --R Type: Expression(Integer) --E 438 @@ -40765,7 +41064,7 @@ r1080:= 2/17*atanh(1/17*(3+2*tanh(x))*17^(1/2))*17^(1/2) a1080:= integrate(t1080,x) --R --R ---R (400) +--R (3) --R log --R +--+ 2 +--+ --R (- 15\|17 + 51)sinh(x) + (22\|17 - 102)cosh(x)sinh(x) @@ -40785,7 +41084,7 @@ a1080:= integrate(t1080,x) m1080:= a1080-r1080 --R --R ---R (401) +--R (4) --R log --R +--+ 2 +--+ --R (- 15\|17 + 51)sinh(x) + (22\|17 - 102)cosh(x)sinh(x) @@ -40810,7 +41109,7 @@ m1080:= a1080-r1080 d1080:= D(m1080,x) --R --R ---R (402) +--R (5) --R +--+ 4 +--+ 3 --R (- 27\|17 + 119)sinh(x) + (112\|17 - 408)cosh(x)sinh(x) --R + @@ -40895,14 +41194,17 @@ d1080:= D(m1080,x) --R Type: Expression(Integer) --E 441 +)clear all + + --S 442 of 531 t1081:= sech(x)^2*(a+b*tanh(x))/(c+d*tanh(x)) --R --R ---R 2 2 ---R b sech(x) tanh(x) + a sech(x) ---R (403) ------------------------------ ---R d tanh(x) + c +--R 2 2 +--R b sech(x) tanh(x) + a sech(x) +--R (1) ------------------------------ +--R d tanh(x) + c --R Type: Expression(Integer) --E 442 @@ -40910,10 +41212,10 @@ t1081:= sech(x)^2*(a+b*tanh(x))/(c+d*tanh(x)) r1081:= -(b*c-a*d)*log(c+d*tanh(x))/d^2+b*tanh(x)/d --R --R ---R (a d - b c)log(d tanh(x) + c) + b d tanh(x) ---R (404) ------------------------------------------- ---R 2 ---R d +--R (a d - b c)log(d tanh(x) + c) + b d tanh(x) +--R (2) ------------------------------------------- +--R 2 +--R d --R Type: Expression(Integer) --E 443 @@ -40921,7 +41223,7 @@ r1081:= -(b*c-a*d)*log(c+d*tanh(x))/d^2+b*tanh(x)/d a1081:= integrate(t1081,x) --R --R ---R (405) +--R (3) --R 2 --R (- a d + b c)sinh(x) + (- 2a d + 2b c)cosh(x)sinh(x) --R + @@ -40953,7 +41255,7 @@ a1081:= integrate(t1081,x) m1081:= a1081-r1081 --R --R ---R (406) +--R (4) --R 2 --R (- a d + b c)sinh(x) + (- 2a d + 2b c)cosh(x)sinh(x) --R + @@ -40994,7 +41296,7 @@ m1081:= a1081-r1081 d1081:= D(m1081,x) --R --R ---R (407) +--R (5) --R 2 5 2 2 4 --R b d cosh(x)sinh(x) + (4b d + b c d)cosh(x) sinh(x) --R + @@ -41132,14 +41434,17 @@ d1081:= D(m1081,x) --R Type: Expression(Integer) --E 446 +)clear all + + --S 447 of 531 t1082:= sech(x)^2*(a+b*tanh(x))^2/(c+d*tanh(x)) --R --R ---R 2 2 2 2 2 2 ---R b sech(x) tanh(x) + 2a b sech(x) tanh(x) + a sech(x) ---R (408) ------------------------------------------------------ ---R d tanh(x) + c +--R 2 2 2 2 2 2 +--R b sech(x) tanh(x) + 2a b sech(x) tanh(x) + a sech(x) +--R (1) ------------------------------------------------------ +--R d tanh(x) + c --R Type: Expression(Integer) --E 447 @@ -41148,7 +41453,7 @@ r1082:= (b*c-a*d)^2*log(c+d*tanh(x))/d^3-b*(b*c-a*d)*tanh(x)/d^2+_ 1/2*(a+b*tanh(x))^2/d --R --R ---R (409) +--R (2) --R 2 2 2 2 2 2 2 --R (2a d - 4a b c d + 2b c )log(d tanh(x) + c) + b d tanh(x) --R + @@ -41164,7 +41469,7 @@ r1082:= (b*c-a*d)^2*log(c+d*tanh(x))/d^3-b*(b*c-a*d)*tanh(x)/d^2+_ a1082:= integrate(t1082,x) --R --R ---R (410) +--R (3) --R 2 2 2 2 4 --R (- a d + 2a b c d - b c )sinh(x) --R + @@ -41246,7 +41551,7 @@ a1082:= integrate(t1082,x) m1082:= a1082-r1082 --R --R ---R (411) +--R (4) --R 2 2 2 2 4 --R (- 2a d + 4a b c d - 2b c )sinh(x) --R + @@ -41400,7 +41705,7 @@ m1082:= a1082-r1082 d1082:= D(m1082,x) --R --R ---R (412) +--R (5) --R 2 3 7 2 3 2 2 2 6 --R b d cosh(x)sinh(x) + (6b d + b c d )cosh(x) sinh(x) --R + @@ -41830,11 +42135,14 @@ d1082:= D(m1082,x) --R Type: Expression(Integer) --E 451 +)clear all + + --S 452 of 531 t1083:= sech(x)^2*(a+b*tanh(x))^3/(c+d*tanh(x)) --R --R ---R (413) +--R (1) --R 3 2 3 2 2 2 2 2 --R b sech(x) tanh(x) + 3a b sech(x) tanh(x) + 3a b sech(x) tanh(x) --R + @@ -41850,7 +42158,7 @@ r1083:= -(b*c-a*d)^3*log(c+d*tanh(x))/d^4+b*(b*c-a*d)^2*tanh(x)/d^3-_ 1/2*(b*c-a*d)*(a+b*tanh(x))^2/d^2+1/3*(a+b*tanh(x))^3/d --R --R ---R (414) +--R (2) --R 3 3 2 2 2 2 3 3 --R (6a d - 18a b c d + 18a b c d - 6b c )log(d tanh(x) + c) --R + @@ -41869,7 +42177,7 @@ r1083:= -(b*c-a*d)^3*log(c+d*tanh(x))/d^4+b*(b*c-a*d)^2*tanh(x)/d^3-_ a1083:= integrate(t1083,x) --R --R ---R (415) +--R (3) --R 3 3 2 2 2 2 3 3 6 --R (- 3a d + 9a b c d - 9a b c d + 3b c )sinh(x) --R + @@ -42055,7 +42363,7 @@ a1083:= integrate(t1083,x) m1083:= a1083-r1083 --R --R ---R (416) +--R (4) --R 3 3 2 2 2 2 3 3 6 --R (- 6a d + 18a b c d - 18a b c d + 6b c )sinh(x) --R + @@ -42477,7 +42785,7 @@ m1083:= a1083-r1083 d1083:= D(m1083,x) --R --R ---R (417) +--R (5) --R 3 4 9 3 4 3 3 2 8 --R b d cosh(x)sinh(x) + (8b d + b c d )cosh(x) sinh(x) --R + @@ -43394,15 +43702,18 @@ d1083:= D(m1083,x) --R Type: Expression(Integer) --E 456 +)clear all + + --S 457 of 531 t1084:= sech(x)^2*tanh(x)^2/(2+tanh(x)^3)^2 --R --R ---R 2 2 ---R sech(x) tanh(x) ---R (418) ------------------------ ---R 6 3 ---R tanh(x) + 4tanh(x) + 4 +--R 2 2 +--R sech(x) tanh(x) +--R (1) ------------------------ +--R 6 3 +--R tanh(x) + 4tanh(x) + 4 --R Type: Expression(Integer) --E 457 @@ -43410,10 +43721,10 @@ t1084:= sech(x)^2*tanh(x)^2/(2+tanh(x)^3)^2 r1084:= -1/(6+3*tanh(x)^3) --R --R ---R 1 ---R (419) - ------------- ---R 3 ---R 3tanh(x) + 6 +--R 1 +--R (2) - ------------- +--R 3 +--R 3tanh(x) + 6 --R Type: Expression(Integer) --E 458 @@ -43421,7 +43732,7 @@ r1084:= -1/(6+3*tanh(x)^3) a1084:= integrate(t1084,x) --R --R ---R (420) +--R (3) --R 2 2 --R - 8sinh(x) - 8cosh(x)sinh(x) - 8cosh(x) --R / @@ -43437,7 +43748,7 @@ a1084:= integrate(t1084,x) m1084:= a1084-r1084 --R --R ---R (421) +--R (4) --R 2 2 3 4 --R (- 8sinh(x) - 8cosh(x)sinh(x) - 8cosh(x) )tanh(x) + 9sinh(x) --R + @@ -43468,7 +43779,7 @@ m1084:= a1084-r1084 d1084:= D(m1084,x) --R --R ---R (422) +--R (5) --R 6 5 2 4 --R 8sinh(x) + 32cosh(x)sinh(x) + 56cosh(x) sinh(x) --R + @@ -43621,15 +43932,18 @@ d1084:= D(m1084,x) --R Type: Expression(Integer) --E 461 +)clear all + + --S 462 of 531 t1085:= sech(x)^2*(2+tanh(x)^2)/(1+tanh(x)^3) --R --R ---R 2 2 2 ---R sech(x) tanh(x) + 2sech(x) ---R (423) ---------------------------- ---R 3 ---R tanh(x) + 1 +--R 2 2 2 +--R sech(x) tanh(x) + 2sech(x) +--R (1) ---------------------------- +--R 3 +--R tanh(x) + 1 --R Type: Expression(Integer) --E 462 @@ -43637,12 +43951,12 @@ t1085:= sech(x)^2*(2+tanh(x)^2)/(1+tanh(x)^3) r1085:= -2/3*atan(1/3*(1-2*tanh(x))*3^(1/2))*3^(1/2)+log(1+tanh(x)) --R --R ---R +-+ +-+ ---R +-+ 2\|3 tanh(x) - \|3 ---R 3log(tanh(x) + 1) + 2\|3 atan(-------------------) ---R 3 ---R (424) -------------------------------------------------- ---R 3 +--R +-+ +-+ +--R +-+ 2\|3 tanh(x) - \|3 +--R 3log(tanh(x) + 1) + 2\|3 atan(-------------------) +--R 3 +--R (2) -------------------------------------------------- +--R 3 --R Type: Expression(Integer) --E 463 @@ -43650,7 +43964,7 @@ r1085:= -2/3*atan(1/3*(1-2*tanh(x))*3^(1/2))*3^(1/2)+log(1+tanh(x)) a1085:= integrate(t1085,x) --R --R ---R (425) +--R (3) --R +-+ +-+ --R +-+ 2cosh(x) \|3 sinh(x) + \|3 cosh(x) +-+ --R - \|3 log(- -----------------) - 2atan(-------------------------) + 2x\|3 @@ -43665,7 +43979,7 @@ a1085:= integrate(t1085,x) m1085:= a1085-r1085 --R --R ---R (426) +--R (4) --R +-+ +-+ 2cosh(x) --R - \|3 log(tanh(x) + 1) - \|3 log(- -----------------) --R sinh(x) - cosh(x) @@ -43684,7 +43998,7 @@ m1085:= a1085-r1085 d1085:= D(m1085,x) --R --R ---R (427) +--R (5) --R 2 2 3 3 --R (cosh(x)sinh(x) - cosh(x) sinh(x) + cosh(x) )tanh(x) --R + @@ -43705,12 +44019,15 @@ d1085:= D(m1085,x) --R Type: Expression(Integer) --E 466 +)clear all + + --S 467 of 531 t1086:= sech(x)^4*(-1+sech(x)^2)^2*tanh(x) --R --R ---R 8 6 4 ---R (428) (sech(x) - 2sech(x) + sech(x) )tanh(x) +--R 8 6 4 +--R (1) (sech(x) - 2sech(x) + sech(x) )tanh(x) --R Type: Expression(Integer) --E 467 @@ -43718,10 +44035,10 @@ t1086:= sech(x)^4*(-1+sech(x)^2)^2*tanh(x) r1086:= -1/24*tanh(x)^6*(-4+3*tanh(x)^2) --R --R ---R 8 6 ---R - 3tanh(x) + 4tanh(x) ---R (429) ----------------------- ---R 24 +--R 8 6 +--R - 3tanh(x) + 4tanh(x) +--R (2) ----------------------- +--R 24 --R Type: Expression(Integer) --E 468 @@ -43729,7 +44046,7 @@ r1086:= -1/24*tanh(x)^6*(-4+3*tanh(x)^2) a1086:= integrate(t1086,x) --R --R ---R (430) +--R (3) --R 6 5 2 4 --R - 12sinh(x) - 72cosh(x)sinh(x) + (- 180cosh(x) + 16)sinh(x) --R + @@ -43780,7 +44097,7 @@ a1086:= integrate(t1086,x) m1086:= a1086-r1086 --R --R ---R (431) +--R (4) --R 10 9 2 8 --R 3sinh(x) + 30cosh(x)sinh(x) + (135cosh(x) + 24)sinh(x) --R + @@ -43912,7 +44229,7 @@ m1086:= a1086-r1086 d1086:= D(m1086,x) --R --R ---R (432) +--R (5) --R 20 19 2 18 --R - 3sinh(x) - 60cosh(x)sinh(x) + (- 570cosh(x) - 48)sinh(x) --R + @@ -44633,14 +44950,17 @@ d1086:= D(m1086,x) --R Type: Expression(Integer) --E 471 +)clear all + + --S 472 of 531 t1087:= csch(x)^2/(a+b*coth(x)) --R --R ---R 2 ---R csch(x) ---R (433) ------------- ---R b coth(x) + a +--R 2 +--R csch(x) +--R (1) ------------- +--R b coth(x) + a --R Type: Expression(Integer) --E 472 @@ -44648,9 +44968,9 @@ t1087:= csch(x)^2/(a+b*coth(x)) r1087:= -log(a+b*coth(x))/b --R --R ---R log(b coth(x) + a) ---R (434) - ------------------ ---R b +--R log(b coth(x) + a) +--R (2) - ------------------ +--R b --R Type: Expression(Integer) --E 473 @@ -44658,11 +44978,11 @@ r1087:= -log(a+b*coth(x))/b a1087:= integrate(t1087,x) --R --R ---R 2sinh(x) - 2a sinh(x) - 2b cosh(x) ---R log(- -----------------) - log(-------------------------) ---R sinh(x) - cosh(x) sinh(x) - cosh(x) ---R (435) --------------------------------------------------------- ---R b +--R 2sinh(x) - 2a sinh(x) - 2b cosh(x) +--R log(- -----------------) - log(-------------------------) +--R sinh(x) - cosh(x) sinh(x) - cosh(x) +--R (3) --------------------------------------------------------- +--R b --R Type: Union(Expression(Integer),...) --E 474 @@ -44670,7 +44990,7 @@ a1087:= integrate(t1087,x) m1087:= a1087-r1087 --R --R ---R (436) +--R (4) --R 2sinh(x) --R log(b coth(x) + a) + log(- -----------------) --R sinh(x) - cosh(x) @@ -44687,7 +45007,7 @@ m1087:= a1087-r1087 d1087:= D(m1087,x) --R --R ---R (437) +--R (5) --R 2 2 --R (- a coth(x) - b coth(x))sinh(x) --R + @@ -44699,12 +45019,15 @@ d1087:= D(m1087,x) --R Type: Expression(Integer) --E 476 +)clear all + + --S 477 of 531 t1088:= csch(x)^2*(a+b*coth(x))^n --R --R ---R 2 n ---R (438) csch(x) (b coth(x) + a) +--R 2 n +--R (1) csch(x) (b coth(x) + a) --R Type: Expression(Integer) --E 477 @@ -44712,10 +45035,10 @@ t1088:= csch(x)^2*(a+b*coth(x))^n r1088:= -(a+b*coth(x))^(1+n)/b/(1+n) --R --R ---R n + 1 ---R (b coth(x) + a) ---R (439) - -------------------- ---R b n + b +--R n + 1 +--R (b coth(x) + a) +--R (2) - -------------------- +--R b n + b --R Type: Expression(Integer) --E 478 @@ -44723,7 +45046,7 @@ r1088:= -(a+b*coth(x))^(1+n)/b/(1+n) a1088:= integrate(t1088,x) --R --R ---R (440) +--R (3) --R a sinh(x) + b cosh(x) --R (- a sinh(x) - b cosh(x))sinh(n log(---------------------)) --R sinh(x) @@ -44740,7 +45063,7 @@ a1088:= integrate(t1088,x) m1088:= a1088-r1088 --R --R ---R (441) +--R (4) --R a sinh(x) + b cosh(x) --R (- a sinh(x) - b cosh(x))sinh(n log(---------------------)) --R sinh(x) @@ -44760,7 +45083,7 @@ m1088:= a1088-r1088 d1088:= D(m1088,x) --R --R ---R (442) +--R (5) --R 2 2 a sinh(x) + b cosh(x) --R (- sinh(x) + cosh(x) )sinh(n log(---------------------)) --R sinh(x) @@ -44777,15 +45100,18 @@ d1088:= D(m1088,x) --R Type: Expression(Integer) --E 481 +)clear all + + --S 482 of 531 t1089:= csch(x)^2*(-1-1/(1-coth(x)^2)) --R --R ---R 2 2 ---R (- coth(x) + 2)csch(x) ---R (443) ------------------------ ---R 2 ---R coth(x) - 1 +--R 2 2 +--R (- coth(x) + 2)csch(x) +--R (1) ------------------------ +--R 2 +--R coth(x) - 1 --R Type: Expression(Integer) --E 482 @@ -44793,7 +45119,7 @@ t1089:= csch(x)^2*(-1-1/(1-coth(x)^2)) r1089:= x+coth(x) --R --R ---R (444) coth(x) + x +--R (2) coth(x) + x --R Type: Expression(Integer) --E 483 @@ -44801,9 +45127,9 @@ r1089:= x+coth(x) a1089:= integrate(t1089,x) --R --R ---R (x - 1)sinh(x) + cosh(x) ---R (445) ------------------------ ---R sinh(x) +--R (x - 1)sinh(x) + cosh(x) +--R (3) ------------------------ +--R sinh(x) --R Type: Union(Expression(Integer),...) --E 484 @@ -44811,9 +45137,9 @@ a1089:= integrate(t1089,x) m1089:= a1089-r1089 --R --R ---R (- coth(x) - 1)sinh(x) + cosh(x) ---R (446) -------------------------------- ---R sinh(x) +--R (- coth(x) - 1)sinh(x) + cosh(x) +--R (4) -------------------------------- +--R sinh(x) --R Type: Expression(Integer) --E 485 @@ -44821,22 +45147,25 @@ m1089:= a1089-r1089 d1089:= D(m1089,x) --R --R ---R 2 2 2 ---R coth(x) sinh(x) - cosh(x) ---R (447) --------------------------- ---R 2 ---R sinh(x) +--R 2 2 2 +--R coth(x) sinh(x) - cosh(x) +--R (5) --------------------------- +--R 2 +--R sinh(x) --R Type: Expression(Integer) --E 486 +)clear all + + --S 487 of 531 t1090:= csch(x)^2*(a+b*coth(x))/(c+d*coth(x)) --R --R ---R 2 ---R (b coth(x) + a)csch(x) ---R (448) ----------------------- ---R d coth(x) + c +--R 2 +--R (b coth(x) + a)csch(x) +--R (1) ----------------------- +--R d coth(x) + c --R Type: Expression(Integer) --E 487 @@ -44844,10 +45173,10 @@ t1090:= csch(x)^2*(a+b*coth(x))/(c+d*coth(x)) r1090:= -b*coth(x)/d+(b*c-a*d)*log(c+d*coth(x))/d^2 --R --R ---R (- a d + b c)log(d coth(x) + c) - b d coth(x) ---R (449) --------------------------------------------- ---R 2 ---R d +--R (- a d + b c)log(d coth(x) + c) - b d coth(x) +--R (2) --------------------------------------------- +--R 2 +--R d --R Type: Expression(Integer) --E 488 @@ -44855,7 +45184,7 @@ r1090:= -b*coth(x)/d+(b*c-a*d)*log(c+d*coth(x))/d^2 a1090:= integrate(t1090,x) --R --R ---R (450) +--R (3) --R 2 --R (a d - b c)sinh(x) + (2a d - 2b c)cosh(x)sinh(x) --R + @@ -44887,7 +45216,7 @@ a1090:= integrate(t1090,x) m1090:= a1090-r1090 --R --R ---R (451) +--R (4) --R 2 --R (a d - b c)sinh(x) + (2a d - 2b c)cosh(x)sinh(x) --R + @@ -44931,7 +45260,7 @@ m1090:= a1090-r1090 d1090:= D(m1090,x) --R --R ---R (452) +--R (5) --R 3 2 2 2 --R (- b c d coth(x) - a c d coth(x) + (- a d + 2b c d)coth(x) + b c ) --R * @@ -45084,14 +45413,17 @@ d1090:= D(m1090,x) --R Type: Expression(Integer) --E 491 +)clear all + + --S 492 of 531 t1091:= csch(x)^2*(a+b*coth(x))^2/(c+d*coth(x)) --R --R ---R 2 2 2 2 ---R (b coth(x) + 2a b coth(x) + a )csch(x) ---R (453) ---------------------------------------- ---R d coth(x) + c +--R 2 2 2 2 +--R (b coth(x) + 2a b coth(x) + a )csch(x) +--R (1) ---------------------------------------- +--R d coth(x) + c --R Type: Expression(Integer) --E 492 @@ -45100,7 +45432,7 @@ r1091:= b*(b*c-a*d)*coth(x)/d^2-1/2*(a+b*coth(x))^2/d-_ (b*c-a*d)^2*log(c+d*coth(x))/d^3 --R --R ---R (454) +--R (2) --R 2 2 2 2 2 2 2 --R (- 2a d + 4a b c d - 2b c )log(d coth(x) + c) - b d coth(x) --R + @@ -45116,7 +45448,7 @@ r1091:= b*(b*c-a*d)*coth(x)/d^2-1/2*(a+b*coth(x))^2/d-_ a1091:= integrate(t1091,x) --R --R ---R (455) +--R (3) --R 2 2 2 2 4 --R (a d - 2a b c d + b c )sinh(x) --R + @@ -45198,7 +45530,7 @@ a1091:= integrate(t1091,x) m1091:= a1091-r1091 --R --R ---R (456) +--R (4) --R 2 2 2 2 4 --R (2a d - 4a b c d + 2b c )sinh(x) --R + @@ -45354,7 +45686,7 @@ m1091:= a1091-r1091 d1091:= D(m1091,x) --R --R ---R (457) +--R (5) --R 2 2 4 2 3 2 2 2 2 --R - b c d coth(x) - 2a b c d coth(x) + (b - a )c d coth(x) --R + @@ -45775,14 +46107,17 @@ d1091:= D(m1091,x) --R Type: Expression(Integer) --E 496 +)clear all + + --S 497 of 531 t1092:= csch(x)^2*(a+b*coth(x))^3/(c+d*coth(x)) --R --R ---R 3 3 2 2 2 3 2 ---R (b coth(x) + 3a b coth(x) + 3a b coth(x) + a )csch(x) ---R (458) -------------------------------------------------------- ---R d coth(x) + c +--R 3 3 2 2 2 3 2 +--R (b coth(x) + 3a b coth(x) + 3a b coth(x) + a )csch(x) +--R (1) -------------------------------------------------------- +--R d coth(x) + c --R Type: Expression(Integer) --E 497 @@ -45791,7 +46126,7 @@ r1092:= -b*(b*c-a*d)^2*coth(x)/d^3+1/2*(b*c-a*d)*(a+b*coth(x))^2/d^2-_ 1/3*(a+b*coth(x))^3/d+(b*c-a*d)^3*log(c+d*coth(x))/d^4 --R --R ---R (459) +--R (2) --R 3 3 2 2 2 2 3 3 --R (- 6a d + 18a b c d - 18a b c d + 6b c )log(d coth(x) + c) --R + @@ -45810,7 +46145,7 @@ r1092:= -b*(b*c-a*d)^2*coth(x)/d^3+1/2*(b*c-a*d)*(a+b*coth(x))^2/d^2-_ a1092:= integrate(t1092,x) --R --R ---R (460) +--R (3) --R 3 3 2 2 2 2 3 3 6 --R (3a d - 9a b c d + 9a b c d - 3b c )sinh(x) --R + @@ -45996,7 +46331,7 @@ a1092:= integrate(t1092,x) m1092:= a1092-r1092 --R --R ---R (461) +--R (4) --R 3 3 2 2 2 2 3 3 6 --R (6a d - 18a b c d + 18a b c d - 6b c )sinh(x) --R + @@ -46413,14 +46748,17 @@ m1092:= a1092-r1092 --d1092:= D(m1092,x) --E 501 +)clear all + + --S 502 of 531 t1093:= (1+sinh(x)^2)/(1+cosh(x)+sinh(x)) --R --R ---R 2 ---R sinh(x) + 1 ---R (462) --------------------- ---R sinh(x) + cosh(x) + 1 +--R 2 +--R sinh(x) + 1 +--R (1) --------------------- +--R sinh(x) + cosh(x) + 1 --R Type: Expression(Integer) --E 502 @@ -46429,7 +46767,7 @@ r1093:= 3/4*x+1/2*cosh(x)-1/4*cosh(x)^2-log(1+cosh(x)+sinh(x))+_ 1/4*cosh(x)*sinh(x)+1/8 --R --R ---R (463) +--R (2) --R 2 --R - 8log(sinh(x) + cosh(x) + 1) + 2cosh(x)sinh(x) - 2cosh(x) + 4cosh(x) --R + @@ -46443,7 +46781,7 @@ r1093:= 3/4*x+1/2*cosh(x)-1/4*cosh(x)^2-log(1+cosh(x)+sinh(x))+_ a1093:= integrate(t1093,x) --R --R ---R (464) +--R (3) --R 2 2 --R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) )log(sinh(x) + cosh(x) + 1) --R + @@ -46464,7 +46802,7 @@ a1093:= integrate(t1093,x) m1093:= a1093-r1093 --R --R ---R (465) +--R (4) --R 3 2 2 --R (- 2cosh(x) + 2)sinh(x) + (- 2cosh(x) + 2cosh(x) - 1)sinh(x) --R + @@ -46483,7 +46821,7 @@ m1093:= a1093-r1093 d1093:= D(m1093,x) --R --R ---R (466) +--R (5) --R 4 3 2 2 --R - sinh(x) - sinh(x) + (2cosh(x) - cosh(x))sinh(x) --R + @@ -46495,15 +46833,18 @@ d1093:= D(m1093,x) --R Type: Expression(Integer) --E 506 +)clear all + + --S 507 of 531 t1094:= cosh(x)^2/(1+exp(x)) --R --R ---R 2 ---R cosh(x) ---R (467) -------- ---R x ---R %e + 1 +--R 2 +--R cosh(x) +--R (1) -------- +--R x +--R %e + 1 --R Type: Expression(Integer) --E 507 @@ -46511,10 +46852,10 @@ t1094:= cosh(x)^2/(1+exp(x)) r1094:= -1/8*exp(-2*x)+1/4*exp(-x)+1/4*exp(x)+3/4*x-log(1+exp(x)) --R --R ---R x x - x - 2x ---R - 8log(%e + 1) + 2%e + 2%e - %e + 6x ---R (468) --------------------------------------------- ---R 8 +--R x x - x - 2x +--R - 8log(%e + 1) + 2%e + 2%e - %e + 6x +--R (2) --------------------------------------------- +--R 8 --R Type: Expression(Integer) --E 508 @@ -46522,7 +46863,7 @@ r1094:= -1/8*exp(-2*x)+1/4*exp(-x)+1/4*exp(x)+3/4*x-log(1+exp(x)) a1094:= integrate(t1094,x) --R --R ---R (469) +--R (3) --R 2 2 --R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) )log(sinh(x) + cosh(x) + 1) --R + @@ -46543,7 +46884,7 @@ a1094:= integrate(t1094,x) m1094:= a1094-r1094 --R --R ---R (470) +--R (4) --R 2 2 --R (- 8sinh(x) - 16cosh(x)sinh(x) - 8cosh(x) )log(sinh(x) + cosh(x) + 1) --R + @@ -46568,7 +46909,7 @@ m1094:= a1094-r1094 d1094:= D(m1094,x) --R --R ---R (471) +--R (5) --R x 4 --R (%e + 1)sinh(x) --R + @@ -46641,12 +46982,15 @@ d1094:= D(m1094,x) --R Type: Expression(Integer) --E 511 +)clear all + + --S 512 of 531 t1095:= (1+sech(x))^(1/2)*sech(x)*tanh(x)^3 --R --R ---R 3 +-----------+ ---R (472) sech(x)tanh(x) \|sech(x) + 1 +--R 3 +-----------+ +--R (1) sech(x)tanh(x) \|sech(x) + 1 --R Type: Expression(Integer) --E 512 @@ -46654,10 +46998,10 @@ t1095:= (1+sech(x))^(1/2)*sech(x)*tanh(x)^3 r1095:= -4/5*(1+sech(x))^(5/2)+2/7*(1+sech(x))^(7/2) --R --R ---R 3 2 +-----------+ ---R (10sech(x) + 2sech(x) - 26sech(x) - 18)\|sech(x) + 1 ---R (473) ------------------------------------------------------- ---R 35 +--R 3 2 +-----------+ +--R (10sech(x) + 2sech(x) - 26sech(x) - 18)\|sech(x) + 1 +--R (2) ------------------------------------------------------- +--R 35 --R Type: Expression(Integer) --E 513 @@ -46665,7 +47009,7 @@ r1095:= -4/5*(1+sech(x))^(5/2)+2/7*(1+sech(x))^(7/2) a1095:= integrate(t1095,x) --R --R ---R (474) +--R (3) --R 12 11 --R 4480sinh(x) + (53760cosh(x) + 2240)sinh(x) --R + @@ -47059,12 +47403,15 @@ a1095:= integrate(t1095,x) --d1095:= D(m1095,x) --E 516 +)clear all + + --S 517 of 531 t1096:= (1+csch(x))^(1/2)*csch(x)*coth(x)^3 --R --R ---R 3 +-----------+ ---R (475) coth(x) csch(x)\|csch(x) + 1 +--R 3 +-----------+ +--R (1) coth(x) csch(x)\|csch(x) + 1 --R Type: Expression(Integer) --E 517 @@ -47072,10 +47419,10 @@ t1096:= (1+csch(x))^(1/2)*csch(x)*coth(x)^3 r1096:= -4/3*(1+csch(x))^(3/2)+4/5*(1+csch(x))^(5/2)-2/7*(1+csch(x))^(7/2) --R --R ---R 3 2 +-----------+ ---R (- 30csch(x) - 6csch(x) - 62csch(x) - 86)\|csch(x) + 1 ---R (476) --------------------------------------------------------- ---R 105 +--R 3 2 +-----------+ +--R (- 30csch(x) - 6csch(x) - 62csch(x) - 86)\|csch(x) + 1 +--R (2) --------------------------------------------------------- +--R 105 --R Type: Expression(Integer) --E 518 @@ -47083,7 +47430,7 @@ r1096:= -4/3*(1+csch(x))^(3/2)+4/5*(1+csch(x))^(5/2)-2/7*(1+csch(x))^(7/2) a1096:= integrate(t1096,x) --R --R ---R (477) +--R (3) --R 6 5 --R - 86sinh(x) + (- 516cosh(x) - 124)sinh(x) --R + @@ -47158,7 +47505,7 @@ a1096:= integrate(t1096,x) m1096:= a1096-r1096 --R --R ---R (478) +--R (4) --R 3 2 10 --R (30csch(x) + 6csch(x) + 62csch(x) + 86)sinh(x) --R + @@ -47420,7 +47767,7 @@ m1096:= a1096-r1096 d1096:= D(m1096,x) --R --R ---R (479) +--R (5) --R 10 9 --R 344sinh(x) + (2752cosh(x) + 964)sinh(x) --R + @@ -47888,12 +48235,15 @@ d1096:= D(m1096,x) --R Type: Expression(Integer) --E 521 +)clear all + + --S 522 of 531 t1097:= cosh(x)^x*(log(cosh(x))+x*tanh(x)) --R --R ---R x ---R (480) (log(cosh(x)) + x tanh(x))cosh(x) +--R x +--R (1) (log(cosh(x)) + x tanh(x))cosh(x) --R Type: Expression(Integer) --E 522 @@ -47901,8 +48251,8 @@ t1097:= cosh(x)^x*(log(cosh(x))+x*tanh(x)) r1097:= cosh(x)^x --R --R ---R x ---R (481) cosh(x) +--R x +--R (2) cosh(x) --R Type: Expression(Integer) --E 523 @@ -47910,7 +48260,7 @@ r1097:= cosh(x)^x a1097:= integrate(t1097,x) --R --R ---R (482) sinh(x log(cosh(x))) + cosh(x log(cosh(x))) +--R (3) sinh(x log(cosh(x))) + cosh(x log(cosh(x))) --R Type: Union(Expression(Integer),...) --E 524 @@ -47918,8 +48268,8 @@ a1097:= integrate(t1097,x) m1097:= a1097-r1097 --R --R ---R x ---R (483) sinh(x log(cosh(x))) + cosh(x log(cosh(x))) - cosh(x) +--R x +--R (4) sinh(x log(cosh(x))) + cosh(x log(cosh(x))) - cosh(x) --R Type: Expression(Integer) --E 525 @@ -47927,7 +48277,7 @@ m1097:= a1097-r1097 d1097:= D(m1097,x) --R --R ---R (484) +--R (5) --R (cosh(x)log(cosh(x)) + x sinh(x))sinh(x log(cosh(x))) --R + --R (cosh(x)log(cosh(x)) + x sinh(x))cosh(x log(cosh(x))) @@ -47939,13 +48289,16 @@ d1097:= D(m1097,x) --R Type: Expression(Integer) --E 526 +)clear all + + --S 527 of 531 t1098:= csch(x)*(1+log(coth(x))^2)^(1/2)*sech(x) --R --R ---R +-----------------+ ---R | 2 ---R (485) csch(x)sech(x)\|log(coth(x)) + 1 +--R +-----------------+ +--R | 2 +--R (1) csch(x)sech(x)\|log(coth(x)) + 1 --R Type: Expression(Integer) --E 527 @@ -47953,11 +48306,11 @@ t1098:= csch(x)*(1+log(coth(x))^2)^(1/2)*sech(x) r1098:= -1/2*asinh(log(coth(x)))-1/2*log(coth(x))*(1+log(coth(x))^2)^(1/2) --R --R ---R +-----------------+ ---R | 2 ---R - log(coth(x))\|log(coth(x)) + 1 - asinh(log(coth(x))) ---R (486) -------------------------------------------------------- ---R 2 +--R +-----------------+ +--R | 2 +--R - log(coth(x))\|log(coth(x)) + 1 - asinh(log(coth(x))) +--R (2) -------------------------------------------------------- +--R 2 --R Type: Expression(Integer) --E 528 @@ -47965,7 +48318,7 @@ r1098:= -1/2*asinh(log(coth(x)))-1/2*log(coth(x))*(1+log(coth(x))^2)^(1/2) a1098:= integrate(t1098,x) --R --R ---R (487) +--R (3) --R +-----------------+ --R cosh(x) | cosh(x) 2 cosh(x) 2 --R (2log(-------) |log(-------) + 1 - 2log(-------) - 1) @@ -47996,7 +48349,7 @@ a1098:= integrate(t1098,x) m1098:= a1098-r1098 --R --R ---R (488) +--R (4) --R +-----------------+ --R cosh(x) | cosh(x) 2 cosh(x) 2 --R (2log(-------) |log(-------) + 1 - 2log(-------) - 1) @@ -48044,7 +48397,7 @@ m1098:= a1098-r1098 d1098:= D(m1098,x) --R --R ---R (489) +--R (5) --R 2 2 cosh(x) 5 --R (8coth(x)sinh(x) - 8cosh(x) coth(x))log(-------) --R sinh(x) diff --git a/src/input/richinvhyper000-099.input.pamphlet b/src/input/richinvhyper000-099.input.pamphlet index 2aa64aa..a7eab02 100644 --- a/src/input/richinvhyper000-099.input.pamphlet +++ b/src/input/richinvhyper000-099.input.pamphlet @@ -16,6 +16,7 @@ )spool richinvhyper000-099.output )set message auto off )clear all + --S 1 of 510 t0000:= asinh(x)^2 @@ -88,12 +89,15 @@ d0000:= D(m0000,x) --R Type: Expression(Integer) --E 5 +)clear all + + --S 6 of 510 t0001:= asinh(x)^3 --R --R --R 3 ---R (6) asinh(x) +--R (1) asinh(x) --R Type: Expression(Integer) --E 6 @@ -103,7 +107,7 @@ r0001:= -6*(1+x^2)^(1/2)+6*x*asinh(x)-3*(1+x^2)^(1/2)*asinh(x)^2+x*asinh(x)^3 --R --R +------+ --R 2 | 2 3 ---R (7) (- 3asinh(x) - 6)\|x + 1 + x asinh(x) + 6x asinh(x) +--R (2) (- 3asinh(x) - 6)\|x + 1 + x asinh(x) + 6x asinh(x) --R Type: Expression(Integer) --E 7 @@ -111,7 +115,7 @@ r0001:= -6*(1+x^2)^(1/2)+6*x*asinh(x)-3*(1+x^2)^(1/2)*asinh(x)^2+x*asinh(x)^3 a0001:= integrate(t0001,x) --R --R ---R (8) +--R (3) --R +------+ +------+ 3 --R | 2 2 | 2 --R (x\|x + 1 - x )log(\|x + 1 + x) @@ -134,7 +138,7 @@ a0001:= integrate(t0001,x) m0001:= a0001-r0001 --R --R ---R (9) +--R (4) --R +------+ +------+ 3 --R | 2 2 | 2 --R (x\|x + 1 - x )log(\|x + 1 + x) @@ -164,18 +168,21 @@ m0001:= a0001-r0001 d0001:= D(m0001,x) --R --R ---R +------+ 3 ---R | 2 3 ---R (10) log(\|x + 1 + x) - asinh(x) +--R +------+ 3 +--R | 2 3 +--R (5) log(\|x + 1 + x) - asinh(x) --R Type: Expression(Integer) --E 10 +)clear all + + --S 11 of 510 t0002:= asinh(x)^4 --R --R ---R 4 ---R (11) asinh(x) +--R 4 +--R (1) asinh(x) --R Type: Expression(Integer) --E 11 @@ -184,7 +191,7 @@ r0002:= 24*x-24*(1+x^2)^(1/2)*asinh(x)+12*x*asinh(x)^2-_ 4*(1+x^2)^(1/2)*asinh(x)^3+x*asinh(x)^4 --R --R ---R (12) +--R (2) --R +------+ --R 3 | 2 4 2 --R (- 4asinh(x) - 24asinh(x))\|x + 1 + x asinh(x) + 12x asinh(x) + 24x @@ -195,7 +202,7 @@ r0002:= 24*x-24*(1+x^2)^(1/2)*asinh(x)+12*x*asinh(x)^2-_ a0002:= integrate(t0002,x) --R --R ---R (13) +--R (3) --R +------+ +------+ 4 --R | 2 2 | 2 --R (x\|x + 1 - x )log(\|x + 1 + x) @@ -222,7 +229,7 @@ a0002:= integrate(t0002,x) m0002:= a0002-r0002 --R --R ---R (14) +--R (4) --R +------+ +------+ 4 --R | 2 2 | 2 --R (x\|x + 1 - x )log(\|x + 1 + x) @@ -256,18 +263,21 @@ m0002:= a0002-r0002 d0002:= D(m0002,x) --R --R ---R +------+ 4 ---R | 2 4 ---R (15) log(\|x + 1 + x) - asinh(x) +--R +------+ 4 +--R | 2 4 +--R (5) log(\|x + 1 + x) - asinh(x) --R Type: Expression(Integer) --E 15 +)clear all + + --S 16 of 510 t0003:= asinh(x)^5 --R --R ---R 5 ---R (16) asinh(x) +--R 5 +--R (1) asinh(x) --R Type: Expression(Integer) --E 16 @@ -276,7 +286,7 @@ r0003:= -120*(1+x^2)^(1/2)+120*x*asinh(x)-60*(1+x^2)^(1/2)*asinh(x)^2+_ 20*x*asinh(x)^3-5*(1+x^2)^(1/2)*asinh(x)^4+x*asinh(x)^5 --R --R ---R (17) +--R (2) --R +------+ --R 4 2 | 2 5 3 --R (- 5asinh(x) - 60asinh(x) - 120)\|x + 1 + x asinh(x) + 20x asinh(x) @@ -289,7 +299,7 @@ r0003:= -120*(1+x^2)^(1/2)+120*x*asinh(x)-60*(1+x^2)^(1/2)*asinh(x)^2+_ a0003:= integrate(t0003,x) --R --R ---R (18) +--R (3) --R +------+ +------+ 5 --R | 2 2 | 2 --R (x\|x + 1 - x )log(\|x + 1 + x) @@ -320,7 +330,7 @@ a0003:= integrate(t0003,x) m0003:= a0003-r0003 --R --R ---R (19) +--R (4) --R +------+ +------+ 5 --R | 2 2 | 2 --R (x\|x + 1 - x )log(\|x + 1 + x) @@ -366,19 +376,22 @@ m0003:= a0003-r0003 d0003:= D(m0003,x) --R --R ---R +------+ 5 ---R | 2 5 ---R (20) log(\|x + 1 + x) - asinh(x) +--R +------+ 5 +--R | 2 5 +--R (5) log(\|x + 1 + x) - asinh(x) --R Type: Expression(Integer) --E 20 +)clear all + + --S 21 of 510 t0004:= 1/asinh(x) --R --R ---R 1 ---R (21) -------- ---R asinh(x) +--R 1 +--R (1) -------- +--R asinh(x) --R Type: Expression(Integer) --E 21 @@ -403,10 +416,10 @@ r0004:= Chi(asinh(x)) a0004:= integrate(t0004,x) --R --R ---R x ---R ++ 1 ---I (22) | --------- d%P ---I ++ asinh(%P) +--R x +--R ++ 1 +--I (2) | --------- d%T +--I ++ asinh(%T) --R Type: Union(Expression(Integer),...) --E 23 @@ -418,14 +431,17 @@ a0004:= integrate(t0004,x) --d0004:= D(m0004,x) --E 25 +)clear all + + --S 26 of 510 t0005:= 1/asinh(x)^2 --R --R ---R 1 ---R (23) --------- ---R 2 ---R asinh(x) +--R 1 +--R (1) --------- +--R 2 +--R asinh(x) --R Type: Expression(Integer) --E 26 @@ -450,11 +466,11 @@ r0005:= -(1+x^2)^(1/2)/asinh(x)+Shi(asinh(x)) a0005:= integrate(t0005,x) --R --R ---R x ---R ++ 1 ---I (24) | ---------- d%P ---R ++ 2 ---I asinh(%P) +--R x +--R ++ 1 +--I (2) | ---------- d%T +--I ++ 2 +--R asinh(%T) --R Type: Union(Expression(Integer),...) --E 28 @@ -466,14 +482,17 @@ a0005:= integrate(t0005,x) --d0005:= D(m0005,x) --E 30 +)clear all + + --S 31 of 510 t0006:= 1/asinh(x)^3 --R --R ---R 1 ---R (25) --------- ---R 3 ---R asinh(x) +--R 1 +--R (1) --------- +--R 3 +--R asinh(x) --R Type: Expression(Integer) --E 31 @@ -498,11 +517,11 @@ r0006:= 1/2*(-(1+x^2)^(1/2)-x*asinh(x)+Chi(asinh(x))*asinh(x)^2)/asinh(x)^2 a0006:= integrate(t0006,x) --R --R ---R x ---R ++ 1 ---I (26) | ---------- d%P ---R ++ 3 ---I asinh(%P) +--R x +--R ++ 1 +--I (2) | ---------- d%T +--R ++ 3 +--I asinh(%T) --R Type: Union(Expression(Integer),...) --E 33 @@ -514,13 +533,16 @@ a0006:= integrate(t0006,x) --d0006:= D(m0006,x) --E 35 +)clear all + + --S 36 of 510 t0007:= asinh(a*x)/x --R --R ---R asinh(a x) ---R (27) ---------- ---R x +--R asinh(a x) +--R (1) ---------- +--R x --R Type: Expression(Integer) --E 36 @@ -547,10 +569,10 @@ r0007:= 1/2*asinh(a*x)^2+asinh(a*x)*log(1-exp(1)^(-2*asinh(a*x)))-_ a0007:= integrate(t0007,x) --R --R ---R x ---I ++ asinh(%P a) ---I (28) | ----------- d%P ---I ++ %P +--R x +--I ++ asinh(%T a) +--I (2) | ----------- d%T +--I ++ %T --R Type: Union(Expression(Integer),...) --E 38 @@ -562,14 +584,17 @@ a0007:= integrate(t0007,x) --d0007:= D(m0007,x) --E 40 +)clear all + + --S 41 of 510 t0008:= 1/(a+b*asinh(c+d*x))^(1/2) --R --R ---R 1 ---R (29) ----------------------- ---R +--------------------+ ---R \|b asinh(d x + c) + a +--R 1 +--R (1) ----------------------- +--R +--------------------+ +--R \|b asinh(d x + c) + a --R Type: Expression(Integer) --E 41 @@ -578,17 +603,17 @@ r0I08:= -1/2*%pi^(1/2)*(-exp(2*a/b)*erf((a+b*asinh(c+d*x))^(1/2)/b^(1/2))+_ %i*erf(%i*(a+b*asinh(c+d*x))^(1/2)/b^(1/2)))*exp(-a/b)/b^(1/2)/d --R --R ---R (30) +--R (2) --R a 2a --R - - -- +--------------------+ --R b b +---+ \|b asinh(d x + c) + a ---I %e %e \|%pi erf(-----------------------) +--R %e %e \|%pi erf(-----------------------) --R +-+ --R \|b --R + --R a --R - - +--------------------+ ---I b +---+ %i\|b asinh(d x + c) + a +--R b +---+ %i\|b asinh(d x + c) + a --R - %i %e \|%pi erf(-------------------------) --R +-+ --R \|b @@ -617,14 +642,17 @@ a0008:= integrate(t0008,x) --d0008:= D(m0008,x) --E 45 +)clear all + + --S 46 of 510 t0009:= 1/(a-b*asinh(c+d*x))^(1/2) --R --R ---R 1 ---R (31) ------------------------- ---R +----------------------+ ---R \|- b asinh(d x + c) + a +--R 1 +--R (1) ------------------------- +--R +----------------------+ +--R \|- b asinh(d x + c) + a --R Type: Expression(Integer) --E 46 @@ -633,7 +661,7 @@ r0009:= -1/2*%pi^(1/2)*(exp(2*a/b)*erf((a-b*asinh(c+d*x))^(1/2)/b^(1/2))-_ %i*erf(%i*(a-b*asinh(c+d*x))^(1/2)/b^(1/2)))*exp(-a/b)/b^(1/2)/d --R --R ---R (32) +--R (2) --R a 2a --R - - -- +----------------------+ --R b b +---+ \|- b asinh(d x + c) + a @@ -672,14 +700,17 @@ a0009:= integrate(t0009,x) --d0009:= D(m0009,x) --E 50 +)clear all + + --S 51 of 510 t0010:= asinh(x^(1/2))/x --R --R ---R +-+ ---R asinh(\|x ) ---R (33) ----------- ---R x +--R +-+ +--R asinh(\|x ) +--R (1) ----------- +--R x --R Type: Expression(Integer) --E 51 @@ -706,10 +737,10 @@ r0010:= asinh(x^(1/2))^2+2*asinh(x^(1/2))*log(1-exp(1)^(-2*asinh(x^(1/2))))-_ a0010:= integrate(t0010,x) --R --R ---R x +--+ ---I ++ asinh(\|%P ) ---I (34) | ------------ d%P ---I ++ %P +--R x +--+ +--I ++ asinh(\|%T ) +--I (2) | ------------ d%T +--I ++ %T --R Type: Union(Expression(Integer),...) --E 53 @@ -721,12 +752,15 @@ a0010:= integrate(t0010,x) --d0010:= D(m0010,x) --E 55 +)clear all + + --S 56 of 510 t0011:= acosh(x)^2 --R --R ---R 2 ---R (35) acosh(x) +--R 2 +--R (1) acosh(x) --R Type: Expression(Integer) --E 56 @@ -734,8 +768,8 @@ t0011:= acosh(x)^2 r0011:= 2*x-2*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)+x*acosh(x)^2 --R --R ---R +-----+ +-----+ 2 ---R (36) - 2acosh(x)\|x - 1 \|x + 1 + x acosh(x) + 2x +--R +-----+ +-----+ 2 +--R (2) - 2acosh(x)\|x - 1 \|x + 1 + x acosh(x) + 2x --R Type: Expression(Integer) --E 57 @@ -743,7 +777,7 @@ r0011:= 2*x-2*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)+x*acosh(x)^2 a0011:= integrate(t0011,x) --R --R ---R (37) +--R (3) --R +------+ +------+ 2 --R | 2 2 | 2 --R (x\|x - 1 - x )log(\|x - 1 + x) @@ -762,7 +796,7 @@ a0011:= integrate(t0011,x) m0011:= a0011-r0011 --R --R ---R (38) +--R (4) --R +------+ +------+ 2 --R | 2 2 | 2 --R (x\|x - 1 - x )log(\|x - 1 + x) @@ -788,7 +822,7 @@ m0011:= a0011-r0011 d0011:= D(m0011,x) --R --R ---R (39) +--R (5) --R +------+ --R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ --R ((2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 ) @@ -819,12 +853,15 @@ d0011:= D(m0011,x) --R Type: Expression(Integer) --E 60 +)clear all + + --S 61 of 510 t0012:= acosh(x)^3 --R --R ---R 3 ---R (40) acosh(x) +--R 3 +--R (1) acosh(x) --R Type: Expression(Integer) --E 61 @@ -833,8 +870,8 @@ r0012:= -6*(-1+x)^(1/2)*(1+x)^(1/2)+6*x*acosh(x)-_ 3*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)^2+x*acosh(x)^3 --R --R ---R 2 +-----+ +-----+ 3 ---R (41) (- 3acosh(x) - 6)\|x - 1 \|x + 1 + x acosh(x) + 6x acosh(x) +--R 2 +-----+ +-----+ 3 +--R (2) (- 3acosh(x) - 6)\|x - 1 \|x + 1 + x acosh(x) + 6x acosh(x) --R Type: Expression(Integer) --E 62 @@ -842,7 +879,7 @@ r0012:= -6*(-1+x)^(1/2)*(1+x)^(1/2)+6*x*acosh(x)-_ a0012:= integrate(t0012,x) --R --R ---R (42) +--R (3) --R +------+ +------+ 3 --R | 2 2 | 2 --R (x\|x - 1 - x )log(\|x - 1 + x) @@ -865,7 +902,7 @@ a0012:= integrate(t0012,x) m0012:= a0012-r0012 --R --R ---R (43) +--R (4) --R +------+ +------+ 3 --R | 2 2 | 2 --R (x\|x - 1 - x )log(\|x - 1 + x) @@ -898,7 +935,7 @@ m0012:= a0012-r0012 d0012:= D(m0012,x) --R --R ---R (44) +--R (5) --R +------+ --R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ --R ((2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 ) @@ -938,12 +975,15 @@ d0012:= D(m0012,x) --R Type: Expression(Integer) --E 65 +)clear all + + --S 66 of 510 t0013:= acosh(x)^4 --R --R ---R 4 ---R (45) acosh(x) +--R 4 +--R (1) acosh(x) --R Type: Expression(Integer) --E 66 @@ -952,7 +992,7 @@ r0013:= 24*x-24*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)+12*x*acosh(x)^2-_ 4*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)^3+x*acosh(x)^4 --R --R ---R (46) +--R (2) --R 3 +-----+ +-----+ 4 2 --R (- 4acosh(x) - 24acosh(x))\|x - 1 \|x + 1 + x acosh(x) + 12x acosh(x) --R + @@ -964,7 +1004,7 @@ r0013:= 24*x-24*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)+12*x*acosh(x)^2-_ a0013:= integrate(t0013,x) --R --R ---R (47) +--R (3) --R +------+ +------+ 4 --R | 2 2 | 2 --R (x\|x - 1 - x )log(\|x - 1 + x) @@ -991,7 +1031,7 @@ a0013:= integrate(t0013,x) m0013:= a0013-r0013 --R --R ---R (48) +--R (4) --R +------+ +------+ 4 --R | 2 2 | 2 --R (x\|x - 1 - x )log(\|x - 1 + x) @@ -1034,7 +1074,7 @@ m0013:= a0013-r0013 d0013:= D(m0013,x) --R --R ---R (49) +--R (5) --R +------+ --R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ --R ((2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 ) @@ -1083,12 +1123,15 @@ d0013:= D(m0013,x) --R Type: Expression(Integer) --E 70 +)clear all + + --S 71 of 510 t0014:= acosh(x)^5 --R --R ---R 5 ---R (50) acosh(x) +--R 5 +--R (1) acosh(x) --R Type: Expression(Integer) --E 71 @@ -1098,7 +1141,7 @@ r0014:= -120*(-1+x)^(1/2)*(1+x)^(1/2)+120*x*acosh(x)-60*(-1+x)^(1/2)*_ 5*(-1+x)^(1/2)*(1+x)^(1/2)*acosh(x)^4+x*acosh(x)^5 --R --R ---R (51) +--R (2) --R 4 2 +-----+ +-----+ 5 --R (- 5acosh(x) - 60acosh(x) - 120)\|x - 1 \|x + 1 + x acosh(x) --R + @@ -1111,7 +1154,7 @@ r0014:= -120*(-1+x)^(1/2)*(1+x)^(1/2)+120*x*acosh(x)-60*(-1+x)^(1/2)*_ a0014:= integrate(t0014,x) --R --R ---R (52) +--R (3) --R +------+ +------+ 5 --R | 2 2 | 2 --R (x\|x - 1 - x )log(\|x - 1 + x) @@ -1142,7 +1185,7 @@ a0014:= integrate(t0014,x) m0014:= a0014-r0014 --R --R ---R (53) +--R (4) --R +------+ +------+ 5 --R | 2 2 | 2 --R (x\|x - 1 - x )log(\|x - 1 + x) @@ -1189,7 +1232,7 @@ m0014:= a0014-r0014 d0014:= D(m0014,x) --R --R ---R (54) +--R (5) --R +------+ --R 2 +-----+ +-----+ | 2 3 +-----+ +-----+ --R ((2x - 1)\|x - 1 \|x + 1 \|x - 1 + (- 2x + 2x)\|x - 1 \|x + 1 ) @@ -1238,13 +1281,16 @@ d0014:= D(m0014,x) --R Type: Expression(Integer) --E 75 +)clear all + + --S 76 of 510 t0015:= 1/acosh(x) --R --R ---R 1 ---R (55) -------- ---R acosh(x) +--R 1 +--R (1) -------- +--R acosh(x) --R Type: Expression(Integer) --E 76 @@ -1269,10 +1315,10 @@ r0015:= Shi(acosh(x)) a0015:= integrate(t0015,x) --R --R ---R x ---R ++ 1 ---I (56) | --------- d%P ---I ++ acosh(%P) +--R x +--R ++ 1 +--I (2) | --------- d%T +--I ++ acosh(%T) --R Type: Union(Expression(Integer),...) --E 78 @@ -1284,14 +1330,17 @@ a0015:= integrate(t0015,x) --d0015:= D(m0015,x) --E 80 +)clear all + + --S 81 of 510 t0016:= 1/acosh(x)^2 --R --R ---R 1 ---R (57) --------- ---R 2 ---R acosh(x) +--R 1 +--R (1) --------- +--R 2 +--R acosh(x) --R Type: Expression(Integer) --E 81 @@ -1316,11 +1365,11 @@ r0016:= -(-1+x)^(1/2)*(1+x)^(1/2)/acosh(x)+Chi(acosh(x)) a0016:= integrate(t0016,x) --R --R ---R x ---R ++ 1 ---I (58) | ---------- d%P ---R ++ 2 ---I acosh(%P) +--R x +--R ++ 1 +--I (2) | ---------- d%T +--R ++ 2 +--I acosh(%T) --R Type: Union(Expression(Integer),...) --E 83 @@ -1332,14 +1381,17 @@ a0016:= integrate(t0016,x) --d0016:= D(m0016,x) --E 85 +)clear all + + --S 86 of 510 t0017:= 1/acosh(x)^3 --R --R ---R 1 ---R (59) --------- ---R 3 ---R acosh(x) +--R 1 +--R (1) --------- +--R 3 +--R acosh(x) --R Type: Expression(Integer) --E 86 @@ -1365,11 +1417,11 @@ r0017:= -1/2*((-1+x)^(1/2)*(1+x)^(1/2)+x*acosh(x)-_ a0017:= integrate(t0017,x) --R --R ---R x ---R ++ 1 ---I (60) | ---------- d%P ---R ++ 3 ---I acosh(%P) +--R x +--R ++ 1 +--I (2) | ---------- d%T +--R ++ 3 +--I acosh(%T) --R Type: Union(Expression(Integer),...) --E 88 @@ -1381,11 +1433,14 @@ a0017:= integrate(t0017,x) --d0017:= D(m0017,x) --E 90 +)clear all + + --S 91 of 510 t0018:= x*acosh(a*x) --R --R ---R (61) x acosh(a x) +--R (1) x acosh(a x) --R Type: Expression(Integer) --E 91 @@ -1394,11 +1449,11 @@ r0018:= -1/4*(x*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a+acosh(a*x)-_ 2*x^2*acosh(a*x)*a^2)/a^2 --R --R ---R +-------+ +-------+ 2 2 ---R - a x\|a x - 1 \|a x + 1 + (2a x - 1)acosh(a x) ---R (62) ------------------------------------------------- ---R 2 ---R 4a +--R +-------+ +-------+ 2 2 +--R - a x\|a x - 1 \|a x + 1 + (2a x - 1)acosh(a x) +--R (2) ------------------------------------------------- +--R 2 +--R 4a --R Type: Expression(Integer) --E 92 @@ -1406,7 +1461,7 @@ r0018:= -1/4*(x*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a+acosh(a*x)-_ a0018:= integrate(t0018,x) --R --R ---R (63) +--R (3) --R +--------+ +--------+ --R 3 3 | 2 2 4 4 2 2 | 2 2 --R ((4a x - 2a x)\|a x - 1 - 4a x + 4a x - 1)log(\|a x - 1 + a x) @@ -1425,7 +1480,7 @@ a0018:= integrate(t0018,x) m0018:= a0018-r0018 --R --R ---R (64) +--R (4) --R +--------+ +--------+ --R 3 3 | 2 2 4 4 2 2 | 2 2 --R ((4a x - 2a x)\|a x - 1 - 4a x + 4a x - 1)log(\|a x - 1 + a x) @@ -1453,7 +1508,7 @@ m0018:= a0018-r0018 d0018:= D(m0018,x) --R --R ---R (65) +--R (5) --R +--------+ --R 5 5 3 3 +-------+ +-------+ | 2 2 --R (32a x - 32a x + 4a x)\|a x - 1 \|a x + 1 \|a x - 1 @@ -1496,12 +1551,15 @@ d0018:= D(m0018,x) --R Type: Expression(Integer) --E 95 +)clear all + + --S 96 of 510 t0019:= x^3*acosh(a*x) --R --R ---R 3 ---R (66) x acosh(a x) +--R 3 +--R (1) x acosh(a x) --R Type: Expression(Integer) --E 96 @@ -1511,11 +1569,11 @@ r0019:= -1/32*(3*x*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a+_ 8*x^4*acosh(a*x)*a^4)/a^4 --R --R ---R 3 3 +-------+ +-------+ 4 4 ---R (- 2a x - 3a x)\|a x - 1 \|a x + 1 + (8a x - 3)acosh(a x) ---R (67) ------------------------------------------------------------ ---R 4 ---R 32a +--R 3 3 +-------+ +-------+ 4 4 +--R (- 2a x - 3a x)\|a x - 1 \|a x + 1 + (8a x - 3)acosh(a x) +--R (2) ------------------------------------------------------------ +--R 4 +--R 32a --R Type: Expression(Integer) --E 97 @@ -1523,7 +1581,7 @@ r0019:= -1/32*(3*x*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a+_ a0019:= integrate(t0019,x) --R --R ---R (68) +--R (3) --R +--------+ --R 7 7 5 5 3 3 | 2 2 8 8 6 6 --R (64a x - 32a x - 24a x + 12a x)\|a x - 1 - 64a x + 64a x @@ -1549,7 +1607,7 @@ a0019:= integrate(t0019,x) m0019:= a0019-r0019 --R --R ---R (69) +--R (4) --R +--------+ --R 7 7 5 5 3 3 | 2 2 8 8 6 6 --R (64a x - 32a x - 24a x + 12a x)\|a x - 1 - 64a x + 64a x @@ -1593,7 +1651,7 @@ m0019:= a0019-r0019 d0019:= D(m0019,x) --R --R ---R (70) +--R (5) --R 11 11 9 9 7 7 5 5 3 3 +-------+ --R (4096a x - 8192a x + 5120a x - 1024a x + 32a x )\|a x - 1 --R * @@ -1656,13 +1714,16 @@ d0019:= D(m0019,x) --R Type: Expression(Integer) --E 100 +)clear all + + --S 101 of 510 t0020:= acosh(a*x)/x --R --R ---R acosh(a x) ---R (71) ---------- ---R x +--R acosh(a x) +--R (1) ---------- +--R x --R Type: Expression(Integer) --E 101 @@ -1689,10 +1750,10 @@ r0020:= 1/2*acosh(a*x)^2+acosh(a*x)*log(1+exp(1)^(-2*acosh(a*x)))-_ a0020:= integrate(t0020,x) --R --R ---R x ---I ++ acosh(%P a) ---I (72) | ----------- d%P ---I ++ %P +--R x +--I ++ acosh(%T a) +--I (2) | ----------- d%T +--I ++ %T --R Type: Union(Expression(Integer),...) --E 103 @@ -1704,14 +1765,17 @@ a0020:= integrate(t0020,x) --d0020:= D(m0020,x) --E 105 +)clear all + + --S 106 of 510 t0021:= acosh(a*x)/x^2 --R --R ---R acosh(a x) ---R (73) ---------- ---R 2 ---R x +--R acosh(a x) +--R (1) ---------- +--R 2 +--R x --R Type: Expression(Integer) --E 106 @@ -1719,13 +1783,13 @@ t0021:= acosh(a*x)/x^2 r0021:= -acosh(a*x)/x+2*a*atan((-1+a*x)^(1/2)/(1+a*x)^(1/2)) --R --R ---R +-------+ ---R \|a x - 1 ---R 2a x atan(----------) - acosh(a x) ---R +-------+ ---R \|a x + 1 ---R (74) ---------------------------------- ---R x +--R +-------+ +--R \|a x - 1 +--R 2a x atan(----------) - acosh(a x) +--R +-------+ +--R \|a x + 1 +--R (2) ---------------------------------- +--R x --R Type: Expression(Integer) --E 107 @@ -1733,11 +1797,11 @@ r0021:= -acosh(a*x)/x+2*a*atan((-1+a*x)^(1/2)/(1+a*x)^(1/2)) a0021:= integrate(t0021,x) --R --R ---R +--------+ +--------+ ---R | 2 2 | 2 2 ---R - log(\|a x - 1 + a x) + 2a x atan(\|a x - 1 - a x) ---R (75) ------------------------------------------------------- ---R x +--R +--------+ +--------+ +--R | 2 2 | 2 2 +--R - log(\|a x - 1 + a x) + 2a x atan(\|a x - 1 - a x) +--R (3) ------------------------------------------------------- +--R x --R Type: Union(Expression(Integer),...) --E 108 @@ -1745,7 +1809,7 @@ a0021:= integrate(t0021,x) m0021:= a0021-r0021 --R --R ---R (76) +--R (4) --R +--------+ +--------+ --R | 2 2 | 2 2 --R - log(\|a x - 1 + a x) + 2a x atan(\|a x - 1 - a x) @@ -1764,7 +1828,7 @@ m0021:= a0021-r0021 d0021:= D(m0021,x) --R --R ---R (77) +--R (5) --R +--------+ +--------+ --R +-------+ +-------+ | 2 2 | 2 2 --R \|a x - 1 \|a x + 1 \|a x - 1 log(\|a x - 1 + a x) @@ -1782,14 +1846,17 @@ d0021:= D(m0021,x) --R Type: Expression(Integer) --E 110 +)clear all + + --S 111 of 510 t0022:= acosh(a*x)/x^4 --R --R ---R acosh(a x) ---R (78) ---------- ---R 4 ---R x +--R acosh(a x) +--R (1) ---------- +--R 4 +--R x --R Type: Expression(Integer) --E 111 @@ -1798,14 +1865,14 @@ r0022:= 1/6*(x*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a-2*acosh(a*x)+_ 2*a^3*atan((-1+a*x)^(1/2)/(1+a*x)^(1/2))*x^3)/x^3 --R --R ---R +-------+ ---R 3 3 \|a x - 1 +-------+ +-------+ ---R 2a x atan(----------) + a x\|a x - 1 \|a x + 1 - 2acosh(a x) ---R +-------+ ---R \|a x + 1 ---R (79) ------------------------------------------------------------- ---R 3 ---R 6x +--R +-------+ +--R 3 3 \|a x - 1 +-------+ +-------+ +--R 2a x atan(----------) + a x\|a x - 1 \|a x + 1 - 2acosh(a x) +--R +-------+ +--R \|a x + 1 +--R (2) ------------------------------------------------------------- +--R 3 +--R 6x --R Type: Expression(Integer) --E 112 @@ -1813,7 +1880,7 @@ r0022:= 1/6*(x*(-1+a*x)^(1/2)*(1+a*x)^(1/2)*a-2*acosh(a*x)+_ a0022:= integrate(t0022,x) --R --R ---R (80) +--R (3) --R +--------+ +--------+ --R | 2 2 2 2 | 2 2 --R (- 4a x\|a x - 1 + 4a x - 2)log(\|a x - 1 + a x) @@ -1836,7 +1903,7 @@ a0022:= integrate(t0022,x) m0022:= a0022-r0022 --R --R ---R (81) +--R (4) --R +--------+ +--------+ --R | 2 2 2 2 | 2 2 --R (- 4a x\|a x - 1 + 4a x - 2)log(\|a x - 1 + a x) @@ -1868,7 +1935,7 @@ m0022:= a0022-r0022 d0022:= D(m0022,x) --R --R ---R (82) +--R (5) --R +--------+ --R 4 4 2 2 +-------+ +-------+ | 2 2 --R (24a x - 24a x + 3)\|a x - 1 \|a x + 1 \|a x - 1 @@ -1911,12 +1978,15 @@ d0022:= D(m0022,x) --R Type: Expression(Integer) --E 115 +)clear all + + --S 116 of 510 t0023:= x^2*acosh(a+b*x) --R --R ---R 2 ---R (83) x acosh(b x + a) +--R 2 +--R (1) x acosh(b x + a) --R Type: Expression(Integer) --E 116 @@ -1929,7 +1999,7 @@ r0023:= -1/18*(4*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)+_ 12*a^3*asinh(1/2*(a+b*x-1)^(1/2)*2^(1/2)))/b^3 --R --R ---R (84) +--R (2) --R +-+ +-----------+ --R 3 \|2 \|b x + a - 1 --R (12a + 18a)asinh(------------------) @@ -1950,7 +2020,7 @@ r0023:= -1/18*(4*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)+_ a0023:= integrate(t0023,x) --R --R ---R (85) +--R (3) --R 5 5 4 4 2 3 3 3 2 2 --R 96b x + 192a b x + (96a - 24)b x + (96a + 144a)b x --R + @@ -2006,7 +2076,7 @@ a0023:= integrate(t0023,x) m0023:= a0023-r0023 --R --R ---R (86) +--R (4) --R 5 5 4 4 2 3 3 3 2 2 --R 96b x + 192a b x + (96a - 24)b x + (96a + 144a)b x --R + @@ -2104,7 +2174,7 @@ m0023:= a0023-r0023 d0023:= D(m0023,x) --R --R ---R (87) +--R (5) --R 6 8 5 7 2 4 6 3 3 5 --R 96b x + 576a b x + (1440a - 144)b x + (1920a - 576a)b x --R + @@ -2232,12 +2302,15 @@ d0023:= D(m0023,x) --R Type: Expression(Integer) --E 120 +)clear all + + --S 121 of 510 t0024:= x^3*acosh(a+b*x) --R --R ---R 3 ---R (88) x acosh(b x + a) +--R 3 +--R (1) x acosh(b x + a) --R Type: Expression(Integer) --E 121 @@ -2253,7 +2326,7 @@ r0024:= 1/96*(55*a*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)+_ 18*asinh(1/2*(a+b*x-1)^(1/2)*2^(1/2)))/b^4 --R --R ---R (89) +--R (2) --R +-+ +-----------+ --R 4 2 \|2 \|b x + a - 1 --R (- 48a - 144a - 18)asinh(------------------) @@ -2277,7 +2350,7 @@ r0024:= 1/96*(55*a*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)+_ a0024:= integrate(t0024,x) --R --R ---R (90) +--R (3) --R 7 7 6 6 2 5 5 3 4 4 --R 1536b x + 4608a b x + (4608a - 768)b x + (1536a - 768a)b x --R + @@ -2356,7 +2429,7 @@ a0024:= integrate(t0024,x) m0024:= a0024-r0024 --R --R ---R (91) +--R (4) --R 7 7 6 6 2 5 5 3 4 4 --R 1536b x + 4608a b x + (4608a - 768)b x + (1536a - 768a)b x --R + @@ -2503,7 +2576,7 @@ m0024:= a0024-r0024 d0024:= D(m0024,x) --R --R ---R (92) +--R (5) --R 8 11 7 10 2 6 9 --R 512b x + 4096a b x + (14336a - 1024)b x --R + @@ -2711,14 +2784,17 @@ d0024:= D(m0024,x) --R Type: Expression(Integer) --E 125 +)clear all + + --S 126 of 510 t0025:= acosh(a+b*x)/x^2 --R --R ---R acosh(b x + a) ---R (93) -------------- ---R 2 ---R x +--R acosh(b x + a) +--R (1) -------------- +--R 2 +--R x --R Type: Expression(Integer) --E 126 @@ -2727,7 +2803,7 @@ r0025:= -acosh(a+b*x)/x-2*b*atan((-1-a)^(1/2)*_ (a+b*x-1)^(1/2)/(-1+a)^(1/2)/(a+1+b*x)^(1/2))/(-1-a)^(1/2)/(-1+a)^(1/2) --R --R ---R (94) +--R (2) --R +-------+ +-----------+ --R \|- a - 1 \|b x + a - 1 +-------+ +-----+ --R - 2b x atan(------------------------) - acosh(b x + a)\|- a - 1 \|a - 1 @@ -2743,7 +2819,7 @@ r0025:= -acosh(a+b*x)/x-2*b*atan((-1-a)^(1/2)*_ a0025:= integrate(t0025,x) --R --R ---R (95) +--R (3) --R [ --R +------+ +----------------------+ --R | 2 | 2 2 2 @@ -2791,7 +2867,7 @@ a0025:= integrate(t0025,x) m0025a:= a0025.1-r0025 --R --R ---R (96) +--R (4) --R +------+ +----------------------+ --R +-------+ +-----+ | 2 | 2 2 2 --R - \|- a - 1 \|a - 1 \|a - 1 log(\|b x + 2a b x + a - 1 + b x + a) @@ -2832,7 +2908,7 @@ m0025a:= a0025.1-r0025 d0025a:= D(m0025a,x) --R --R ---R (97) +--R (5) --R +----------------------+ --R +-----------+ +-----------+ | 2 2 2 --R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 @@ -2861,7 +2937,7 @@ d0025a:= D(m0025a,x) m0025b:= a0025.2-r0025 --R --R ---R (98) +--R (6) --R +--------+ +----------------------+ --R | 2 +-------+ +-----+ | 2 2 2 --R - \|- a + 1 \|- a - 1 \|a - 1 log(\|b x + 2a b x + a - 1 + b x + a) @@ -2897,7 +2973,7 @@ m0025b:= a0025.2-r0025 d0025b:= D(m0025b,x) --R --R ---R (99) +--R (7) --R +----------------------+ --R +-----------+ +-----------+ | 2 2 2 --R \|b x + a - 1 \|b x + a + 1 \|b x + 2a b x + a - 1 @@ -2922,14 +2998,17 @@ d0025b:= D(m0025b,x) --R Type: Expression(Integer) --E 132 +)clear all + + --S 133 of 510 t0026:= acosh(a+b*x)/x^3 --R --R ---R acosh(b x + a) ---R (100) -------------- ---R 3 ---R x +--R acosh(b x + a) +--R (1) -------------- +--R 3 +--R x --R Type: Expression(Integer) --E 133 @@ -2939,7 +3018,7 @@ r0026:= 1/2*b*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)/(1-a^2)/x-_ (a+b*x-1)^(1/2)/(-1+a)^(1/2)/(a+1+b*x)^(1/2))/(-1-a)^(3/2)/(-1+a)^(3/2) --R --R ---R (101) +--R (2) --R +-------+ +-----------+ --R 2 2 \|- a - 1 \|b x + a - 1 --R 2a b x atan(------------------------) @@ -2961,7 +3040,7 @@ r0026:= 1/2*b*(a+b*x-1)^(1/2)*(a+1+b*x)^(1/2)/(1-a^2)/x-_ a0026:= integrate(t0026,x) --R --R ---R (102) +--R (3) --R [ --R +------+ +----------------------+ --R 2 | 2 | 2 2 2 @@ -3055,7 +3134,7 @@ a0026:= integrate(t0026,x) m0026a:= a0026.1-r0026 --R --R ---R (103) +--R (4) --R +------+ +----------------------+ --R 2 +-------+ +-----+ | 2 | 2 2 2 --R (- a + 1)\|- a - 1 \|a - 1 \|a - 1 \|b x + 2a b x + a - 1 @@ -3139,7 +3218,7 @@ m0026a:= a0026.1-r0026 d0026a:= D(m0026a,x) --R --R ---R (104) +--R (5) --R 6 6 5 5 2 4 4 3 3 3 --R 32b x + 160a b x + (336a - 56)b x + (384a - 184a)b x --R + @@ -3394,7 +3473,7 @@ d0026a:= D(m0026a,x) m0026b:= a0026.2-r0026 --R --R ---R (105) +--R (6) --R +--------+ +----------------------+ --R 2 | 2 +-------+ +-----+ | 2 2 2 --R (- a + 1)\|- a + 1 \|- a - 1 \|a - 1 \|b x + 2a b x + a - 1 @@ -3472,7 +3551,7 @@ m0026b:= a0026.2-r0026 d0026b:= D(m0026b,x) --R --R ---R (106) +--R (7) --R 2 2 2 +-----------+ +-----------+ --R (4b x + 8a b x + 4a - 2)\|b x + a - 1 \|b x + a + 1 --R * @@ -3530,14 +3609,17 @@ d0026b:= D(m0026b,x) --R Type: Expression(Integer) --E 139 +)clear all + + --S 140 of 510 t0027:= 1/(a+b*acosh(c+d*x))^(1/2) --R --R ---R 1 ---R (107) ----------------------- ---R +--------------------+ ---R \|b acosh(d x + c) + a +--R 1 +--R (1) ----------------------- +--R +--------------------+ +--R \|b acosh(d x + c) + a --R Type: Expression(Integer) --E 140 @@ -3546,7 +3628,7 @@ r0027:= -1/2*%pi^(1/2)*(exp(2*a/b)*erf((a+b*acosh(c+d*x))^(1/2)/b^(1/2))+_ %i*erf(%i*(a+b*acosh(c+d*x))^(1/2)/b^(1/2)))*exp(-a/b)/b^(1/2)/d --R --R ---R (108) +--R (2) --R a 2a --R - - -- +--------------------+ --R b b +---+ \|b acosh(d x + c) + a @@ -3585,14 +3667,17 @@ a0027:= integrate(t0027,x) --d0027:= D(m0027,x) --E 144 +)clear all + + --S 145 of 510 t0028:= 1/(a-b*acosh(c+d*x))^(1/2) --R --R ---R 1 ---R (109) ------------------------- ---R +----------------------+ ---R \|- b acosh(d x + c) + a +--R 1 +--R (1) ------------------------- +--R +----------------------+ +--R \|- b acosh(d x + c) + a --R Type: Expression(Integer) --E 145 @@ -3601,7 +3686,7 @@ r0028:= -1/2*%pi^(1/2)*(exp(2*a/b)*erf((a-b*acosh(c+d*x))^(1/2)/b^(1/2))+_ %i*erf(%i*(a-b*acosh(c+d*x))^(1/2)/b^(1/2)))*exp(-a/b)/b^(1/2)/d --R --R ---R (110) +--R (2) --R a 2a --R - - -- +----------------------+ --R b b +---+ \|- b acosh(d x + c) + a @@ -3640,12 +3725,15 @@ a0028:= integrate(t0028,x) --d0028:= D(m0028,x) --E 149 +)clear all + + --S 150 of 510 t0029:= acosh(x^(1/2)) --R --R ---R +-+ ---R (111) acosh(\|x ) +--R +-+ +--R (1) acosh(\|x ) --R Type: Expression(Integer) --E 150 @@ -3654,15 +3742,29 @@ r0029:= -1/2*(-1+x^(1/2))^(1/2)*(1+x^(1/2))^(1/2)*x^(1/2)-_ 1/2*acosh(x^(1/2))+x*acosh(x^(1/2)) --R --R ---R +--------+ +--------+ ---R +-+ | +-+ | +-+ +-+ ---R - \|x \|\|x - 1 \|\|x + 1 + (2x - 1)acosh(\|x ) ---R (112) -------------------------------------------------- ---R 2 +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ +-+ +--R - \|x \|\|x - 1 \|\|x + 1 + (2x - 1)acosh(\|x ) +--R (2) -------------------------------------------------- +--R 2 --R Type: Expression(Integer) --E 151 ---S 152 of 510 +-- sometimes this seems to come out with a different sign +-- +-- +-- (113) +-- +-----+ +-+ 2 +-+ +-----+ +-- ((4x - 2)\|x - 1 \|x + 4x - 4x + 1)log(\|x + \|x - 1 ) +-- + +-- +-----+ +-+ 2 +-- (- 2x + 1)\|x - 1 \|x - 2x + 2x +-- / +-- +-----+ +-+ +-- 4\|x - 1 \|x + 4x - 2 +-- Type: Union(Expression(Integer),...) + +--S 152 of 510 ok if failed. sometimes has different sign (see above) a0029:= integrate(t0029,x) --R --R @@ -3673,23 +3775,71 @@ a0029:= integrate(t0029,x) --R --E 152 ---S 153 of 510 +-- sometimes this seems sometimes have different sign +-- +-- +-- (114) +-- +--------+ +--------+ +-- +-+ +-----+ | +-+ | +-+ +-- ((2x - 1)\|x + 2x\|x - 1 )\|\|x - 1 \|\|x + 1 +-- + +-- +-----+ +-+ 2 +-+ +-----+ +-- ((4x - 2)\|x - 1 \|x + 4x - 4x + 1)log(\|x + \|x - 1 ) +-- + +-- +-----+ +-+ 2 +-+ +-- ((- 4x + 2)\|x - 1 \|x - 4x + 4x - 1)acosh(\|x ) +-- + +-- +-----+ +-+ 2 +-- (- 2x + 1)\|x - 1 \|x - 2x + 2x +-- / +-- +-----+ +-+ +-- 4\|x - 1 \|x + 4x - 2 +-- Type: Expression(Integer) +--S 153 of 510 ok if failed. sometimes has different sign (see above) m0029:= a0029-r0029 --R --R ---R +--------+ +--------+ ---R +-+ | +-+ | +-+ +-+ ---R \|x \|\|x - 1 \|\|x + 1 + (- 2x + 1)acosh(\|x ) + 2a0029 ---R (113) ----------------------------------------------------------- ---R 2 +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ +-+ +--R \|x \|\|x - 1 \|\|x + 1 + (- 2x + 1)acosh(\|x ) + 2a0029 +--R (3) ----------------------------------------------------------- +--R 2 --R Type: Expression(Integer) --E 153 ---S 154 of 510 +-- sometimes this seems sometimes have different sign +-- +-- +-- (115) +-- 2 +-----+ +-+ 3 2 +-- ((32x - 32x + 4)\|x - 1 \|x + 32x - 48x + 16x) +-- * +-- +-+ +-----+ +-- log(\|x + \|x - 1 ) +-- + +-- 2 +-----+ +-+ 3 2 +-+ +-- ((- 32x + 32x - 4)\|x - 1 \|x - 32x + 48x - 16x)acosh(\|x ) +-- + +-- 2 +-----+ +-+ 3 2 +-- (- 16x + 16x - 4)\|x - 1 \|x - 16x + 24x - 10x + 1 +-- * +-- +--------+ +--------+ +-- | +-+ | +-+ +-- \|\|x - 1 \|\|x + 1 +-- + +-- 3 2 +-+ 3 2 +-----+ +-- (16x - 32x + 20x - 4)\|x + (16x - 24x + 10x - 1)\|x - 1 +-- / +-- +--------+ +--------+ +-- 2 +-----+ +-+ 3 2 | +-+ | +-+ +-- ((32x - 32x + 4)\|x - 1 \|x + 32x - 48x + 16x)\|\|x - 1 \|\|x + 1 +-- Type: Expression(Integer) + +--S 154 of 510 ok if failed. sometimes has different sign (see above) d0029:= D(m0029,x) --R --R ---R (114) +--R (4) --R +--------+ +--------+ --R +-----+ +-+ +-+ | +-+ | +-+ --R (- 4\|x - 1 \|x acosh(\|x ) - 2x + 1)\|\|x - 1 \|\|x + 1 @@ -3703,14 +3853,17 @@ d0029:= D(m0029,x) --R Type: Expression(Integer) --E 154 +)clear all + + --S 155 of 510 t0030:= acosh(x^(1/2))/x --R --R ---R +-+ ---R acosh(\|x ) ---R (115) ----------- ---R x +--R +-+ +--R acosh(\|x ) +--R (1) ----------- +--R x --R Type: Expression(Integer) --E 155 @@ -3737,10 +3890,10 @@ r0030:= acosh(x^(1/2))^2+2*acosh(x^(1/2))*log(1+exp(1)^(-2*acosh(x^(1/2))))-_ a0030:= integrate(t0030,x) --R --R ---R x +--+ ---I ++ acosh(\|%P ) ---I (116) | ------------ d%P ---I ++ %P +--R x +--+ +--I ++ acosh(\|%T ) +--I (2) | ------------ d%T +--I ++ %T --R Type: Union(Expression(Integer),...) --E 157 @@ -3752,11 +3905,14 @@ a0030:= integrate(t0030,x) --d0030:= D(m0030,x) --E 159 +)clear all + + --S 160 of 510 t0031:= x*atanh(a*x) --R --R ---R (117) x atanh(a x) +--R (1) x atanh(a x) --R Type: Expression(Integer) --E 160 @@ -3764,11 +3920,11 @@ t0031:= x*atanh(a*x) r0031:= 1/2*(a*x-atanh(a*x)+x^2*atanh(a*x)*a^2)/a^2 --R --R ---R 2 2 ---R (a x - 1)atanh(a x) + a x ---R (118) -------------------------- ---R 2 ---R 2a +--R 2 2 +--R (a x - 1)atanh(a x) + a x +--R (2) -------------------------- +--R 2 +--R 2a --R Type: Expression(Integer) --E 161 @@ -3776,12 +3932,12 @@ r0031:= 1/2*(a*x-atanh(a*x)+x^2*atanh(a*x)*a^2)/a^2 a0031:= integrate(t0031,x) --R --R ---R 2 2 - a x - 1 ---R (a x - 1)log(---------) + 2a x ---R a x - 1 ---R (119) ------------------------------- ---R 2 ---R 4a +--R 2 2 - a x - 1 +--R (a x - 1)log(---------) + 2a x +--R a x - 1 +--R (3) ------------------------------- +--R 2 +--R 4a --R Type: Union(Expression(Integer),...) --E 162 @@ -3789,12 +3945,12 @@ a0031:= integrate(t0031,x) m0031:= a0031-r0031 --R --R ---R 2 2 - a x - 1 2 2 ---R (a x - 1)log(---------) + (- 2a x + 2)atanh(a x) ---R a x - 1 ---R (120) -------------------------------------------------- ---R 2 ---R 4a +--R 2 2 - a x - 1 2 2 +--R (a x - 1)log(---------) + (- 2a x + 2)atanh(a x) +--R a x - 1 +--R (4) -------------------------------------------------- +--R 2 +--R 4a --R Type: Expression(Integer) --E 163 @@ -3802,21 +3958,24 @@ m0031:= a0031-r0031 d0031:= D(m0031,x) --R --R ---R - a x - 1 ---R x log(---------) - 2x atanh(a x) ---R a x - 1 ---R (121) -------------------------------- ---R 2 +--R - a x - 1 +--R x log(---------) - 2x atanh(a x) +--R a x - 1 +--R (5) -------------------------------- +--R 2 --R Type: Expression(Integer) --E 164 +)clear all + + --S 165 of 510 t0032:= atanh(a*x)/x --R --R ---R atanh(a x) ---R (122) ---------- ---R x +--R atanh(a x) +--R (1) ---------- +--R x --R Type: Expression(Integer) --E 165 @@ -3842,10 +4001,10 @@ r0032:= -1/2*polylog(2,-a*x)+1/2*polylog(2,a*x) a0032:= integrate(t0032,x) --R --R ---R x ---I ++ atanh(%P a) ---I (123) | ----------- d%P ---I ++ %P +--R x +--I ++ atanh(%T a) +--I (2) | ----------- d%T +--I ++ %T --R Type: Union(Expression(Integer),...) --E 167 @@ -3857,14 +4016,17 @@ a0032:= integrate(t0032,x) --d0032:= D(m0032,x) --E 169 +)clear all + + --S 170 of 510 t0033:= atanh(a*x)/x^3 --R --R ---R atanh(a x) ---R (124) ---------- ---R 3 ---R x +--R atanh(a x) +--R (1) ---------- +--R 3 +--R x --R Type: Expression(Integer) --E 170 @@ -3872,11 +4034,11 @@ t0033:= atanh(a*x)/x^3 r0033:= 1/2*(-atanh(a*x)+x^2*atanh(a*x)*a^2-a*x)/x^2 --R --R ---R 2 2 ---R (a x - 1)atanh(a x) - a x ---R (125) -------------------------- ---R 2 ---R 2x +--R 2 2 +--R (a x - 1)atanh(a x) - a x +--R (2) -------------------------- +--R 2 +--R 2x --R Type: Expression(Integer) --E 171 @@ -3884,12 +4046,12 @@ r0033:= 1/2*(-atanh(a*x)+x^2*atanh(a*x)*a^2-a*x)/x^2 a0033:= integrate(t0033,x) --R --R ---R 2 2 - a x - 1 ---R (a x - 1)log(---------) - 2a x ---R a x - 1 ---R (126) ------------------------------- ---R 2 ---R 4x +--R 2 2 - a x - 1 +--R (a x - 1)log(---------) - 2a x +--R a x - 1 +--R (3) ------------------------------- +--R 2 +--R 4x --R Type: Union(Expression(Integer),...) --E 172 @@ -3897,12 +4059,12 @@ a0033:= integrate(t0033,x) m0033:= a0033-r0033 --R --R ---R 2 2 - a x - 1 2 2 ---R (a x - 1)log(---------) + (- 2a x + 2)atanh(a x) ---R a x - 1 ---R (127) -------------------------------------------------- ---R 2 ---R 4x +--R 2 2 - a x - 1 2 2 +--R (a x - 1)log(---------) + (- 2a x + 2)atanh(a x) +--R a x - 1 +--R (4) -------------------------------------------------- +--R 2 +--R 4x --R Type: Expression(Integer) --E 173 @@ -3910,20 +4072,23 @@ m0033:= a0033-r0033 d0033:= D(m0033,x) --R --R ---R - a x - 1 ---R log(---------) - 2atanh(a x) ---R a x - 1 ---R (128) ---------------------------- ---R 3 ---R 2x +--R - a x - 1 +--R log(---------) - 2atanh(a x) +--R a x - 1 +--R (5) ---------------------------- +--R 3 +--R 2x --R Type: Expression(Integer) --E 174 +)clear all + + --S 175 of 510 t0034:= (a+b*x)*atanh(a+b*x) --R --R ---R (129) (b x + a)atanh(b x + a) +--R (1) (b x + a)atanh(b x + a) --R Type: Expression(Integer) --E 175 @@ -3931,10 +4096,10 @@ t0034:= (a+b*x)*atanh(a+b*x) r0034:= 1/2/b*(a+b*x)-1/2*atanh(a+b*x)/b+1/2*(a+b*x)^2*atanh(a+b*x)/b --R --R ---R 2 2 2 ---R (b x + 2a b x + a - 1)atanh(b x + a) + b x + a ---R (130) ------------------------------------------------ ---R 2b +--R 2 2 2 +--R (b x + 2a b x + a - 1)atanh(b x + a) + b x + a +--R (2) ------------------------------------------------ +--R 2b --R Type: Expression(Integer) --E 176 @@ -3942,11 +4107,11 @@ r0034:= 1/2/b*(a+b*x)-1/2*atanh(a+b*x)/b+1/2*(a+b*x)^2*atanh(a+b*x)/b a0034:= integrate(t0034,x) --R --R ---R 2 2 2 - b x - a - 1 ---R (b x + 2a b x + a - 1)log(-------------) + 2b x ---R b x + a - 1 ---R (131) ------------------------------------------------- ---R 4b +--R 2 2 2 - b x - a - 1 +--R (b x + 2a b x + a - 1)log(-------------) + 2b x +--R b x + a - 1 +--R (3) ------------------------------------------------- +--R 4b --R Type: Union(Expression(Integer),...) --E 177 @@ -3954,7 +4119,7 @@ a0034:= integrate(t0034,x) m0034:= a0034-r0034 --R --R ---R (132) +--R (4) --R 2 2 2 - b x - a - 1 --R (b x + 2a b x + a - 1)log(-------------) --R b x + a - 1 @@ -3970,20 +4135,23 @@ m0034:= a0034-r0034 d0034:= D(m0034,x) --R --R ---R - b x - a - 1 ---R (b x + a)log(-------------) + (- 2b x - 2a)atanh(b x + a) ---R b x + a - 1 ---R (133) --------------------------------------------------------- ---R 2 +--R - b x - a - 1 +--R (b x + a)log(-------------) + (- 2b x - 2a)atanh(b x + a) +--R b x + a - 1 +--R (5) --------------------------------------------------------- +--R 2 --R Type: Expression(Integer) --E 179 +)clear all + + --S 180 of 510 t0035:= (a+b*x)^2*atanh(a+b*x) --R --R ---R 2 2 2 ---R (134) (b x + 2a b x + a )atanh(b x + a) +--R 2 2 2 +--R (1) (b x + 2a b x + a )atanh(b x + a) --R Type: Expression(Integer) --E 180 @@ -3991,7 +4159,7 @@ t0035:= (a+b*x)^2*atanh(a+b*x) r0035:= 1/6*(a+b*x)^2/b+1/3*(a+b*x)^3*atanh(a+b*x)/b+1/6*log(1-(a+b*x)^2)/b --R --R ---R (135) +--R (2) --R 2 2 2 --R log(- b x - 2a b x - a + 1) --R + @@ -4006,7 +4174,7 @@ r0035:= 1/6*(a+b*x)^2/b+1/3*(a+b*x)^3*atanh(a+b*x)/b+1/6*log(1-(a+b*x)^2)/b a0035:= integrate(t0035,x) --R --R ---R (136) +--R (3) --R 3 3 --R (a + 1)log(b x + a + 1) + (- a + 1)log(b x + a - 1) --R + @@ -4022,7 +4190,7 @@ a0035:= integrate(t0035,x) m0035:= a0035-r0035 --R --R ---R (137) +--R (4) --R 3 3 --R (a + 1)log(b x + a + 1) + (- a + 1)log(b x + a - 1) --R + @@ -4044,7 +4212,7 @@ m0035:= a0035-r0035 d0035:= D(m0035,x) --R --R ---R (138) +--R (5) --R 2 2 2 - b x - a - 1 --R (b x + 2a b x + a )log(-------------) --R b x + a - 1 @@ -4056,13 +4224,16 @@ d0035:= D(m0035,x) --R Type: Expression(Integer) --E 184 +)clear all + + --S 185 of 510 t0036:= atanh(1+x)/(2+2*x) --R --R ---R atanh(x + 1) ---R (139) ------------ ---R 2x + 2 +--R atanh(x + 1) +--R (1) ------------ +--R 2x + 2 --R Type: Expression(Integer) --E 185 @@ -4088,10 +4259,10 @@ r0036:= -1/4*polylog(2,-1-x)+1/4*polylog(2,1+x) a0036:= integrate(t0036,x) --R --R ---R x ---I ++ atanh(%P + 1) ---I (140) | ------------- d%P ---I ++ 2%P + 2 +--R x +--I ++ atanh(%T + 1) +--I (2) | ------------- d%T +--I ++ 2%T + 2 --R Type: Union(Expression(Integer),...) --E 187 @@ -4103,13 +4274,16 @@ a0036:= integrate(t0036,x) --d0036:= D(m0036,x) --E 189 +)clear all + + --S 190 of 510 t0037:= atanh(a+b*x)/(a+b*x) --R --R ---R atanh(b x + a) ---R (141) -------------- ---R b x + a +--R atanh(b x + a) +--R (1) -------------- +--R b x + a --R Type: Expression(Integer) --E 190 @@ -4135,10 +4309,10 @@ r0037:= -1/2*(polylog(2,-a-b*x)-polylog(2,a+b*x))/b a0037:= integrate(t0037,x) --R --R ---R x ---I ++ atanh(%P b + a) ---I (142) | --------------- d%P ---I ++ %P b + a +--R x +--I ++ atanh(%T b + a) +--I (2) | --------------- d%T +--I ++ %T b + a --R Type: Union(Expression(Integer),...) --E 192 @@ -4150,14 +4324,17 @@ a0037:= integrate(t0037,x) --d0037:= D(m0037,x) --E 194 +)clear all + + --S 195 of 510 t0038:= atanh(x)/(1-x^2)^2 --R --R ---R atanh(x) ---R (143) ------------ ---R 4 2 ---R x - 2x + 1 +--R atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 195 @@ -4165,11 +4342,11 @@ t0038:= atanh(x)/(1-x^2)^2 r0038:= 1/4*(1-2*x*atanh(x)-atanh(x)^2+x^2*atanh(x)^2)/(-1+x^2) --R --R ---R 2 2 ---R (x - 1)atanh(x) - 2x atanh(x) + 1 ---R (144) ----------------------------------- ---R 2 ---R 4x - 4 +--R 2 2 +--R (x - 1)atanh(x) - 2x atanh(x) + 1 +--R (2) ----------------------------------- +--R 2 +--R 4x - 4 --R Type: Expression(Integer) --E 196 @@ -4177,12 +4354,12 @@ r0038:= 1/4*(1-2*x*atanh(x)-atanh(x)^2+x^2*atanh(x)^2)/(-1+x^2) a0038:= integrate(t0038,x) --R --R ---R 2 - x - 1 2 - x - 1 ---R (x - 1)log(-------) - 4x log(-------) + 4 ---R x - 1 x - 1 ---R (145) ------------------------------------------- ---R 2 ---R 16x - 16 +--R 2 - x - 1 2 - x - 1 +--R (x - 1)log(-------) - 4x log(-------) + 4 +--R x - 1 x - 1 +--R (3) ------------------------------------------- +--R 2 +--R 16x - 16 --R Type: Union(Expression(Integer),...) --E 197 @@ -4190,7 +4367,7 @@ a0038:= integrate(t0038,x) m0038:= a0038-r0038 --R --R ---R (146) +--R (4) --R 2 - x - 1 2 - x - 1 2 2 --R (x - 1)log(-------) - 4x log(-------) + (- 4x + 4)atanh(x) + 8x atanh(x) --R x - 1 x - 1 @@ -4204,24 +4381,27 @@ m0038:= a0038-r0038 d0038:= D(m0038,x) --R --R ---R - x - 1 ---R log(-------) - 2atanh(x) ---R x - 1 ---R (147) ------------------------ ---R 4 2 ---R 2x - 4x + 2 +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (5) ------------------------ +--R 4 2 +--R 2x - 4x + 2 --R Type: Expression(Integer) --E 199 +)clear all + + --S 200 of 510 t0039:= atanh(x)^2/(1-x^2)^2 --R --R ---R 2 ---R atanh(x) ---R (148) ------------ ---R 4 2 ---R x - 2x + 1 +--R 2 +--R atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 200 @@ -4230,11 +4410,11 @@ r0039:= 1/12*(-3*x+3*atanh(x)+3*x^2*atanh(x)-6*x*atanh(x)^2-2*atanh(x)^3+_ 2*x^2*atanh(x)^3)/(-1+x^2) --R --R ---R 2 3 2 2 ---R (2x - 2)atanh(x) - 6x atanh(x) + (3x + 3)atanh(x) - 3x ---R (149) ---------------------------------------------------------- ---R 2 ---R 12x - 12 +--R 2 3 2 2 +--R (2x - 2)atanh(x) - 6x atanh(x) + (3x + 3)atanh(x) - 3x +--R (2) ---------------------------------------------------------- +--R 2 +--R 12x - 12 --R Type: Expression(Integer) --E 201 @@ -4242,13 +4422,12 @@ r0039:= 1/12*(-3*x+3*atanh(x)+3*x^2*atanh(x)-6*x*atanh(x)^2-2*atanh(x)^3+_ a0039:= integrate(t0039,x) --R --R ---R (150) ---R 2 - x - 1 3 - x - 1 2 2 - x - 1 ---R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) - 12x ---R x - 1 x - 1 x - 1 ---R ---------------------------------------------------------------------- ---R 2 ---R 48x - 48 +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) - 12x +--R x - 1 x - 1 x - 1 +--R (3) ---------------------------------------------------------------------- +--R 2 +--R 48x - 48 --R Type: Union(Expression(Integer),...) --E 202 @@ -4256,7 +4435,7 @@ a0039:= integrate(t0039,x) m0039:= a0039-r0039 --R --R ---R (151) +--R (4) --R 2 - x - 1 3 - x - 1 2 2 - x - 1 --R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) --R x - 1 x - 1 x - 1 @@ -4273,23 +4452,26 @@ m0039:= a0039-r0039 d0039:= D(m0039,x) --R --R ---R - x - 1 2 2 ---R log(-------) - 4atanh(x) ---R x - 1 ---R (152) -------------------------- ---R 4 2 ---R 4x - 8x + 4 +--R - x - 1 2 2 +--R log(-------) - 4atanh(x) +--R x - 1 +--R (5) -------------------------- +--R 4 2 +--R 4x - 8x + 4 --R Type: Expression(Integer) --E 204 +)clear all + + --S 205 of 510 t0040:= 1/(a-a*x^2)/(b-2*b*atanh(x)) --R --R ---R 1 ---R (153) --------------------------------------- ---R 2 2 ---R (2a b x - 2a b)atanh(x) - a b x + a b +--R 1 +--R (1) --------------------------------------- +--R 2 2 +--R (2a b x - 2a b)atanh(x) - a b x + a b --R Type: Expression(Integer) --E 205 @@ -4297,9 +4479,9 @@ t0040:= 1/(a-a*x^2)/(b-2*b*atanh(x)) r0040:= -1/2*log(1-2*atanh(x))/a/b --R --R ---R log(- 2atanh(x) + 1) ---R (154) - -------------------- ---R 2a b +--R log(- 2atanh(x) + 1) +--R (2) - -------------------- +--R 2a b --R Type: Expression(Integer) --E 206 @@ -4307,11 +4489,11 @@ r0040:= -1/2*log(1-2*atanh(x))/a/b a0040:= integrate(t0040,x) --R --R ---R - x - 1 ---R log(log(-------) - 1) ---R x - 1 ---R (155) - --------------------- ---R 2a b +--R - x - 1 +--R log(log(-------) - 1) +--R x - 1 +--R (3) - --------------------- +--R 2a b --R Type: Union(Expression(Integer),...) --E 207 @@ -4319,11 +4501,11 @@ a0040:= integrate(t0040,x) m0040:= a0040-r0040 --R --R ---R - x - 1 ---R - log(log(-------) - 1) + log(- 2atanh(x) + 1) ---R x - 1 ---R (156) ---------------------------------------------- ---R 2a b +--R - x - 1 +--R - log(log(-------) - 1) + log(- 2atanh(x) + 1) +--R x - 1 +--R (4) ---------------------------------------------- +--R 2a b --R Type: Expression(Integer) --E 208 @@ -4331,7 +4513,7 @@ m0040:= a0040-r0040 d0040:= D(m0040,x) --R --R ---R (157) +--R (5) --R - x - 1 --R - log(-------) + 2atanh(x) --R x - 1 @@ -4345,14 +4527,17 @@ d0040:= D(m0040,x) --R Type: Expression(Integer) --E 209 +)clear all + + --S 210 of 510 t0041:= x*atanh(x)/(1-x^2) --R --R ---R x atanh(x) ---R (158) - ---------- ---R 2 ---R x - 1 +--R x atanh(x) +--R (1) - ---------- +--R 2 +--R x - 1 --R Type: Expression(Integer) --E 210 @@ -4378,11 +4563,11 @@ r0041:= -1/2*atanh(x)^2+atanh(x)*log(2/(1-x))+1/2*polylog(2,1-2/(1-x)) a0041:= integrate(t0041,x) --R --R ---R x ---I ++ %P atanh(%P) ---I (159) | - ------------ d%P ---R ++ 2 ---I %P - 1 +--R x +--I ++ %T atanh(%T) +--I (2) | - ------------ d%T +--R ++ 2 +--I %T - 1 --R Type: Union(Expression(Integer),...) --E 212 @@ -4394,14 +4579,17 @@ a0041:= integrate(t0041,x) --d0041:= D(m0041,x) --E 214 +)clear all + + --S 215 of 510 t0042:= x*atanh(x)/(1-x^2)^2 --R --R ---R x atanh(x) ---R (160) ------------ ---R 4 2 ---R x - 2x + 1 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 215 @@ -4409,11 +4597,11 @@ t0042:= x*atanh(x)/(1-x^2)^2 r0042:= -1/4*(-x+atanh(x)+x^2*atanh(x))/(-1+x^2) --R --R ---R 2 ---R (- x - 1)atanh(x) + x ---R (161) ---------------------- ---R 2 ---R 4x - 4 +--R 2 +--R (- x - 1)atanh(x) + x +--R (2) ---------------------- +--R 2 +--R 4x - 4 --R Type: Expression(Integer) --E 216 @@ -4421,12 +4609,12 @@ r0042:= -1/4*(-x+atanh(x)+x^2*atanh(x))/(-1+x^2) a0042:= integrate(t0042,x) --R --R ---R 2 - x - 1 ---R (- x - 1)log(-------) + 2x ---R x - 1 ---R (162) --------------------------- ---R 2 ---R 8x - 8 +--R 2 - x - 1 +--R (- x - 1)log(-------) + 2x +--R x - 1 +--R (3) --------------------------- +--R 2 +--R 8x - 8 --R Type: Union(Expression(Integer),...) --E 217 @@ -4434,12 +4622,12 @@ a0042:= integrate(t0042,x) m0042:= a0042-r0042 --R --R ---R 2 - x - 1 2 ---R (- x - 1)log(-------) + (2x + 2)atanh(x) ---R x - 1 ---R (163) ------------------------------------------ ---R 2 ---R 8x - 8 +--R 2 - x - 1 2 +--R (- x - 1)log(-------) + (2x + 2)atanh(x) +--R x - 1 +--R (4) ------------------------------------------ +--R 2 +--R 8x - 8 --R Type: Expression(Integer) --E 218 @@ -4447,23 +4635,26 @@ m0042:= a0042-r0042 d0042:= D(m0042,x) --R --R ---R - x - 1 ---R x log(-------) - 2x atanh(x) ---R x - 1 ---R (164) ---------------------------- ---R 4 2 ---R 2x - 4x + 2 +--R - x - 1 +--R x log(-------) - 2x atanh(x) +--R x - 1 +--R (5) ---------------------------- +--R 4 2 +--R 2x - 4x + 2 --R Type: Expression(Integer) --E 219 +)clear all + + --S 220 of 510 t0043:= x*atanh(x)/(1-x^2)^3 --R --R ---R x atanh(x) ---R (165) - ------------------ ---R 6 4 2 ---R x - 3x + 3x - 1 +--R x atanh(x) +--R (1) - ------------------ +--R 6 4 2 +--R x - 3x + 3x - 1 --R Type: Expression(Integer) --E 220 @@ -4471,11 +4662,11 @@ t0043:= x*atanh(x)/(1-x^2)^3 r0043:= -1/32*(5*x-3*x^3-5*atanh(x)-6*x^2*atanh(x)+3*atanh(x)*x^4)/(-1+x^2)^2 --R --R ---R 4 2 3 ---R (- 3x + 6x + 5)atanh(x) + 3x - 5x ---R (166) ------------------------------------ ---R 4 2 ---R 32x - 64x + 32 +--R 4 2 3 +--R (- 3x + 6x + 5)atanh(x) + 3x - 5x +--R (2) ------------------------------------ +--R 4 2 +--R 32x - 64x + 32 --R Type: Expression(Integer) --E 221 @@ -4483,12 +4674,12 @@ r0043:= -1/32*(5*x-3*x^3-5*atanh(x)-6*x^2*atanh(x)+3*atanh(x)*x^4)/(-1+x^2)^2 a0043:= integrate(t0043,x) --R --R ---R 4 2 - x - 1 3 ---R (- 3x + 6x + 5)log(-------) + 6x - 10x ---R x - 1 ---R (167) ----------------------------------------- ---R 4 2 ---R 64x - 128x + 64 +--R 4 2 - x - 1 3 +--R (- 3x + 6x + 5)log(-------) + 6x - 10x +--R x - 1 +--R (3) ----------------------------------------- +--R 4 2 +--R 64x - 128x + 64 --R Type: Union(Expression(Integer),...) --E 222 @@ -4496,12 +4687,12 @@ a0043:= integrate(t0043,x) m0043:= a0043-r0043 --R --R ---R 4 2 - x - 1 4 2 ---R (- 3x + 6x + 5)log(-------) + (6x - 12x - 10)atanh(x) ---R x - 1 ---R (168) --------------------------------------------------------- ---R 4 2 ---R 64x - 128x + 64 +--R 4 2 - x - 1 4 2 +--R (- 3x + 6x + 5)log(-------) + (6x - 12x - 10)atanh(x) +--R x - 1 +--R (4) --------------------------------------------------------- +--R 4 2 +--R 64x - 128x + 64 --R Type: Expression(Integer) --E 223 @@ -4509,24 +4700,27 @@ m0043:= a0043-r0043 d0043:= D(m0043,x) --R --R ---R - x - 1 ---R - x log(-------) + 2x atanh(x) ---R x - 1 ---R (169) ------------------------------ ---R 6 4 2 ---R 2x - 6x + 6x - 2 +--R - x - 1 +--R - x log(-------) + 2x atanh(x) +--R x - 1 +--R (5) ------------------------------ +--R 6 4 2 +--R 2x - 6x + 6x - 2 --R Type: Expression(Integer) --E 224 +)clear all + + --S 225 of 510 t0044:= x^3*atanh(x)/(1-x^2) --R --R ---R 3 ---R x atanh(x) ---R (170) - ---------- ---R 2 ---R x - 1 +--R 3 +--R x atanh(x) +--R (1) - ---------- +--R 2 +--R x - 1 --R Type: Expression(Integer) --E 225 @@ -4553,11 +4747,11 @@ r0044:= -1/2*x+1/2*atanh(x)-1/2*x^2*atanh(x)-1/2*atanh(x)^2+_ a0044:= integrate(t0044,x) --R --R ---R x 3 ---I ++ %P atanh(%P) ---I (171) | - ------------ d%P ---R ++ 2 ---I %P - 1 +--R x 3 +--I ++ %T atanh(%T) +--I (2) | - ------------ d%T +--R ++ 2 +--I %T - 1 --R Type: Union(Expression(Integer),...) --E 227 @@ -4569,15 +4763,18 @@ a0044:= integrate(t0044,x) --d0044:= D(m0044,x) --E 229 +)clear all + + --S 230 of 510 t0045:= x^2*atanh(x)/(1-x^2) --R --R +--R 2 +--R x atanh(x) +--R (1) - ---------- --R 2 ---R x atanh(x) ---R (172) - ---------- ---R 2 ---R x - 1 +--R x - 1 --R Type: Expression(Integer) --E 230 @@ -4585,10 +4782,10 @@ t0045:= x^2*atanh(x)/(1-x^2) r0045:= -x*atanh(x)+1/2*atanh(x)^2-1/2*log(1-x^2) --R --R ---R 2 2 ---R - log(- x + 1) + atanh(x) - 2x atanh(x) ---R (173) ----------------------------------------- ---R 2 +--R 2 2 +--R - log(- x + 1) + atanh(x) - 2x atanh(x) +--R (2) ----------------------------------------- +--R 2 --R Type: Expression(Integer) --E 231 @@ -4596,11 +4793,11 @@ r0045:= -x*atanh(x)+1/2*atanh(x)^2-1/2*log(1-x^2) a0045:= integrate(t0045,x) --R --R ---R 2 - x - 1 2 - x - 1 ---R - 4log(x - 1) + log(-------) - 4x log(-------) ---R x - 1 x - 1 ---R (174) ------------------------------------------------ ---R 8 +--R 2 - x - 1 2 - x - 1 +--R - 4log(x - 1) + log(-------) - 4x log(-------) +--R x - 1 x - 1 +--R (3) ------------------------------------------------ +--R 8 --R Type: Union(Expression(Integer),...) --E 232 @@ -4608,7 +4805,7 @@ a0045:= integrate(t0045,x) m0045:= a0045-r0045 --R --R ---R (175) +--R (4) --R 2 - x - 1 2 - x - 1 2 --R - 4log(x - 1) + log(-------) - 4x log(-------) + 4log(- x + 1) --R x - 1 x - 1 @@ -4624,23 +4821,26 @@ m0045:= a0045-r0045 d0045:= D(m0045,x) --R --R ---R 2 - x - 1 2 ---R - x log(-------) + 2x atanh(x) ---R x - 1 ---R (176) ------------------------------ ---R 2 ---R 2x - 2 +--R 2 - x - 1 2 +--R - x log(-------) + 2x atanh(x) +--R x - 1 +--R (5) ------------------------------ +--R 2 +--R 2x - 2 --R Type: Expression(Integer) --E 234 +)clear all + + --S 235 of 510 t0046:= x*atanh(x)/(1-x^2) --R --R ---R x atanh(x) ---R (177) - ---------- ---R 2 ---R x - 1 +--R x atanh(x) +--R (1) - ---------- +--R 2 +--R x - 1 --R Type: Expression(Integer) --E 235 @@ -4666,11 +4866,11 @@ r0046:= -1/2*atanh(x)^2+atanh(x)*log(2/(1-x))+1/2*polylog(2,1-2/(1-x)) a0046:= integrate(t0046,x) --R --R ---R x ---I ++ %P atanh(%P) ---I (178) | - ------------ d%P ---R ++ 2 ---I %P - 1 +--R x +--I ++ %T atanh(%T) +--I (2) | - ------------ d%T +--R ++ 2 +--I %T - 1 --R Type: Union(Expression(Integer),...) --E 237 @@ -4682,14 +4882,17 @@ a0046:= integrate(t0046,x) --d0046:= D(m0046,x) --E 239 +)clear all + + --S 240 of 510 t0047:= atanh(x)/x/(1-x^2) --R --R ---R atanh(x) ---R (179) - -------- ---R 3 ---R x - x +--R atanh(x) +--R (1) - -------- +--R 3 +--R x - x --R Type: Expression(Integer) --E 240 @@ -4715,11 +4918,11 @@ r0047:= -1/2*atanh(x)^2+atanh(x)*log(-2*x/(1-x))+1/2*polylog(2,-1+2/(1-x)) a0047:= integrate(t0047,x) --R --R ---R x ---I ++ atanh(%P) ---I (180) | - --------- d%P ---R ++ 3 ---I %P - %P +--R x +--I ++ atanh(%T) +--I (2) | - --------- d%T +--R ++ 3 +--I %T - %T --R Type: Union(Expression(Integer),...) --E 242 @@ -4731,14 +4934,17 @@ a0047:= integrate(t0047,x) --d0047:= D(m0047,x) --E 244 +)clear all + + --S 245 of 510 t0048:= atanh(x)/x^2/(1-x^2) --R --R ---R atanh(x) ---R (181) - -------- ---R 4 2 ---R x - x +--R atanh(x) +--R (1) - -------- +--R 4 2 +--R x - x --R Type: Expression(Integer) --E 245 @@ -4746,13 +4952,13 @@ t0048:= atanh(x)/x^2/(1-x^2) r0048:= -atanh(x)/x+1/2*atanh(x)^2+log(x/(1-x^2)^(1/2)) --R --R ---R x 2 ---R 2x log(-----------) + x atanh(x) - 2atanh(x) ---R +--------+ ---R | 2 ---R \|- x + 1 ---R (182) --------------------------------------------- ---R 2x +--R x 2 +--R 2x log(-----------) + x atanh(x) - 2atanh(x) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R (2) --------------------------------------------- +--R 2x --R Type: Expression(Integer) --E 246 @@ -4760,11 +4966,11 @@ r0048:= -atanh(x)/x+1/2*atanh(x)^2+log(x/(1-x^2)^(1/2)) a0048:= integrate(t0048,x) --R --R ---R 2 - x - 1 2 - x - 1 ---R - 4x log(x - 1) + 8x log(x) + x log(-------) - 4log(-------) ---R x - 1 x - 1 ---R (183) -------------------------------------------------------------- ---R 8x +--R 2 - x - 1 2 - x - 1 +--R - 4x log(x - 1) + 8x log(x) + x log(-------) - 4log(-------) +--R x - 1 x - 1 +--R (3) -------------------------------------------------------------- +--R 8x --R Type: Union(Expression(Integer),...) --E 247 @@ -4772,7 +4978,7 @@ a0048:= integrate(t0048,x) m0048:= a0048-r0048 --R --R ---R (184) +--R (4) --R x 2 - x - 1 2 --R - 8x log(-----------) - 4x log(x - 1) + 8x log(x) + x log(-------) --R +--------+ x - 1 @@ -4791,23 +4997,26 @@ m0048:= a0048-r0048 d0048:= D(m0048,x) --R --R ---R - x - 1 ---R - log(-------) + 2atanh(x) ---R x - 1 ---R (185) -------------------------- ---R 4 2 ---R 2x - 2x +--R - x - 1 +--R - log(-------) + 2atanh(x) +--R x - 1 +--R (5) -------------------------- +--R 4 2 +--R 2x - 2x --R Type: Expression(Integer) --E 249 +)clear all + + --S 250 of 510 t0049:= atanh(x)/x^3/(1-x^2) --R --R ---R atanh(x) ---R (186) - -------- ---R 5 3 ---R x - x +--R atanh(x) +--R (1) - -------- +--R 5 3 +--R x - x --R Type: Expression(Integer) --E 250 @@ -4834,11 +5043,11 @@ r0049:= -1/2/x+1/2*atanh(x)-1/2*atanh(x)/x^2-1/2*atanh(x)^2+_ a0049:= integrate(t0049,x) --R --R ---R x ---I ++ atanh(%P) ---I (187) | - --------- d%P ---R ++ 5 3 ---I %P - %P +--R x +--I ++ atanh(%T) +--I (2) | - --------- d%T +--R ++ 5 3 +--I %T - %T --R Type: Union(Expression(Integer),...) --E 252 @@ -4850,15 +5059,18 @@ a0049:= integrate(t0049,x) --d0049:= D(m0049,x) --E 254 +)clear all + + --S 255 of 510 t0050:= x^3*atanh(x)^2/(1-x^2) --R --R ---R 3 2 ---R x atanh(x) ---R (188) - ----------- ---R 2 ---R x - 1 +--R 3 2 +--R x atanh(x) +--R (1) - ----------- +--R 2 +--R x - 1 --R Type: Expression(Integer) --E 255 @@ -4887,11 +5099,11 @@ r0050:= -x*atanh(x)+1/2*atanh(x)^2-1/2*x^2*atanh(x)^2-_ a0050:= integrate(t0050,x) --R --R ---R x 3 2 ---I ++ %P atanh(%P) ---I (189) | - ------------- d%P ---R ++ 2 ---I %P - 1 +--R x 3 2 +--I ++ %T atanh(%T) +--I (2) | - ------------- d%T +--R ++ 2 +--I %T - 1 --R Type: Union(Expression(Integer),...) --E 257 @@ -4903,15 +5115,18 @@ a0050:= integrate(t0050,x) --d0050:= D(m0050,x) --E 259 +)clear all + + --S 260 of 510 t0051:= x^2*atanh(x)^2/(1-x^2) --R --R ---R 2 2 ---R x atanh(x) ---R (190) - ----------- ---R 2 ---R x - 1 +--R 2 2 +--R x atanh(x) +--R (1) - ----------- +--R 2 +--R x - 1 --R Type: Expression(Integer) --E 260 @@ -4938,11 +5153,11 @@ r0051:= -atanh(x)^2-x*atanh(x)^2+1/3*atanh(x)^3+_ a0051:= integrate(t0051,x) --R --R ---R x 2 2 ---I ++ %P atanh(%P) ---I (191) | - ------------- d%P ---R ++ 2 ---I %P - 1 +--R x 2 2 +--I ++ %T atanh(%T) +--I (2) | - ------------- d%T +--R ++ 2 +--I %T - 1 --R Type: Union(Expression(Integer),...) --E 262 @@ -4954,15 +5169,18 @@ a0051:= integrate(t0051,x) --d0051:= D(m0051,x) --E 264 +)clear all + + --S 265 of 510 t0052:= x*atanh(x)^2/(1-x^2) --R --R ---R 2 ---R x atanh(x) ---R (192) - ----------- ---R 2 ---R x - 1 +--R 2 +--R x atanh(x) +--R (1) - ----------- +--R 2 +--R x - 1 --R Type: Expression(Integer) --E 265 @@ -4989,11 +5207,11 @@ r0052:= -1/3*atanh(x)^3+atanh(x)^2*log(2/(1-x))+_ a0052:= integrate(t0052,x) --R --R ---R x 2 ---I ++ %P atanh(%P) ---I (193) | - ------------- d%P ---R ++ 2 ---I %P - 1 +--R x 2 +--I ++ %T atanh(%T) +--I (2) | - ------------- d%T +--R ++ 2 +--I %T - 1 --R Type: Union(Expression(Integer),...) --E 267 @@ -5005,15 +5223,18 @@ a0052:= integrate(t0052,x) --d0052:= D(m0052,x) --E 269 +)clear all + + --S 270 of 510 t0053:= atanh(x)^2/x/(1-x^2) --R --R ---R 2 ---R atanh(x) ---R (194) - --------- ---R 3 ---R x - x +--R 2 +--R atanh(x) +--R (1) - --------- +--R 3 +--R x - x --R Type: Expression(Integer) --E 270 @@ -5040,11 +5261,11 @@ r0053:= -1/3*atanh(x)^3+atanh(x)^2*log(-2*x/(1-x))+_ a0053:= integrate(t0053,x) --R --R ---R x 2 ---I ++ atanh(%P) ---I (195) | - ---------- d%P ---R ++ 3 ---I %P - %P +--R x 2 +--I ++ atanh(%T) +--I (2) | - ---------- d%T +--R ++ 3 +--I %T - %T --R Type: Union(Expression(Integer),...) --E 272 @@ -5056,15 +5277,18 @@ a0053:= integrate(t0053,x) --d0053:= D(m0053,x) --E 274 +)clear all + + --S 275 of 510 t0054:= atanh(x)^2/x^2/(1-x^2) --R --R ---R 2 ---R atanh(x) ---R (196) - --------- ---R 4 2 ---R x - x +--R 2 +--R atanh(x) +--R (1) - --------- +--R 4 2 +--R x - x --R Type: Expression(Integer) --E 275 @@ -5091,11 +5315,11 @@ r0054:= -atanh(x)^2-atanh(x)^2/x+1/3*atanh(x)^3+_ a0054:= integrate(t0054,x) --R --R ---R x 2 ---I ++ atanh(%P) ---I (197) | - ---------- d%P ---R ++ 4 2 ---I %P - %P +--R x 2 +--I ++ atanh(%T) +--I (2) | - ---------- d%T +--R ++ 4 2 +--I %T - %T --R Type: Union(Expression(Integer),...) --E 277 @@ -5107,15 +5331,18 @@ a0054:= integrate(t0054,x) --d0054:= D(m0054,x) --E 279 +)clear all + + --S 280 of 510 t0055:= atanh(x)^2/x^3/(1-x^2) --R --R ---R 2 ---R atanh(x) ---R (198) - --------- ---R 5 3 ---R x - x +--R 2 +--R atanh(x) +--R (1) - --------- +--R 5 3 +--R x - x --R Type: Expression(Integer) --E 280 @@ -5144,11 +5371,11 @@ r0055:= -atanh(x)/x+1/2*atanh(x)^2-1/2*atanh(x)^2/x^2-_ a0055:= integrate(t0055,x) --R --R ---R x 2 ---I ++ atanh(%P) ---I (199) | - ---------- d%P ---R ++ 5 3 ---I %P - %P +--R x 2 +--I ++ atanh(%T) +--I (2) | - ---------- d%T +--R ++ 5 3 +--I %T - %T --R Type: Union(Expression(Integer),...) --E 282 @@ -5160,15 +5387,18 @@ a0055:= integrate(t0055,x) --d0055:= D(m0055,x) --E 284 +)clear all + + --S 285 of 510 t0056:= x^3*atanh(x)^3/(1-x^2) --R --R ---R 3 3 ---R x atanh(x) ---R (200) - ----------- ---R 2 ---R x - 1 +--R 3 3 +--R x atanh(x) +--R (1) - ----------- +--R 2 +--R x - 1 --R Type: Expression(Integer) --E 285 @@ -5198,11 +5428,11 @@ r0056:= -3/2*atanh(x)^2-3/2*x*atanh(x)^2+1/2*atanh(x)^3-_ a0056:= integrate(t0056,x) --R --R ---R x 3 3 ---I ++ %P atanh(%P) ---I (201) | - ------------- d%P ---R ++ 2 ---I %P - 1 +--R x 3 3 +--I ++ %T atanh(%T) +--I (2) | - ------------- d%T +--R ++ 2 +--I %T - 1 --R Type: Union(Expression(Integer),...) --E 287 @@ -5214,15 +5444,18 @@ a0056:= integrate(t0056,x) --d0056:= D(m0056,x) --E 289 +)clear all + + --S 290 of 510 t0057:= x^2*atanh(x)^3/(1-x^2) --R --R ---R 2 3 ---R x atanh(x) ---R (202) - ----------- ---R 2 ---R x - 1 +--R 2 3 +--R x atanh(x) +--R (1) - ----------- +--R 2 +--R x - 1 --R Type: Expression(Integer) --E 290 @@ -5250,11 +5483,11 @@ r0057:= -atanh(x)^3-x*atanh(x)^3+1/4*atanh(x)^4+_ a0057:= integrate(t0057,x) --R --R ---R x 2 3 ---I ++ %P atanh(%P) ---I (203) | - ------------- d%P ---R ++ 2 ---I %P - 1 +--R x 2 3 +--I ++ %T atanh(%T) +--I (2) | - ------------- d%T +--R ++ 2 +--I %T - 1 --R Type: Union(Expression(Integer),...) --E 292 @@ -5266,15 +5499,18 @@ a0057:= integrate(t0057,x) --d0057:= D(m0057,x) --E 294 +)clear all + + --S 295 of 510 t0058:= x*atanh(x)^3/(1-x^2) --R --R ---R 3 ---R x atanh(x) ---R (204) - ----------- ---R 2 ---R x - 1 +--R 3 +--R x atanh(x) +--R (1) - ----------- +--R 2 +--R x - 1 --R Type: Expression(Integer) --E 295 @@ -5302,11 +5538,11 @@ r0058:= -1/4*atanh(x)^4+atanh(x)^3*log(2)+atanh(x)^3*log(-1/(-1+x))+_ a0058:= integrate(t0058,x) --R --R ---R x 3 ---I ++ %P atanh(%P) ---I (205) | - ------------- d%P ---R ++ 2 ---I %P - 1 +--R x 3 +--I ++ %T atanh(%T) +--I (2) | - ------------- d%T +--R ++ 2 +--I %T - 1 --R Type: Union(Expression(Integer),...) --E 297 @@ -5318,15 +5554,18 @@ a0058:= integrate(t0058,x) --d0058:= D(m0058,x) --E 299 +)clear all + + --S 300 of 510 t0059:= atanh(x)^3/x/(1-x^2) --R --R ---R 3 ---R atanh(x) ---R (206) - --------- ---R 3 ---R x - x +--R 3 +--R atanh(x) +--R (1) - --------- +--R 3 +--R x - x --R Type: Expression(Integer) --E 300 @@ -5354,11 +5593,11 @@ r0059:= -1/4*atanh(x)^4+atanh(x)^3*log(-2*x/(1-x))+_ a0059:= integrate(t0059,x) --R --R ---R x 3 ---I ++ atanh(%P) ---I (207) | - ---------- d%P ---R ++ 3 ---I %P - %P +--R x 3 +--I ++ atanh(%T) +--I (2) | - ---------- d%T +--R ++ 3 +--I %T - %T --R Type: Union(Expression(Integer),...) --E 302 @@ -5370,15 +5609,18 @@ a0059:= integrate(t0059,x) --d0059:= D(m0059,x) --E 304 +)clear all + + --S 305 of 510 t0060:= atanh(x)^3/x^2/(1-x^2) --R --R ---R 3 ---R atanh(x) ---R (208) - --------- ---R 4 2 ---R x - x +--R 3 +--R atanh(x) +--R (1) - --------- +--R 4 2 +--R x - x --R Type: Expression(Integer) --E 305 @@ -5406,11 +5648,11 @@ r0060:= -atanh(x)^3-atanh(x)^3/x+1/4*atanh(x)^4+_ a0060:= integrate(t0060,x) --R --R ---R x 3 ---I ++ atanh(%P) ---I (209) | - ---------- d%P ---R ++ 4 2 ---I %P - %P +--R x 3 +--I ++ atanh(%T) +--I (2) | - ---------- d%T +--R ++ 4 2 +--I %T - %T --R Type: Union(Expression(Integer),...) --E 307 @@ -5422,15 +5664,18 @@ a0060:= integrate(t0060,x) --d0060:= D(m0060,x) --E 309 +)clear all + + --S 310 of 510 t0061:= atanh(x)^3/x^3/(1-x^2) --R --R ---R 3 ---R atanh(x) ---R (210) - --------- ---R 5 3 ---R x - x +--R 3 +--R atanh(x) +--R (1) - --------- +--R 5 3 +--R x - x --R Type: Expression(Integer) --E 310 @@ -5460,11 +5705,11 @@ r0061:= -3/2*atanh(x)^2-3/2*atanh(x)^2/x+1/2*atanh(x)^3-_ a0061:= integrate(t0061,x) --R --R ---R x 3 ---I ++ atanh(%P) ---I (211) | - ---------- d%P ---R ++ 5 3 ---I %P - %P +--R x 3 +--I ++ atanh(%T) +--I (2) | - ---------- d%T +--R ++ 5 3 +--I %T - %T --R Type: Union(Expression(Integer),...) --E 312 @@ -5476,15 +5721,18 @@ a0061:= integrate(t0061,x) --d0061:= D(m0061,x) --E 314 +)clear all + + --S 315 of 510 t0062:= x^3*atanh(x)/(1-x^2)^2 --R --R ---R 3 ---R x atanh(x) ---R (212) ------------ ---R 4 2 ---R x - 2x + 1 +--R 3 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 315 @@ -5511,11 +5759,11 @@ r0062:= 1/2*atanh(x)^2+1/4*atanh(x)*cosh(2*atanh(x))-_ a0062:= integrate(t0062,x) --R --R ---R x 3 ---I ++ %P atanh(%P) ---I (213) | -------------- d%P ---R ++ 4 2 ---I %P - 2%P + 1 +--R x 3 +--I ++ %T atanh(%T) +--I (2) | -------------- d%T +--R ++ 4 2 +--I %T - 2%T + 1 --R Type: Union(Expression(Integer),...) --E 317 @@ -5527,15 +5775,18 @@ a0062:= integrate(t0062,x) --d0062:= D(m0062,x) --E 319 +)clear all + + --S 320 of 510 t0063:= x^2*atanh(x)/(1-x^2)^2 --R --R ---R 2 ---R x atanh(x) ---R (214) ------------ ---R 4 2 ---R x - 2x + 1 +--R 2 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 320 @@ -5543,11 +5794,11 @@ t0063:= x^2*atanh(x)/(1-x^2)^2 r0063:= -x^2/(4-4*x^2)+x*atanh(x)/(2-2*x^2)-1/4*atanh(x)^2 --R --R ---R 2 2 2 ---R (- x + 1)atanh(x) - 2x atanh(x) + x ---R (215) -------------------------------------- ---R 2 ---R 4x - 4 +--R 2 2 2 +--R (- x + 1)atanh(x) - 2x atanh(x) + x +--R (2) -------------------------------------- +--R 2 +--R 4x - 4 --R Type: Expression(Integer) --E 321 @@ -5555,12 +5806,12 @@ r0063:= -x^2/(4-4*x^2)+x*atanh(x)/(2-2*x^2)-1/4*atanh(x)^2 a0063:= integrate(t0063,x) --R --R ---R 2 - x - 1 2 - x - 1 ---R (- x + 1)log(-------) - 4x log(-------) + 4 ---R x - 1 x - 1 ---R (216) --------------------------------------------- ---R 2 ---R 16x - 16 +--R 2 - x - 1 2 - x - 1 +--R (- x + 1)log(-------) - 4x log(-------) + 4 +--R x - 1 x - 1 +--R (3) --------------------------------------------- +--R 2 +--R 16x - 16 --R Type: Union(Expression(Integer),...) --E 322 @@ -5568,7 +5819,7 @@ a0063:= integrate(t0063,x) m0063:= a0063-r0063 --R --R ---R (217) +--R (4) --R 2 - x - 1 2 - x - 1 2 2 --R (- x + 1)log(-------) - 4x log(-------) + (4x - 4)atanh(x) --R x - 1 x - 1 @@ -5585,23 +5836,26 @@ m0063:= a0063-r0063 d0063:= D(m0063,x) --R --R ---R 2 - x - 1 2 ---R x log(-------) - 2x atanh(x) ---R x - 1 ---R (218) ---------------------------- ---R 4 2 ---R 2x - 4x + 2 +--R 2 - x - 1 2 +--R x log(-------) - 2x atanh(x) +--R x - 1 +--R (5) ---------------------------- +--R 4 2 +--R 2x - 4x + 2 --R Type: Expression(Integer) --E 324 +)clear all + + --S 325 of 510 t0064:= x*atanh(x)/(1-x^2)^2 --R --R ---R x atanh(x) ---R (219) ------------ ---R 4 2 ---R x - 2x + 1 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 325 @@ -5609,11 +5863,11 @@ t0064:= x*atanh(x)/(1-x^2)^2 r0064:= -1/4*(-x+atanh(x)+x^2*atanh(x))/(-1+x^2) --R --R ---R 2 ---R (- x - 1)atanh(x) + x ---R (220) ---------------------- ---R 2 ---R 4x - 4 +--R 2 +--R (- x - 1)atanh(x) + x +--R (2) ---------------------- +--R 2 +--R 4x - 4 --R Type: Expression(Integer) --E 326 @@ -5621,12 +5875,12 @@ r0064:= -1/4*(-x+atanh(x)+x^2*atanh(x))/(-1+x^2) a0064:= integrate(t0064,x) --R --R ---R 2 - x - 1 ---R (- x - 1)log(-------) + 2x ---R x - 1 ---R (221) --------------------------- ---R 2 ---R 8x - 8 +--R 2 - x - 1 +--R (- x - 1)log(-------) + 2x +--R x - 1 +--R (3) --------------------------- +--R 2 +--R 8x - 8 --R Type: Union(Expression(Integer),...) --E 327 @@ -5634,12 +5888,12 @@ a0064:= integrate(t0064,x) m0064:= a0064-r0064 --R --R ---R 2 - x - 1 2 ---R (- x - 1)log(-------) + (2x + 2)atanh(x) ---R x - 1 ---R (222) ------------------------------------------ ---R 2 ---R 8x - 8 +--R 2 - x - 1 2 +--R (- x - 1)log(-------) + (2x + 2)atanh(x) +--R x - 1 +--R (4) ------------------------------------------ +--R 2 +--R 8x - 8 --R Type: Expression(Integer) --E 328 @@ -5647,23 +5901,26 @@ m0064:= a0064-r0064 d0064:= D(m0064,x) --R --R ---R - x - 1 ---R x log(-------) - 2x atanh(x) ---R x - 1 ---R (223) ---------------------------- ---R 4 2 ---R 2x - 4x + 2 +--R - x - 1 +--R x log(-------) - 2x atanh(x) +--R x - 1 +--R (5) ---------------------------- +--R 4 2 +--R 2x - 4x + 2 --R Type: Expression(Integer) --E 329 +)clear all + + --S 330 of 510 t0065:= atanh(x)/(1-x^2)^2 --R --R ---R atanh(x) ---R (224) ------------ ---R 4 2 ---R x - 2x + 1 +--R atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 330 @@ -5671,11 +5928,11 @@ t0065:= atanh(x)/(1-x^2)^2 r0065:= 1/4*(1-2*x*atanh(x)-atanh(x)^2+x^2*atanh(x)^2)/(-1+x^2) --R --R ---R 2 2 ---R (x - 1)atanh(x) - 2x atanh(x) + 1 ---R (225) ----------------------------------- ---R 2 ---R 4x - 4 +--R 2 2 +--R (x - 1)atanh(x) - 2x atanh(x) + 1 +--R (2) ----------------------------------- +--R 2 +--R 4x - 4 --R Type: Expression(Integer) --E 331 @@ -5683,12 +5940,12 @@ r0065:= 1/4*(1-2*x*atanh(x)-atanh(x)^2+x^2*atanh(x)^2)/(-1+x^2) a0065:= integrate(t0065,x) --R --R ---R 2 - x - 1 2 - x - 1 ---R (x - 1)log(-------) - 4x log(-------) + 4 ---R x - 1 x - 1 ---R (226) ------------------------------------------- ---R 2 ---R 16x - 16 +--R 2 - x - 1 2 - x - 1 +--R (x - 1)log(-------) - 4x log(-------) + 4 +--R x - 1 x - 1 +--R (3) ------------------------------------------- +--R 2 +--R 16x - 16 --R Type: Union(Expression(Integer),...) --E 332 @@ -5696,7 +5953,7 @@ a0065:= integrate(t0065,x) m0065:= a0065-r0065 --R --R ---R (227) +--R (4) --R 2 - x - 1 2 - x - 1 2 2 --R (x - 1)log(-------) - 4x log(-------) + (- 4x + 4)atanh(x) + 8x atanh(x) --R x - 1 x - 1 @@ -5710,23 +5967,26 @@ m0065:= a0065-r0065 d0065:= D(m0065,x) --R --R ---R - x - 1 ---R log(-------) - 2atanh(x) ---R x - 1 ---R (228) ------------------------ ---R 4 2 ---R 2x - 4x + 2 +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (5) ------------------------ +--R 4 2 +--R 2x - 4x + 2 --R Type: Expression(Integer) --E 334 +)clear all + + --S 335 of 510 t0066:= atanh(x)/x/(1-x^2)^2 --R --R ---R atanh(x) ---R (229) ------------ ---R 5 3 ---R x - 2x + x +--R atanh(x) +--R (1) ------------ +--R 5 3 +--R x - 2x + x --R Type: Expression(Integer) --E 335 @@ -5753,11 +6013,11 @@ r0066:= -1/2*atanh(x)^2+1/4*atanh(x)*cosh(2*atanh(x))+_ a0066:= integrate(t0066,x) --R --R ---R x ---I ++ atanh(%P) ---I (230) | --------------- d%P ---R ++ 5 3 ---I %P - 2%P + %P +--R x +--I ++ atanh(%T) +--I (2) | --------------- d%T +--R ++ 5 3 +--I %T - 2%T + %T --R Type: Union(Expression(Integer),...) --E 337 @@ -5769,14 +6029,17 @@ a0066:= integrate(t0066,x) --d0066:= D(m0066,x) --E 339 +)clear all + + --S 340 of 510 t0067:= atanh(x)/x^2/(1-x^2)^2 --R --R ---R atanh(x) ---R (231) ------------- ---R 6 4 2 ---R x - 2x + x +--R atanh(x) +--R (1) ------------- +--R 6 4 2 +--R x - 2x + x --R Type: Expression(Integer) --E 340 @@ -5785,7 +6048,7 @@ r0067:= -atanh(x)/x+3/4*atanh(x)^2-1/8*cosh(2*atanh(x))+_ log(x/(1-x^2)^(1/2))+1/4*atanh(x)*sinh(2*atanh(x)) --R --R ---R (232) +--R (2) --R x --R 2x atanh(x)sinh(2atanh(x)) + 8x log(-----------) - x cosh(2atanh(x)) --R +--------+ @@ -5803,7 +6066,7 @@ r0067:= -atanh(x)/x+3/4*atanh(x)^2-1/8*cosh(2*atanh(x))+_ a0067:= integrate(t0067,x) --R --R ---R (233) +--R (3) --R 3 2 3 3 - x - 1 2 --R (- 8x + 8x)log(x - 1) + (16x - 16x)log(x) + (3x - 3x)log(-------) --R x - 1 @@ -5821,7 +6084,7 @@ a0067:= integrate(t0067,x) m0067:= a0067-r0067 --R --R ---R (234) +--R (4) --R 3 3 x --R (- 4x + 4x)atanh(x)sinh(2atanh(x)) + (- 16x + 16x)log(-----------) --R +--------+ @@ -5847,7 +6110,7 @@ m0067:= a0067-r0067 d0067:= D(m0067,x) --R --R ---R (235) +--R (5) --R 4 2 - x - 1 4 2 --R (x - x )atanh(x)cosh(2atanh(x)) + log(-------) + (x + x - 2)atanh(x) --R x - 1 @@ -5857,14 +6120,17 @@ d0067:= D(m0067,x) --R Type: Expression(Integer) --E 344 +)clear all + + --S 345 of 510 t0068:= atanh(x)/x^3/(1-x^2)^2 --R --R ---R atanh(x) ---R (236) ------------- ---R 7 5 3 ---R x - 2x + x +--R atanh(x) +--R (1) ------------- +--R 7 5 3 +--R x - 2x + x --R Type: Expression(Integer) --E 345 @@ -5892,11 +6158,11 @@ r0068:= -1/2/x-1/2*(1-x^2)*atanh(x)/x^2-atanh(x)^2+_ a0068:= integrate(t0068,x) --R --R ---R x ---I ++ atanh(%P) ---I (237) | ---------------- d%P ---R ++ 7 5 3 ---I %P - 2%P + %P +--R x +--I ++ atanh(%T) +--I (2) | ---------------- d%T +--R ++ 7 5 3 +--I %T - 2%T + %T --R Type: Union(Expression(Integer),...) --E 347 @@ -5908,15 +6174,18 @@ a0068:= integrate(t0068,x) --d0068:= D(m0068,x) --E 349 +)clear all + + --S 350 of 510 t0069:= x^3*atanh(x)^2/(1-x^2)^2 --R --R ---R 3 2 ---R x atanh(x) ---R (238) ------------ ---R 4 2 ---R x - 2x + 1 +--R 3 2 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 350 @@ -5945,11 +6214,11 @@ r0069:= 1/3*atanh(x)^3+1/8*cosh(2*atanh(x))+_ a0069:= integrate(t0069,x) --R --R ---R x 3 2 ---I ++ %P atanh(%P) ---I (239) | -------------- d%P ---R ++ 4 2 ---I %P - 2%P + 1 +--R x 3 2 +--I ++ %T atanh(%T) +--I (2) | -------------- d%T +--R ++ 4 2 +--I %T - 2%T + 1 --R Type: Union(Expression(Integer),...) --E 352 @@ -5961,15 +6230,18 @@ a0069:= integrate(t0069,x) --d0069:= D(m0069,x) --E 354 +)clear all + + --S 355 of 510 t0070:= x^2*atanh(x)^2/(1-x^2)^2 --R --R ---R 2 2 ---R x atanh(x) ---R (240) ------------ ---R 4 2 ---R x - 2x + 1 +--R 2 2 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 355 @@ -5978,11 +6250,11 @@ r0070:= -1/12*(3*x-3*atanh(x)-3*x^2*atanh(x)+6*x*atanh(x)^2-_ 2*atanh(x)^3+2*x^2*atanh(x)^3)/(-1+x^2) --R --R ---R 2 3 2 2 ---R (- 2x + 2)atanh(x) - 6x atanh(x) + (3x + 3)atanh(x) - 3x ---R (241) ------------------------------------------------------------ ---R 2 ---R 12x - 12 +--R 2 3 2 2 +--R (- 2x + 2)atanh(x) - 6x atanh(x) + (3x + 3)atanh(x) - 3x +--R (2) ------------------------------------------------------------ +--R 2 +--R 12x - 12 --R Type: Expression(Integer) --E 356 @@ -5990,7 +6262,7 @@ r0070:= -1/12*(3*x-3*atanh(x)-3*x^2*atanh(x)+6*x*atanh(x)^2-_ a0070:= integrate(t0070,x) --R --R ---R (242) +--R (3) --R 2 - x - 1 3 - x - 1 2 2 - x - 1 --R (- x + 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) - 12x --R x - 1 x - 1 x - 1 @@ -6004,7 +6276,7 @@ a0070:= integrate(t0070,x) m0070:= a0070-r0070 --R --R ---R (243) +--R (4) --R 2 - x - 1 3 - x - 1 2 2 - x - 1 --R (- x + 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) --R x - 1 x - 1 x - 1 @@ -6021,24 +6293,27 @@ m0070:= a0070-r0070 d0070:= D(m0070,x) --R --R ---R 2 - x - 1 2 2 2 ---R x log(-------) - 4x atanh(x) ---R x - 1 ---R (244) ------------------------------ ---R 4 2 ---R 4x - 8x + 4 +--R 2 - x - 1 2 2 2 +--R x log(-------) - 4x atanh(x) +--R x - 1 +--R (5) ------------------------------ +--R 4 2 +--R 4x - 8x + 4 --R Type: Expression(Integer) --E 359 +)clear all + + --S 360 of 510 t0071:= x*atanh(x)^2/(1-x^2)^2 --R --R ---R 2 ---R x atanh(x) ---R (245) ------------ ---R 4 2 ---R x - 2x + 1 +--R 2 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 360 @@ -6046,11 +6321,11 @@ t0071:= x*atanh(x)^2/(1-x^2)^2 r0071:= -1/4*(1-2*x*atanh(x)+atanh(x)^2+x^2*atanh(x)^2)/(-1+x^2) --R --R ---R 2 2 ---R (- x - 1)atanh(x) + 2x atanh(x) - 1 ---R (246) ------------------------------------- ---R 2 ---R 4x - 4 +--R 2 2 +--R (- x - 1)atanh(x) + 2x atanh(x) - 1 +--R (2) ------------------------------------- +--R 2 +--R 4x - 4 --R Type: Expression(Integer) --E 361 @@ -6058,12 +6333,12 @@ r0071:= -1/4*(1-2*x*atanh(x)+atanh(x)^2+x^2*atanh(x)^2)/(-1+x^2) a0071:= integrate(t0071,x) --R --R ---R 2 - x - 1 2 - x - 1 ---R (- x - 1)log(-------) + 4x log(-------) - 4 ---R x - 1 x - 1 ---R (247) --------------------------------------------- ---R 2 ---R 16x - 16 +--R 2 - x - 1 2 - x - 1 +--R (- x - 1)log(-------) + 4x log(-------) - 4 +--R x - 1 x - 1 +--R (3) --------------------------------------------- +--R 2 +--R 16x - 16 --R Type: Union(Expression(Integer),...) --E 362 @@ -6071,7 +6346,7 @@ a0071:= integrate(t0071,x) m0071:= a0071-r0071 --R --R ---R (248) +--R (4) --R 2 - x - 1 2 - x - 1 2 2 --R (- x - 1)log(-------) + 4x log(-------) + (4x + 4)atanh(x) - 8x atanh(x) --R x - 1 x - 1 @@ -6085,24 +6360,27 @@ m0071:= a0071-r0071 d0071:= D(m0071,x) --R --R ---R - x - 1 2 2 ---R x log(-------) - 4x atanh(x) ---R x - 1 ---R (249) ------------------------------ ---R 4 2 ---R 4x - 8x + 4 +--R - x - 1 2 2 +--R x log(-------) - 4x atanh(x) +--R x - 1 +--R (5) ------------------------------ +--R 4 2 +--R 4x - 8x + 4 --R Type: Expression(Integer) --E 364 +)clear all + + --S 365 of 510 t0072:= atanh(x)^2/(1-x^2)^2 --R --R ---R 2 ---R atanh(x) ---R (250) ------------ ---R 4 2 ---R x - 2x + 1 +--R 2 +--R atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 365 @@ -6111,11 +6389,11 @@ r0072:= 1/12*(-3*x+3*atanh(x)+3*x^2*atanh(x)-6*x*atanh(x)^2-_ 2*atanh(x)^3+2*x^2*atanh(x)^3)/(-1+x^2) --R --R ---R 2 3 2 2 ---R (2x - 2)atanh(x) - 6x atanh(x) + (3x + 3)atanh(x) - 3x ---R (251) ---------------------------------------------------------- ---R 2 ---R 12x - 12 +--R 2 3 2 2 +--R (2x - 2)atanh(x) - 6x atanh(x) + (3x + 3)atanh(x) - 3x +--R (2) ---------------------------------------------------------- +--R 2 +--R 12x - 12 --R Type: Expression(Integer) --E 366 @@ -6123,13 +6401,12 @@ r0072:= 1/12*(-3*x+3*atanh(x)+3*x^2*atanh(x)-6*x*atanh(x)^2-_ a0072:= integrate(t0072,x) --R --R ---R (252) ---R 2 - x - 1 3 - x - 1 2 2 - x - 1 ---R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) - 12x ---R x - 1 x - 1 x - 1 ---R ---------------------------------------------------------------------- ---R 2 ---R 48x - 48 +--R 2 - x - 1 3 - x - 1 2 2 - x - 1 +--R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) - 12x +--R x - 1 x - 1 x - 1 +--R (3) ---------------------------------------------------------------------- +--R 2 +--R 48x - 48 --R Type: Union(Expression(Integer),...) --E 367 @@ -6137,7 +6414,7 @@ a0072:= integrate(t0072,x) m0072:= a0072-r0072 --R --R ---R (253) +--R (4) --R 2 - x - 1 3 - x - 1 2 2 - x - 1 --R (x - 1)log(-------) - 6x log(-------) + (6x + 6)log(-------) --R x - 1 x - 1 x - 1 @@ -6154,24 +6431,27 @@ m0072:= a0072-r0072 d0072:= D(m0072,x) --R --R ---R - x - 1 2 2 ---R log(-------) - 4atanh(x) ---R x - 1 ---R (254) -------------------------- ---R 4 2 ---R 4x - 8x + 4 +--R - x - 1 2 2 +--R log(-------) - 4atanh(x) +--R x - 1 +--R (5) -------------------------- +--R 4 2 +--R 4x - 8x + 4 --R Type: Expression(Integer) --E 369 +)clear all + + --S 370 of 510 t0073:= atanh(x)^2/x/(1-x^2)^2 --R --R ---R 2 ---R atanh(x) ---R (255) ------------ ---R 5 3 ---R x - 2x + x +--R 2 +--R atanh(x) +--R (1) ------------ +--R 5 3 +--R x - 2x + x --R Type: Expression(Integer) --E 370 @@ -6200,11 +6480,11 @@ r0073:= -1/3*atanh(x)^3+1/8*cosh(2*atanh(x))+_ a0073:= integrate(t0073,x) --R --R ---R x 2 ---I ++ atanh(%P) ---I (256) | --------------- d%P ---R ++ 5 3 ---I %P - 2%P + %P +--R x 2 +--I ++ atanh(%T) +--I (2) | --------------- d%T +--R ++ 5 3 +--I %T - 2%T + %T --R Type: Union(Expression(Integer),...) --E 372 @@ -6216,15 +6496,18 @@ a0073:= integrate(t0073,x) --d0073:= D(m0073,x) --E 374 +)clear all + + --S 375 of 510 t0074:= atanh(x)^2/x^2/(1-x^2)^2 --R --R ---R 2 ---R atanh(x) ---R (257) ------------- ---R 6 4 2 ---R x - 2x + x +--R 2 +--R atanh(x) +--R (1) ------------- +--R 6 4 2 +--R x - 2x + x --R Type: Expression(Integer) --E 375 @@ -6253,11 +6536,11 @@ r0074:= -atanh(x)^2-atanh(x)^2/x+1/2*atanh(x)^3-_ a0074:= integrate(t0074,x) --R --R ---R x 2 ---I ++ atanh(%P) ---I (258) | ---------------- d%P ---R ++ 6 4 2 ---I %P - 2%P + %P +--R x 2 +--I ++ atanh(%T) +--I (2) | ---------------- d%T +--R ++ 6 4 2 +--I %T - 2%T + %T --R Type: Union(Expression(Integer),...) --E 377 @@ -6269,15 +6552,18 @@ a0074:= integrate(t0074,x) --d0074:= D(m0074,x) --E 379 +)clear all + + --S 380 of 510 t0075:= atanh(x)^2/x^3/(1-x^2)^2 --R --R ---R 2 ---R atanh(x) ---R (259) ------------- ---R 7 5 3 ---R x - 2x + x +--R 2 +--R atanh(x) +--R (1) ------------- +--R 7 5 3 +--R x - 2x + x --R Type: Expression(Integer) --E 380 @@ -6307,11 +6593,11 @@ r0075:= -atanh(x)/x-1/2*(1-x^2)*atanh(x)^2/x^2-2/3*atanh(x)^3+_ a0075:= integrate(t0075,x) --R --R ---R x 2 ---I ++ atanh(%P) ---I (260) | ---------------- d%P ---R ++ 7 5 3 ---I %P - 2%P + %P +--R x 2 +--I ++ atanh(%T) +--I (2) | ---------------- d%T +--R ++ 7 5 3 +--I %T - 2%T + %T --R Type: Union(Expression(Integer),...) --E 382 @@ -6323,15 +6609,18 @@ a0075:= integrate(t0075,x) --d0075:= D(m0075,x) --E 384 +)clear all + + --S 385 of 510 t0076:= x^3*atanh(x)^3/(1-x^2)^2 --R --R ---R 3 3 ---R x atanh(x) ---R (261) ------------ ---R 4 2 ---R x - 2x + 1 +--R 3 3 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 385 @@ -6362,11 +6651,11 @@ r0076:= 1/4*atanh(x)^4+3/8*atanh(x)*cosh(2*atanh(x))+_ a0076:= integrate(t0076,x) --R --R ---R x 3 3 ---I ++ %P atanh(%P) ---I (262) | -------------- d%P ---R ++ 4 2 ---I %P - 2%P + 1 +--R x 3 3 +--I ++ %T atanh(%T) +--I (2) | -------------- d%T +--R ++ 4 2 +--I %T - 2%T + 1 --R Type: Union(Expression(Integer),...) --E 387 @@ -6378,15 +6667,18 @@ a0076:= integrate(t0076,x) --d0076:= D(m0076,x) --E 389 +)clear all + + --S 390 of 510 t0077:= x^2*atanh(x)^3/(1-x^2)^2 --R --R ---R 2 3 ---R x atanh(x) ---R (263) ------------ ---R 4 2 ---R x - 2x + 1 +--R 2 3 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 390 @@ -6395,7 +6687,7 @@ r0077:= -1/8*(-3*x^2+6*x*atanh(x)-3*atanh(x)^2-3*x^2*atanh(x)^2+_ 4*x*atanh(x)^3-atanh(x)^4+atanh(x)^4*x^2)/(-1+x^2) --R --R ---R (264) +--R (2) --R 2 4 3 2 2 2 --R (- x + 1)atanh(x) - 4x atanh(x) + (3x + 3)atanh(x) - 6x atanh(x) + 3x --R --------------------------------------------------------------------------- @@ -6408,7 +6700,7 @@ r0077:= -1/8*(-3*x^2+6*x*atanh(x)-3*atanh(x)^2-3*x^2*atanh(x)^2+_ a0077:= integrate(t0077,x) --R --R ---R (265) +--R (3) --R 2 - x - 1 4 - x - 1 3 2 - x - 1 2 --R (- x + 1)log(-------) - 8x log(-------) + (12x + 12)log(-------) --R x - 1 x - 1 x - 1 @@ -6426,7 +6718,7 @@ a0077:= integrate(t0077,x) m0077:= a0077-r0077 --R --R ---R (266) +--R (4) --R 2 - x - 1 4 - x - 1 3 2 - x - 1 2 --R (- x + 1)log(-------) - 8x log(-------) + (12x + 12)log(-------) --R x - 1 x - 1 x - 1 @@ -6447,24 +6739,27 @@ m0077:= a0077-r0077 d0077:= D(m0077,x) --R --R ---R 2 - x - 1 3 2 3 ---R x log(-------) - 8x atanh(x) ---R x - 1 ---R (267) ------------------------------ ---R 4 2 ---R 8x - 16x + 8 +--R 2 - x - 1 3 2 3 +--R x log(-------) - 8x atanh(x) +--R x - 1 +--R (5) ------------------------------ +--R 4 2 +--R 8x - 16x + 8 --R Type: Expression(Integer) --E 394 +)clear all + + --S 395 of 510 t0078:= x*atanh(x)^3/(1-x^2)^2 --R --R ---R 3 ---R x atanh(x) ---R (268) ------------ ---R 4 2 ---R x - 2x + 1 +--R 3 +--R x atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 395 @@ -6473,11 +6768,11 @@ r0078:= -1/8*(-3*x+3*atanh(x)+3*x^2*atanh(x)-6*x*atanh(x)^2+2*atanh(x)^3+_ 2*x^2*atanh(x)^3)/(-1+x^2) --R --R ---R 2 3 2 2 ---R (- 2x - 2)atanh(x) + 6x atanh(x) + (- 3x - 3)atanh(x) + 3x ---R (269) -------------------------------------------------------------- ---R 2 ---R 8x - 8 +--R 2 3 2 2 +--R (- 2x - 2)atanh(x) + 6x atanh(x) + (- 3x - 3)atanh(x) + 3x +--R (2) -------------------------------------------------------------- +--R 2 +--R 8x - 8 --R Type: Expression(Integer) --E 396 @@ -6485,7 +6780,7 @@ r0078:= -1/8*(-3*x+3*atanh(x)+3*x^2*atanh(x)-6*x*atanh(x)^2+2*atanh(x)^3+_ a0078:= integrate(t0078,x) --R --R ---R (270) +--R (3) --R 2 - x - 1 3 - x - 1 2 2 - x - 1 --R (- x - 1)log(-------) + 6x log(-------) + (- 6x - 6)log(-------) + 12x --R x - 1 x - 1 x - 1 @@ -6499,7 +6794,7 @@ a0078:= integrate(t0078,x) m0078:= a0078-r0078 --R --R ---R (271) +--R (4) --R 2 - x - 1 3 - x - 1 2 2 - x - 1 --R (- x - 1)log(-------) + 6x log(-------) + (- 6x - 6)log(-------) --R x - 1 x - 1 x - 1 @@ -6516,24 +6811,27 @@ m0078:= a0078-r0078 d0078:= D(m0078,x) --R --R ---R - x - 1 3 3 ---R x log(-------) - 8x atanh(x) ---R x - 1 ---R (272) ------------------------------ ---R 4 2 ---R 8x - 16x + 8 +--R - x - 1 3 3 +--R x log(-------) - 8x atanh(x) +--R x - 1 +--R (5) ------------------------------ +--R 4 2 +--R 8x - 16x + 8 --R Type: Expression(Integer) --E 399 +)clear all + + --S 400 of 510 t0079:= atanh(x)^3/(1-x^2)^2 --R --R ---R 3 ---R atanh(x) ---R (273) ------------ ---R 4 2 ---R x - 2x + 1 +--R 3 +--R atanh(x) +--R (1) ------------ +--R 4 2 +--R x - 2x + 1 --R Type: Expression(Integer) --E 400 @@ -6542,7 +6840,7 @@ r0079:= 1/8*(3-6*x*atanh(x)+3*atanh(x)^2+3*x^2*atanh(x)^2-_ 4*x*atanh(x)^3-atanh(x)^4+atanh(x)^4*x^2)/(-1+x^2) --R --R ---R (274) +--R (2) --R 2 4 3 2 2 --R (x - 1)atanh(x) - 4x atanh(x) + (3x + 3)atanh(x) - 6x atanh(x) + 3 --R ----------------------------------------------------------------------- @@ -6555,7 +6853,7 @@ r0079:= 1/8*(3-6*x*atanh(x)+3*atanh(x)^2+3*x^2*atanh(x)^2-_ a0079:= integrate(t0079,x) --R --R ---R (275) +--R (3) --R 2 - x - 1 4 - x - 1 3 2 - x - 1 2 --R (x - 1)log(-------) - 8x log(-------) + (12x + 12)log(-------) --R x - 1 x - 1 x - 1 @@ -6573,7 +6871,7 @@ a0079:= integrate(t0079,x) m0079:= a0079-r0079 --R --R ---R (276) +--R (4) --R 2 - x - 1 4 - x - 1 3 2 - x - 1 2 --R (x - 1)log(-------) - 8x log(-------) + (12x + 12)log(-------) --R x - 1 x - 1 x - 1 @@ -6594,24 +6892,27 @@ m0079:= a0079-r0079 d0079:= D(m0079,x) --R --R ---R - x - 1 3 3 ---R log(-------) - 8atanh(x) ---R x - 1 ---R (277) -------------------------- ---R 4 2 ---R 8x - 16x + 8 +--R - x - 1 3 3 +--R log(-------) - 8atanh(x) +--R x - 1 +--R (5) -------------------------- +--R 4 2 +--R 8x - 16x + 8 --R Type: Expression(Integer) --E 404 +)clear all + + --S 405 of 510 t0080:= atanh(x)^3/x/(1-x^2)^2 --R --R ---R 3 ---R atanh(x) ---R (278) ------------ ---R 5 3 ---R x - 2x + x +--R 3 +--R atanh(x) +--R (1) ------------ +--R 5 3 +--R x - 2x + x --R Type: Expression(Integer) --E 405 @@ -6641,11 +6942,11 @@ r0080:= -1/4*atanh(x)^4+3/8*atanh(x)*cosh(2*atanh(x))+_ a0080:= integrate(t0080,x) --R --R ---R x 3 ---I ++ atanh(%P) ---I (279) | --------------- d%P ---R ++ 5 3 ---I %P - 2%P + %P +--R x 3 +--I ++ atanh(%T) +--I (2) | --------------- d%T +--R ++ 5 3 +--I %T - 2%T + %T --R Type: Union(Expression(Integer),...) --E 407 @@ -6657,15 +6958,18 @@ a0080:= integrate(t0080,x) --d0080:= D(m0080,x) --E 409 +)clear all + + --S 410 of 510 t0081:= atanh(x)^3/x^2/(1-x^2)^2 --R --R ---R 3 ---R atanh(x) ---R (280) ------------- ---R 6 4 2 ---R x - 2x + x +--R 3 +--R atanh(x) +--R (1) ------------- +--R 6 4 2 +--R x - 2x + x --R Type: Expression(Integer) --E 410 @@ -6695,11 +6999,11 @@ r0081:= -atanh(x)^3-atanh(x)^3/x+3/8*atanh(x)^4-_ a0081:= integrate(t0081,x) --R --R ---R x 3 ---I ++ atanh(%P) ---I (281) | ---------------- d%P ---R ++ 6 4 2 ---I %P - 2%P + %P +--R x 3 +--I ++ atanh(%T) +--I (2) | ---------------- d%T +--R ++ 6 4 2 +--I %T - 2%T + %T --R Type: Union(Expression(Integer),...) --E 412 @@ -6711,15 +7015,18 @@ a0081:= integrate(t0081,x) --d0081:= D(m0081,x) --E 414 +)clear all + + --S 415 of 510 t0082:= atanh(x)^3/x^3/(1-x^2)^2 --R --R ---R 3 ---R atanh(x) ---R (282) ------------- ---R 7 5 3 ---R x - 2x + x +--R 3 +--R atanh(x) +--R (1) ------------- +--R 7 5 3 +--R x - 2x + x --R Type: Expression(Integer) --E 415 @@ -6752,11 +7059,11 @@ r0082:= -3/2*atanh(x)^2-3/2*atanh(x)^2/x-1/2*(1-x^2)*atanh(x)^3/x^2-_ a0082:= integrate(t0082,x) --R --R ---R x 3 ---I ++ atanh(%P) ---I (283) | ---------------- d%P ---R ++ 7 5 3 ---I %P - 2%P + %P +--R x 3 +--I ++ atanh(%T) +--I (2) | ---------------- d%T +--R ++ 7 5 3 +--I %T - 2%T + %T --R Type: Union(Expression(Integer),...) --E 417 @@ -6768,15 +7075,18 @@ a0082:= integrate(t0082,x) --d0082:= D(m0082,x) --E 419 +)clear all + + --S 420 of 510 t0083:= x^2/(1-x^2)^2/atanh(x) --R --R ---R 2 ---R x ---R (284) ---------------------- ---R 4 2 ---R (x - 2x + 1)atanh(x) +--R 2 +--R x +--R (1) ---------------------- +--R 4 2 +--R (x - 2x + 1)atanh(x) --R Type: Expression(Integer) --E 420 @@ -6801,11 +7111,11 @@ r0083:= 1/2*Chi(2*atanh(x))-1/2*log(atanh(x)) a0083:= integrate(t0083,x) --R --R ---R x 2 ---I ++ %P ---I (285) | ------------------------- d%P ---R ++ 4 2 ---I (%P - 2%P + 1)atanh(%P) +--R x 2 +--I ++ %T +--I (2) | ------------------------- d%T +--R ++ 4 2 +--I (%T - 2%T + 1)atanh(%T) --R Type: Union(Expression(Integer),...) --E 422 @@ -6817,14 +7127,17 @@ a0083:= integrate(t0083,x) --d0083:= D(m0083,x) --E 424 +)clear all + + --S 425 of 510 t0084:= x/(1-x^2)^2/atanh(x) --R --R ---R x ---R (286) ---------------------- ---R 4 2 ---R (x - 2x + 1)atanh(x) +--R x +--R (1) ---------------------- +--R 4 2 +--R (x - 2x + 1)atanh(x) --R Type: Expression(Integer) --E 425 @@ -6849,11 +7162,11 @@ r0084:= 1/2*Shi(2*atanh(x)) a0084:= integrate(t0084,x) --R --R ---R x ---I ++ %P ---I (287) | ------------------------- d%P ---R ++ 4 2 ---I (%P - 2%P + 1)atanh(%P) +--R x +--I ++ %T +--I (2) | ------------------------- d%T +--R ++ 4 2 +--I (%T - 2%T + 1)atanh(%T) --R Type: Union(Expression(Integer),...) --E 427 @@ -6865,14 +7178,17 @@ a0084:= integrate(t0084,x) --d0084:= D(m0084,x) --E 429 +)clear all + + --S 430 of 510 t0085:= 1/(1-x^2)^2/atanh(x) --R --R ---R 1 ---R (288) ---------------------- ---R 4 2 ---R (x - 2x + 1)atanh(x) +--R 1 +--R (1) ---------------------- +--R 4 2 +--R (x - 2x + 1)atanh(x) --R Type: Expression(Integer) --E 430 @@ -6897,11 +7213,11 @@ r0085:= 1/2*Chi(2*atanh(x))+1/2*log(atanh(x)) a0085:= integrate(t0085,x) --R --R ---R x ---R ++ 1 ---I (289) | ------------------------- d%P ---R ++ 4 2 ---I (%P - 2%P + 1)atanh(%P) +--R x +--R ++ 1 +--I (2) | ------------------------- d%T +--R ++ 4 2 +--I (%T - 2%T + 1)atanh(%T) --R Type: Union(Expression(Integer),...) --E 432 @@ -6913,15 +7229,18 @@ a0085:= integrate(t0085,x) --d0085:= D(m0085,x) --E 434 +)clear all + + --S 435 of 510 t0086:= x^2/(1-x^2)^2/atanh(x)^2 --R --R ---R 2 ---R x ---R (290) ----------------------- ---R 4 2 2 ---R (x - 2x + 1)atanh(x) +--R 2 +--R x +--R (1) ----------------------- +--R 4 2 2 +--R (x - 2x + 1)atanh(x) --R Type: Expression(Integer) --E 435 @@ -6946,11 +7265,11 @@ r0086:= -x^2/(1-x^2)/atanh(x)+Shi(2*atanh(x)) a0086:= integrate(t0086,x) --R --R ---R x 2 ---I ++ %P ---I (291) | -------------------------- d%P ---R ++ 4 2 2 ---I (%P - 2%P + 1)atanh(%P) +--R x 2 +--I ++ %T +--I (2) | -------------------------- d%T +--R ++ 4 2 2 +--I (%T - 2%T + 1)atanh(%T) --R Type: Union(Expression(Integer),...) --E 437 @@ -6962,14 +7281,17 @@ a0086:= integrate(t0086,x) --d0086:= D(m0086,x) --E 439 +)clear all + + --S 440 of 510 t0087:= x/(1-x^2)^2/atanh(x)^2 --R --R ---R x ---R (292) ----------------------- ---R 4 2 2 ---R (x - 2x + 1)atanh(x) +--R x +--R (1) ----------------------- +--R 4 2 2 +--R (x - 2x + 1)atanh(x) --R Type: Expression(Integer) --E 440 @@ -6994,11 +7316,11 @@ r0087:= Chi(2*atanh(x))-1/2*sinh(2*atanh(x))/atanh(x) a0087:= integrate(t0087,x) --R --R ---R x ---I ++ %P ---I (293) | -------------------------- d%P ---R ++ 4 2 2 ---I (%P - 2%P + 1)atanh(%P) +--R x +--I ++ %T +--I (2) | -------------------------- d%T +--R ++ 4 2 2 +--I (%T - 2%T + 1)atanh(%T) --R Type: Union(Expression(Integer),...) --E 442 @@ -7010,14 +7332,17 @@ a0087:= integrate(t0087,x) --d0087:= D(m0087,x) --E 444 +)clear all + + --S 445 of 510 t0088:= 1/(1-x^2)^2/atanh(x)^2 --R --R ---R 1 ---R (294) ----------------------- ---R 4 2 2 ---R (x - 2x + 1)atanh(x) +--R 1 +--R (1) ----------------------- +--R 4 2 2 +--R (x - 2x + 1)atanh(x) --R Type: Expression(Integer) --E 445 @@ -7042,11 +7367,11 @@ r0088:= -1/(1-x^2)/atanh(x)+Shi(2*atanh(x)) a0088:= integrate(t0088,x) --R --R ---R x ---R ++ 1 ---I (295) | -------------------------- d%P ---R ++ 4 2 2 ---I (%P - 2%P + 1)atanh(%P) +--R x +--R ++ 1 +--I (2) | -------------------------- d%T +--R ++ 4 2 2 +--I (%T - 2%T + 1)atanh(%T) --R Type: Union(Expression(Integer),...) --E 447 @@ -7058,15 +7383,18 @@ a0088:= integrate(t0088,x) --d0088:= D(m0088,x) --E 449 +)clear all + + --S 450 of 510 t0089:= x^2/(1-x^2)^2/atanh(x)^3 --R --R ---R 2 ---R x ---R (296) ----------------------- ---R 4 2 3 ---R (x - 2x + 1)atanh(x) +--R 2 +--R x +--R (1) ----------------------- +--R 4 2 3 +--R (x - 2x + 1)atanh(x) --R Type: Expression(Integer) --E 450 @@ -7091,11 +7419,11 @@ r0089:= -1/2*x^2/(1-x^2)/atanh(x)^2-x/(1-x^2)/atanh(x)+Chi(2*atanh(x)) a0089:= integrate(t0089,x) --R --R ---R x 2 ---I ++ %P ---I (297) | -------------------------- d%P ---R ++ 4 2 3 ---I (%P - 2%P + 1)atanh(%P) +--R x 2 +--I ++ %T +--I (2) | -------------------------- d%T +--R ++ 4 2 3 +--I (%T - 2%T + 1)atanh(%T) --R Type: Union(Expression(Integer),...) --E 452 @@ -7107,14 +7435,17 @@ a0089:= integrate(t0089,x) --d0089:= D(m0089,x) --E 454 +)clear all + + --S 455 of 510 t0090:= x/(1-x^2)^2/atanh(x)^3 --R --R ---R x ---R (298) ----------------------- ---R 4 2 3 ---R (x - 2x + 1)atanh(x) +--R x +--R (1) ----------------------- +--R 4 2 3 +--R (x - 2x + 1)atanh(x) --R Type: Expression(Integer) --E 455 @@ -7140,11 +7471,11 @@ r0090:= -1/2*cosh(2*atanh(x))/atanh(x)-_ a0090:= integrate(t0090,x) --R --R ---R x ---I ++ %P ---I (299) | -------------------------- d%P ---R ++ 4 2 3 ---I (%P - 2%P + 1)atanh(%P) +--R x +--I ++ %T +--I (2) | -------------------------- d%T +--R ++ 4 2 3 +--I (%T - 2%T + 1)atanh(%T) --R Type: Union(Expression(Integer),...) --E 457 @@ -7156,14 +7487,17 @@ a0090:= integrate(t0090,x) --d0090:= D(m0090,x) --E 459 +)clear all + + --S 460 of 510 t0091:= 1/(1-x^2)^2/atanh(x)^3 --R --R ---R 1 ---R (300) ----------------------- ---R 4 2 3 ---R (x - 2x + 1)atanh(x) +--R 1 +--R (1) ----------------------- +--R 4 2 3 +--R (x - 2x + 1)atanh(x) --R Type: Expression(Integer) --E 460 @@ -7188,11 +7522,11 @@ r0091:= -1/2/(1-x^2)/atanh(x)^2-x/(1-x^2)/atanh(x)+Chi(2*atanh(x)) a0091:= integrate(t0091,x) --R --R ---R x ---R ++ 1 ---I (301) | -------------------------- d%P ---R ++ 4 2 3 ---I (%P - 2%P + 1)atanh(%P) +--R x +--R ++ 1 +--I (2) | -------------------------- d%T +--R ++ 4 2 3 +--I (%T - 2%T + 1)atanh(%T) --R Type: Union(Expression(Integer),...) --E 462 @@ -7204,15 +7538,18 @@ a0091:= integrate(t0091,x) --d0091:= D(m0091,x) --E 464 +)clear all + + --S 465 of 510 t0092:= atanh(x)/(a+b*x^2)^(3/2) --R --R ---R atanh(x) ---R (302) --------------------- ---R +--------+ ---R 2 | 2 ---R (b x + a)\|b x + a +--R atanh(x) +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a --R Type: Expression(Integer) --E 465 @@ -7221,16 +7558,16 @@ r0092:= x*atanh(x)/a/(a+b*x^2)^(1/2)-_ atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a/(a+b)^(1/2) --R --R ---R +--------+ ---R +--------+ | 2 ---R | 2 \|b x + a +-----+ ---R - \|b x + a atanh(-----------) + x atanh(x)\|b + a ---R +-----+ ---R \|b + a ---R (303) ---------------------------------------------------- ---R +--------+ ---R +-----+ | 2 ---R a\|b + a \|b x + a +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +-----+ +--R - \|b x + a atanh(-----------) + x atanh(x)\|b + a +--R +-----+ +--R \|b + a +--R (2) ---------------------------------------------------- +--R +--------+ +--R +-----+ | 2 +--R a\|b + a \|b x + a --R Type: Expression(Integer) --E 466 @@ -7238,7 +7575,7 @@ r0092:= x*atanh(x)/a/(a+b*x^2)^(1/2)-_ a0092:= integrate(t0092,x) --R --R ---R (304) +--R (3) --R [ --R +--------+ --R +-+ | 2 2 @@ -7308,7 +7645,7 @@ a0092:= integrate(t0092,x) m0092a:= a0092.1-r0092 --R --R ---R (305) +--R (4) --R +--------+ --R 2 | 2 2 +-+ --R ((b x + a)\|b x + a + (- b x - a)\|a ) @@ -7366,13 +7703,13 @@ m0092a:= a0092.1-r0092 d0092a:= D(m0092a,x) --R --R ---R - x - 1 ---R log(-------) - 2atanh(x) ---R x - 1 ---R (306) ------------------------ ---R +--------+ ---R 2 | 2 ---R (2b x + 2a)\|b x + a +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (5) ------------------------ +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a --R Type: Expression(Integer) --E 469 @@ -7380,7 +7717,7 @@ d0092a:= D(m0092a,x) m0092b:= a0092.2-r0092 --R --R ---R (307) +--R (6) --R +--------+ --R 2 +-------+ | 2 2 +-------+ +-+ --R ((2b x + 2a)\|- b - a \|b x + a + (- 2b x - 2a)\|- b - a \|a ) @@ -7425,25 +7762,28 @@ m0092b:= a0092.2-r0092 d0092b:= D(m0092b,x) --R --R ---R - x - 1 ---R log(-------) - 2atanh(x) ---R x - 1 ---R (308) ------------------------ ---R +--------+ ---R 2 | 2 ---R (2b x + 2a)\|b x + a +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (7) ------------------------ +--R +--------+ +--R 2 | 2 +--R (2b x + 2a)\|b x + a --R Type: Expression(Integer) --E 471 +)clear all + + --S 472 of 510 t0093:= atanh(x)/(a+b*x^2)^(5/2) --R --R ---R atanh(x) ---R (309) -------------------------------- ---R +--------+ ---R 2 4 2 2 | 2 ---R (b x + 2a b x + a )\|b x + a +--R atanh(x) +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a --R Type: Expression(Integer) --E 472 @@ -7453,7 +7793,7 @@ r0093:= 1/3/a/(a+b)/(a+b*x^2)^(1/2)+_ 1/3*(3*a+2*b)*atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a^2/(a+b)^(3/2) --R --R ---R (310) +--R (2) --R +--------+ --R +--------+ | 2 --R 2 2 2 | 2 \|b x + a @@ -7474,7 +7814,7 @@ r0093:= 1/3/a/(a+b)/(a+b*x^2)^(1/2)+_ a0093:= integrate(t0093,x) --R --R ---R (311) +--R (3) --R [ --R 4 3 6 3 2 2 4 2 2 3 2 --R (8b + 12a b )x + (32a b + 48a b )x + (40a b + 60a b)x @@ -7654,7 +7994,7 @@ a0093:= integrate(t0093,x) m0093a:= a0093.1-r0093 --R --R ---R (312) +--R (4) --R 4 3 6 3 2 2 4 2 2 3 2 --R (2b + 3a b )x + (18a b + 27a b )x + (32a b + 48a b)x --R + @@ -7793,13 +8133,13 @@ m0093a:= a0093.1-r0093 d0093a:= D(m0093a,x) --R --R ---R - x - 1 ---R log(-------) - 2atanh(x) ---R x - 1 ---R (313) ---------------------------------- ---R +--------+ ---R 2 4 2 2 | 2 ---R (2b x + 4a b x + 2a )\|b x + a +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (5) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a --R Type: Expression(Integer) --E 476 @@ -7807,7 +8147,7 @@ d0093a:= D(m0093a,x) m0093b:= a0093.2-r0093 --R --R ---R (314) +--R (6) --R 4 3 6 3 2 2 4 2 2 3 2 --R (4b + 6a b )x + (36a b + 54a b )x + (64a b + 96a b)x --R + @@ -7926,25 +8266,28 @@ m0093b:= a0093.2-r0093 d0093b:= D(m0093b,x) --R --R ---R - x - 1 ---R log(-------) - 2atanh(x) ---R x - 1 ---R (315) ---------------------------------- ---R +--------+ ---R 2 4 2 2 | 2 ---R (2b x + 4a b x + 2a )\|b x + a +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (7) ---------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x + 4a b x + 2a )\|b x + a --R Type: Expression(Integer) --E 478 +)clear all + + --S 479 of 510 t0094:= atanh(x)/(a+b*x^2)^(7/2) --R --R ---R atanh(x) ---R (316) ------------------------------------------ ---R +--------+ ---R 3 6 2 4 2 2 3 | 2 ---R (b x + 3a b x + 3a b x + a )\|b x + a +--R atanh(x) +--R (1) ------------------------------------------ +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (b x + 3a b x + 3a b x + a )\|b x + a --R Type: Expression(Integer) --E 479 @@ -7956,7 +8299,7 @@ r0094:= 1/15/a/(a+b)/(a+b*x^2)^(3/2)+_ atanh((a+b*x^2)^(1/2)/(a+b)^(1/2))/a^3/(a+b)^(5/2) --R --R ---R (317) +--R (2) --R 4 3 2 2 4 3 2 2 3 2 2 2 --R (- 8b - 20a b - 15a b )x + (- 16a b - 40a b - 30a b)x - 8a b --R + @@ -8000,7 +8343,7 @@ r0094:= 1/15/a/(a+b)/(a+b*x^2)^(3/2)+_ a0094:= integrate(t0094,x) --R --R ---R (318) +--R (3) --R [ --R 8 7 2 6 12 --R (64b + 160a b + 120a b )x @@ -8381,7 +8724,7 @@ a0094:= integrate(t0094,x) m0094a:= a0094.1-r0094 --R --R ---R (319) +--R (4) --R 8 7 2 6 12 7 2 6 3 5 10 --R (8b + 20a b + 15a b )x + (272a b + 680a b + 510a b )x --R + @@ -8654,13 +8997,13 @@ m0094a:= a0094.1-r0094 d0094a:= D(m0094a,x) --R --R ---R - x - 1 ---R log(-------) - 2atanh(x) ---R x - 1 ---R (320) -------------------------------------------- ---R +--------+ ---R 3 6 2 4 2 2 3 | 2 ---R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (5) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a --R Type: Expression(Integer) --E 483 @@ -8668,7 +9011,7 @@ d0094a:= D(m0094a,x) m0094b:= a0094.2-r0094 --R --R ---R (321) +--R (6) --R 8 7 2 6 12 7 2 6 3 5 10 --R (16b + 40a b + 30a b )x + (544a b + 1360a b + 1020a b )x --R + @@ -8924,23 +9267,26 @@ m0094b:= a0094.2-r0094 d0094b:= D(m0094b,x) --R --R ---R - x - 1 ---R log(-------) - 2atanh(x) ---R x - 1 ---R (322) -------------------------------------------- ---R +--------+ ---R 3 6 2 4 2 2 3 | 2 ---R (2b x + 6a b x + 6a b x + 2a )\|b x + a +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (7) -------------------------------------------- +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x + 6a b x + 6a b x + 2a )\|b x + a --R Type: Expression(Integer) --E 485 +)clear all + + --S 486 of 510 t0095:= atanh(x)*(a-a*x^2)^(1/2) --R --R ---R +----------+ ---R | 2 ---R (323) atanh(x)\|- a x + a +--R +----------+ +--R | 2 +--R (1) atanh(x)\|- a x + a --R Type: Expression(Integer) --E 486 @@ -8968,10 +9314,10 @@ r0095:= 1/2/(1-x^2)^(1/2)*(a*(1-x^2))^(1/2)*((1-x^2)^(1/2)+_ a0095:= integrate(t0095,x) --R --R ---R x +------------+ ---R ++ | 2 ---I (324) | atanh(%P)\|(- %P + 1)a d%P ---R ++ +--R x +------------+ +--R ++ | 2 +--I (2) | atanh(%T)\|(- %T + 1)a d%T +--R ++ --R Type: Union(Expression(Integer),...) --E 488 @@ -8983,15 +9329,18 @@ a0095:= integrate(t0095,x) --d0095:= D(m0095,x) --E 490 +)clear all + + --S 491 of 510 t0096:= atanh(x)/(a-a*x^2)^(1/2) --R --R ---R atanh(x) ---R (325) ------------- ---R +----------+ ---R | 2 ---R \|- a x + a +--R atanh(x) +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|- a x + a --R Type: Expression(Integer) --E 491 @@ -9019,12 +9368,12 @@ r0096:= (1-x^2)^(1/2)*(2*atan(exp(1)^atanh(x))*atanh(x)-_ a0096:= integrate(t0096,x) --R --R ---R x ---I ++ atanh(%P) ---I (326) | --------------- d%P ---R ++ +------------+ ---R | 2 ---I \|(- %P + 1)a +--R x +--I ++ atanh(%T) +--I (2) | --------------- d%T +--R ++ +------------+ +--R | 2 +--I \|(- %T + 1)a --R Type: Union(Expression(Integer),...) --E 493 @@ -9036,15 +9385,18 @@ a0096:= integrate(t0096,x) --d0096:= D(m0096,x) --E 495 +)clear all + + --S 496 of 510 t0097:= atanh(x)/(a-a*x^2)^(3/2) --R --R ---R atanh(x) ---R (327) - ----------------------- ---R +----------+ ---R 2 | 2 ---R (a x - a)\|- a x + a +--R atanh(x) +--R (1) - ----------------------- +--R +----------+ +--R 2 | 2 +--R (a x - a)\|- a x + a --R Type: Expression(Integer) --E 496 @@ -9052,11 +9404,11 @@ t0097:= atanh(x)/(a-a*x^2)^(3/2) r0097:= (x*atanh(x)-1)/(-a*(-1+x^2))^(1/2)/a --R --R ---R x atanh(x) - 1 ---R (328) -------------- ---R +----------+ ---R | 2 ---R a\|- a x + a +--R x atanh(x) - 1 +--R (2) -------------- +--R +----------+ +--R | 2 +--R a\|- a x + a --R Type: Expression(Integer) --E 497 @@ -9064,14 +9416,14 @@ r0097:= (x*atanh(x)-1)/(-a*(-1+x^2))^(1/2)/a a0097:= integrate(t0097,x) --R --R ---R +----------+ ---R - x - 1 2 +-+ - x - 1 | 2 ---R (x log(-------) - 2x )\|a - x log(-------)\|- a x + a ---R x - 1 x - 1 ---R (329) -------------------------------------------------------- ---R +----------+ ---R | 2 +-+ 2 2 2 ---R 2a\|- a x + a \|a + 2a x - 2a +--R +----------+ +--R - x - 1 2 +-+ - x - 1 | 2 +--R (x log(-------) - 2x )\|a - x log(-------)\|- a x + a +--R x - 1 x - 1 +--R (3) -------------------------------------------------------- +--R +----------+ +--R | 2 +-+ 2 2 2 +--R 2a\|- a x + a \|a + 2a x - 2a --R Type: Union(Expression(Integer),...) --E 498 @@ -9079,7 +9431,7 @@ a0097:= integrate(t0097,x) m0097:= a0097-r0097 --R --R ---R (330) +--R (4) --R +----------+ --R - x - 1 2 | 2 +-+ --R (- x log(-------) + 2x atanh(x) + 2x - 2)\|- a x + a \|a @@ -9099,25 +9451,28 @@ m0097:= a0097-r0097 d0097:= D(m0097,x) --R --R ---R - x - 1 ---R - log(-------) + 2atanh(x) ---R x - 1 ---R (331) -------------------------- ---R +----------+ ---R 2 | 2 ---R (2a x - 2a)\|- a x + a +--R - x - 1 +--R - log(-------) + 2atanh(x) +--R x - 1 +--R (5) -------------------------- +--R +----------+ +--R 2 | 2 +--R (2a x - 2a)\|- a x + a --R Type: Expression(Integer) --E 500 +)clear all + + --S 501 of 510 t0098:= atanh(x)/(a-a*x^2)^(5/2) --R --R ---R atanh(x) ---R (332) -------------------------------- ---R +----------+ ---R 2 4 2 2 2 | 2 ---R (a x - 2a x + a )\|- a x + a +--R atanh(x) +--R (1) -------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (a x - 2a x + a )\|- a x + a --R Type: Expression(Integer) --E 501 @@ -9126,12 +9481,12 @@ r0098:= 1/9*(7-6*x^2-9*x*atanh(x)+_ 6*atanh(x)*x^3)/(-1+x^2)/(-a*(-1+x^2))^(1/2)/a^2 --R --R ---R 3 2 ---R (6x - 9x)atanh(x) - 6x + 7 ---R (333) ---------------------------- ---R +----------+ ---R 2 2 2 | 2 ---R (9a x - 9a )\|- a x + a +--R 3 2 +--R (6x - 9x)atanh(x) - 6x + 7 +--R (2) ---------------------------- +--R +----------+ +--R 2 2 2 | 2 +--R (9a x - 9a )\|- a x + a --R Type: Expression(Integer) --E 502 @@ -9139,7 +9494,7 @@ r0098:= 1/9*(7-6*x^2-9*x*atanh(x)+_ a0098:= integrate(t0098,x) --R --R ---R (334) +--R (3) --R 5 3 - x - 1 6 4 2 +-+ --R ((18x - 51x + 36x)log(-------) - 14x + 48x - 36x )\|a --R x - 1 @@ -9162,7 +9517,7 @@ a0098:= integrate(t0098,x) m0098:= a0098-r0098 --R --R ---R (335) +--R (4) --R 5 3 - x - 1 5 3 --R (- 18x + 51x - 36x)log(-------) + (36x - 102x + 72x)atanh(x) --R x - 1 @@ -9196,25 +9551,28 @@ m0098:= a0098-r0098 d0098:= D(m0098,x) --R --R ---R - x - 1 ---R log(-------) - 2atanh(x) ---R x - 1 ---R (336) ---------------------------------- ---R +----------+ ---R 2 4 2 2 2 | 2 ---R (2a x - 4a x + 2a )\|- a x + a +--R - x - 1 +--R log(-------) - 2atanh(x) +--R x - 1 +--R (5) ---------------------------------- +--R +----------+ +--R 2 4 2 2 2 | 2 +--R (2a x - 4a x + 2a )\|- a x + a --R Type: Expression(Integer) --E 505 +)clear all + + --S 506 of 510 t0099:= atanh(x)/(a-a*x^2)^(7/2) --R --R ---R atanh(x) ---R (337) - ---------------------------------------- ---R +----------+ ---R 3 6 3 4 3 2 3 | 2 ---R (a x - 3a x + 3a x - a )\|- a x + a +--R atanh(x) +--R (1) - ---------------------------------------- +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (a x - 3a x + 3a x - a )\|- a x + a --R Type: Expression(Integer) --E 506 @@ -9223,12 +9581,12 @@ r0099:= 1/225*(-149-120*x^4+260*x^2+225*x*atanh(x)+120*x^5*atanh(x)-_ 300*atanh(x)*x^3)/(-1+x^2)^2/(-a*(-1+x^2))^(1/2)/a^3 --R --R ---R 5 3 4 2 ---R (120x - 300x + 225x)atanh(x) - 120x + 260x - 149 ---R (338) ---------------------------------------------------- ---R +----------+ ---R 3 4 3 2 3 | 2 ---R (225a x - 450a x + 225a )\|- a x + a +--R 5 3 4 2 +--R (120x - 300x + 225x)atanh(x) - 120x + 260x - 149 +--R (2) ---------------------------------------------------- +--R +----------+ +--R 3 4 3 2 3 | 2 +--R (225a x - 450a x + 225a )\|- a x + a --R Type: Expression(Integer) --E 507 @@ -9236,7 +9594,7 @@ r0099:= 1/225*(-149-120*x^4+260*x^2+225*x*atanh(x)+120*x^5*atanh(x)-_ a0099:= integrate(t0099,x) --R --R ---R (339) +--R (3) --R 9 7 5 3 - x - 1 10 --R (600x - 3900x + 9045x - 9300x + 3600x)log(-------) - 298x --R x - 1 @@ -9271,7 +9629,7 @@ a0099:= integrate(t0099,x) m0099:= a0099-r0099 --R --R ---R (340) +--R (4) --R 9 7 5 3 - x - 1 --R (- 600x + 3900x - 9045x + 9300x - 3600x)log(-------) --R x - 1 @@ -9317,17 +9675,18 @@ m0099:= a0099-r0099 d0099:= D(m0099,x) --R --R ---R - x - 1 ---R - log(-------) + 2atanh(x) ---R x - 1 ---R (341) ------------------------------------------ ---R +----------+ ---R 3 6 3 4 3 2 3 | 2 ---R (2a x - 6a x + 6a x - 2a )\|- a x + a +--R - x - 1 +--R - log(-------) + 2atanh(x) +--R x - 1 +--R (5) ------------------------------------------ +--R +----------+ +--R 3 6 3 4 3 2 3 | 2 +--R (2a x - 6a x + 6a x - 2a )\|- a x + a --R Type: Expression(Integer) --E 510 )spool + \end{chunk} \eject \begin{thebibliography}{99} diff --git a/src/input/richlog300-391.input.pamphlet b/src/input/richlog300-391.input.pamphlet index c30a8bb..3b4aeb4 100644 --- a/src/input/richlog300-391.input.pamphlet +++ b/src/input/richlog300-391.input.pamphlet @@ -14,6 +14,7 @@ )set break resume )sys rm -f richlog300-391.output )spool richlog300-391.output +)set message test on )set message auto off )clear all @@ -39,6 +40,7 @@ r0300:= 2/3*EllipticF(1/2*a+1/2*b*log(c*x^n),2)/b/n+_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Integer) @@ -69,6 +71,8 @@ a0300:= integrate(t0300,x) --d0300:= D(m0300,x) --E 5 +)clear all + --S 6 of 460 t0301:= sec(a+b*log(c*x^n))^(1/2)/x --R @@ -76,7 +80,7 @@ t0301:= sec(a+b*log(c*x^n))^(1/2)/x --R +--------------------+ --R | n --R \|sec(b log(c x ) + a) ---R (3) ----------------------- +--R (1) ----------------------- --R x --R Type: Expression(Integer) --E 6 @@ -91,6 +95,7 @@ r0301:= 2*cos(a+b*log(c*x^n))^(1/2)*EllipticF(1/2*a+1/2*b*log(c*x^n),2)*_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Integer) @@ -107,7 +112,7 @@ a0301:= integrate(t0301,x) --R +---------------------+ --R x | n --R ++ \|sec(b log(c %R ) + a) ---R (4) | ------------------------ d%R +--R (2) | ------------------------ d%R --R ++ %R --R Type: Union(Expression(Integer),...) --E 8 @@ -120,6 +125,8 @@ a0301:= integrate(t0301,x) --d0301:= D(m0301,x) --E 10 +)clear all + --S 11 of 460 t0302:= sec(a+b*log(c*x^n))^(3/2)/x --R @@ -127,7 +134,7 @@ t0302:= sec(a+b*log(c*x^n))^(3/2)/x --R +--------------------+ --R n | n --R sec(b log(c x ) + a)\|sec(b log(c x ) + a) ---R (5) ------------------------------------------- +--R (1) ------------------------------------------- --R x --R Type: Expression(Integer) --E 11 @@ -143,6 +150,7 @@ r0302:= -2*cos(a+b*log(c*x^n))^(1/2)*EllipticE(1/2*a+1/2*b*log(c*x^n),2)*_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Integer) @@ -159,7 +167,7 @@ a0302:= integrate(t0302,x) --R +---------------------+ --R x n | n --R ++ sec(b log(c %R ) + a)\|sec(b log(c %R ) + a) ---R (6) | --------------------------------------------- d%R +--R (2) | --------------------------------------------- d%R --R ++ %R --R Type: Union(Expression(Integer),...) --E 13 @@ -172,6 +180,8 @@ a0302:= integrate(t0302,x) --d0302:= D(m0302,x) --E 15 +)clear all + --S 16 of 460 t0303:= sec(a+b*log(c*x^n))^(5/2)/x --R @@ -179,7 +189,7 @@ t0303:= sec(a+b*log(c*x^n))^(5/2)/x --R +--------------------+ --R n 2 | n --R sec(b log(c x ) + a) \|sec(b log(c x ) + a) ---R (7) -------------------------------------------- +--R (1) -------------------------------------------- --R x --R Type: Expression(Integer) --E 16 @@ -195,6 +205,7 @@ r0303:= 2/3*cos(a+b*log(c*x^n))^(1/2)*EllipticF(1/2*a+1/2*b*log(c*x^n),2)*_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Integer) @@ -211,7 +222,7 @@ a0303:= integrate(t0303,x) --R +---------------------+ --R x n 2 | n --R ++ sec(b log(c %R ) + a) \|sec(b log(c %R ) + a) ---R (8) | ---------------------------------------------- d%R +--R (2) | ---------------------------------------------- d%R --R ++ %R --R Type: Union(Expression(Integer),...) --E 18 @@ -224,12 +235,14 @@ a0303:= integrate(t0303,x) --d0303:= D(m0303,x) --E 20 +)clear all + --S 21 of 460 t0304:= 1/x/sec(a+b*log(c*x^n))^(1/2) --R --R --R 1 ---R (9) ------------------------ +--R (1) ------------------------ --R +--------------------+ --R | n --R x\|sec(b log(c x ) + a) @@ -246,6 +259,7 @@ r0304:= 2*cos(a+b*log(c*x^n))^(1/2)*EllipticE(1/2*a+1/2*b*log(c*x^n),2)*_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Integer) @@ -259,12 +273,12 @@ r0304:= 2*cos(a+b*log(c*x^n))^(1/2)*EllipticE(1/2*a+1/2*b*log(c*x^n),2)*_ a0304:= integrate(t0304,x) --R --R ---R x ---R ++ 1 ---R (10) | -------------------------- d%R ---R ++ +---------------------+ ---R | n ---R %R\|sec(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | -------------------------- d%R +--R ++ +---------------------+ +--R | n +--R %R\|sec(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 23 @@ -276,15 +290,17 @@ a0304:= integrate(t0304,x) --d0304:= D(m0304,x) --E 25 +)clear all + --S 26 of 460 t0305:= 1/x/sec(a+b*log(c*x^n))^(3/2) --R --R ---R 1 ---R (11) --------------------------------------------- ---R +--------------------+ ---R n | n ---R x sec(b log(c x ) + a)\|sec(b log(c x ) + a) +--R 1 +--R (1) --------------------------------------------- +--R +--------------------+ +--R n | n +--R x sec(b log(c x ) + a)\|sec(b log(c x ) + a) --R Type: Expression(Integer) --E 26 @@ -299,6 +315,7 @@ r0305:= 2/3*cos(a+b*log(c*x^n))^(1/2)*EllipticF(1/2*a+_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Integer) @@ -312,12 +329,12 @@ r0305:= 2/3*cos(a+b*log(c*x^n))^(1/2)*EllipticF(1/2*a+_ a0305:= integrate(t0305,x) --R --R ---R x ---R ++ 1 ---R (12) | ------------------------------------------------ d%R ---R ++ +---------------------+ ---R n | n ---R %R sec(b log(c %R ) + a)\|sec(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | ------------------------------------------------ d%R +--R ++ +---------------------+ +--R n | n +--R %R sec(b log(c %R ) + a)\|sec(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 28 @@ -329,15 +346,17 @@ a0305:= integrate(t0305,x) --d0305:= D(m0305,x) --E 30 +)clear all + --S 31 of 460 t0306:= 1/x/sec(a+b*log(c*x^n))^(5/2) --R --R ---R 1 ---R (13) ---------------------------------------------- ---R +--------------------+ ---R n 2 | n ---R x sec(b log(c x ) + a) \|sec(b log(c x ) + a) +--R 1 +--R (1) ---------------------------------------------- +--R +--------------------+ +--R n 2 | n +--R x sec(b log(c x ) + a) \|sec(b log(c x ) + a) --R Type: Expression(Integer) --E 31 @@ -352,6 +371,7 @@ r0306:= 6/5*cos(a+b*log(c*x^n))^(1/2)*EllipticE(1/2*a+_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Integer) @@ -365,12 +385,12 @@ r0306:= 6/5*cos(a+b*log(c*x^n))^(1/2)*EllipticE(1/2*a+_ a0306:= integrate(t0306,x) --R --R ---R x ---R ++ 1 ---R (14) | ------------------------------------------------- d%R ---R ++ +---------------------+ ---R n 2 | n ---R %R sec(b log(c %R ) + a) \|sec(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | ------------------------------------------------- d%R +--R ++ +---------------------+ +--R n 2 | n +--R %R sec(b log(c %R ) + a) \|sec(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 33 @@ -382,15 +402,17 @@ a0306:= integrate(t0306,x) --d0306:= D(m0306,x) --E 35 +)clear all + --S 36 of 460 t0307:= csc(a+b*log(c*x^n))^(1/2)/x --R --R ---R +--------------------+ ---R | n ---R \|csc(b log(c x ) + a) ---R (15) ----------------------- ---R x +--R +--------------------+ +--R | n +--R \|csc(b log(c x ) + a) +--R (1) ----------------------- +--R x --R Type: Expression(Integer) --E 36 @@ -404,6 +426,7 @@ r0307:= 2*csc(a+b*log(c*x^n))^(1/2)*EllipticF(1/2*a-1/4*%pi+_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Integer) @@ -417,11 +440,11 @@ r0307:= 2*csc(a+b*log(c*x^n))^(1/2)*EllipticF(1/2*a-1/4*%pi+_ a0307:= integrate(t0307,x) --R --R ---R +---------------------+ ---R x | n ---R ++ \|csc(b log(c %R ) + a) ---R (16) | ------------------------ d%R ---R ++ %R +--R +---------------------+ +--R x | n +--R ++ \|csc(b log(c %R ) + a) +--R (2) | ------------------------ d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 38 @@ -433,15 +456,17 @@ a0307:= integrate(t0307,x) --d0307:= D(m0307,x) --E 40 +)clear all + --S 41 of 460 t0308:= csc(a+b*log(c*x^n))^(3/2)/x --R --R ---R +--------------------+ ---R n | n ---R csc(b log(c x ) + a)\|csc(b log(c x ) + a) ---R (17) ------------------------------------------- ---R x +--R +--------------------+ +--R n | n +--R csc(b log(c x ) + a)\|csc(b log(c x ) + a) +--R (1) ------------------------------------------- +--R x --R Type: Expression(Integer) --E 41 @@ -456,6 +481,7 @@ r0308:= -2*cos(a+b*log(c*x^n))*csc(a+b*log(c*x^n))^(1/2)/b/n-_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Integer) @@ -469,11 +495,11 @@ r0308:= -2*cos(a+b*log(c*x^n))*csc(a+b*log(c*x^n))^(1/2)/b/n-_ a0308:= integrate(t0308,x) --R --R ---R +---------------------+ ---R x n | n ---R ++ csc(b log(c %R ) + a)\|csc(b log(c %R ) + a) ---R (18) | --------------------------------------------- d%R ---R ++ %R +--R +---------------------+ +--R x n | n +--R ++ csc(b log(c %R ) + a)\|csc(b log(c %R ) + a) +--R (2) | --------------------------------------------- d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 43 @@ -485,15 +511,17 @@ a0308:= integrate(t0308,x) --d0308:= D(m0308,x) --E 45 +)clear all + --S 46 of 460 t0309:= csc(a+b*log(c*x^n))^(5/2)/x --R --R ---R +--------------------+ ---R n 2 | n ---R csc(b log(c x ) + a) \|csc(b log(c x ) + a) ---R (19) -------------------------------------------- ---R x +--R +--------------------+ +--R n 2 | n +--R csc(b log(c x ) + a) \|csc(b log(c x ) + a) +--R (1) -------------------------------------------- +--R x --R Type: Expression(Integer) --E 46 @@ -508,6 +536,7 @@ r0309:= -2/3*cos(a+b*log(c*x^n))*csc(a+b*log(c*x^n))^(3/2)/b/n+_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Integer) @@ -521,11 +550,11 @@ r0309:= -2/3*cos(a+b*log(c*x^n))*csc(a+b*log(c*x^n))^(3/2)/b/n+_ a0309:= integrate(t0309,x) --R --R ---R +---------------------+ ---R x n 2 | n ---R ++ csc(b log(c %R ) + a) \|csc(b log(c %R ) + a) ---R (20) | ---------------------------------------------- d%R ---R ++ %R +--R +---------------------+ +--R x n 2 | n +--R ++ csc(b log(c %R ) + a) \|csc(b log(c %R ) + a) +--R (2) | ---------------------------------------------- d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 48 @@ -537,15 +566,17 @@ a0309:= integrate(t0309,x) --d0309:= D(m0309,x) --E 50 +)clear all + --S 51 of 460 t0310:= 1/x/csc(a+b*log(c*x^n))^(1/2) --R --R ---R 1 ---R (21) ------------------------ ---R +--------------------+ ---R | n ---R x\|csc(b log(c x ) + a) +--R 1 +--R (1) ------------------------ +--R +--------------------+ +--R | n +--R x\|csc(b log(c x ) + a) --R Type: Expression(Integer) --E 51 @@ -559,6 +590,7 @@ r0310:= 2*csc(a+b*log(c*x^n))^(1/2)*EllipticE(1/2*a-1/4*%pi+_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Integer) @@ -572,12 +604,12 @@ r0310:= 2*csc(a+b*log(c*x^n))^(1/2)*EllipticE(1/2*a-1/4*%pi+_ a0310:= integrate(t0310,x) --R --R ---R x ---R ++ 1 ---R (22) | -------------------------- d%R ---R ++ +---------------------+ ---R | n ---R %R\|csc(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | -------------------------- d%R +--R ++ +---------------------+ +--R | n +--R %R\|csc(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 53 @@ -589,15 +621,17 @@ a0310:= integrate(t0310,x) --d0310:= D(m0310,x) --E 55 +)clear all + --S 56 of 460 t0311:= 1/x/csc(a+b*log(c*x^n))^(3/2) --R --R ---R 1 ---R (23) --------------------------------------------- ---R +--------------------+ ---R n | n ---R x csc(b log(c x ) + a)\|csc(b log(c x ) + a) +--R 1 +--R (1) --------------------------------------------- +--R +--------------------+ +--R n | n +--R x csc(b log(c x ) + a)\|csc(b log(c x ) + a) --R Type: Expression(Integer) --E 56 @@ -612,6 +646,7 @@ r0311:= -2/3*cos(a+b*log(c*x^n))/b/n/csc(a+b*log(c*x^n))^(1/2)+_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Integer) @@ -625,12 +660,12 @@ r0311:= -2/3*cos(a+b*log(c*x^n))/b/n/csc(a+b*log(c*x^n))^(1/2)+_ a0311:= integrate(t0311,x) --R --R ---R x ---R ++ 1 ---R (24) | ------------------------------------------------ d%R ---R ++ +---------------------+ ---R n | n ---R %R csc(b log(c %R ) + a)\|csc(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | ------------------------------------------------ d%R +--R ++ +---------------------+ +--R n | n +--R %R csc(b log(c %R ) + a)\|csc(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 58 @@ -642,15 +677,17 @@ a0311:= integrate(t0311,x) --d0311:= D(m0311,x) --E 60 +)clear all + --S 61 of 460 t0312:= 1/x/csc(a+b*log(c*x^n))^(5/2) --R --R ---R 1 ---R (25) ---------------------------------------------- ---R +--------------------+ ---R n 2 | n ---R x csc(b log(c x ) + a) \|csc(b log(c x ) + a) +--R 1 +--R (1) ---------------------------------------------- +--R +--------------------+ +--R n 2 | n +--R x csc(b log(c x ) + a) \|csc(b log(c x ) + a) --R Type: Expression(Integer) --E 61 @@ -665,6 +702,7 @@ r0312:= -2/5*cos(a+b*log(c*x^n))/b/n/csc(a+b*log(c*x^n))^(3/2)+_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Integer) @@ -678,12 +716,12 @@ r0312:= -2/5*cos(a+b*log(c*x^n))/b/n/csc(a+b*log(c*x^n))^(3/2)+_ a0312:= integrate(t0312,x) --R --R ---R x ---R ++ 1 ---R (26) | ------------------------------------------------- d%R ---R ++ +---------------------+ ---R n 2 | n ---R %R csc(b log(c %R ) + a) \|csc(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | ------------------------------------------------- d%R +--R ++ +---------------------+ +--R n 2 | n +--R %R csc(b log(c %R ) + a) \|csc(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 63 @@ -695,11 +733,13 @@ a0312:= integrate(t0312,x) --d0312:= D(m0312,x) --E 65 +)clear all + --S 66 of 460 t0313:= sin(log(a+b*x)) --R --R ---R (27) sin(log(b x + a)) +--R (1) sin(log(b x + a)) --R Type: Expression(Integer) --E 66 @@ -707,9 +747,9 @@ t0313:= sin(log(a+b*x)) r0313:= -1/2*(a+b*x)*(cos(log(a+b*x))-sin(log(a+b*x)))/b --R --R ---R (b x + a)sin(log(b x + a)) + (- b x - a)cos(log(b x + a)) ---R (28) --------------------------------------------------------- ---R 2b +--R (b x + a)sin(log(b x + a)) + (- b x - a)cos(log(b x + a)) +--R (2) --------------------------------------------------------- +--R 2b --R Type: Expression(Integer) --E 67 @@ -717,9 +757,9 @@ r0313:= -1/2*(a+b*x)*(cos(log(a+b*x))-sin(log(a+b*x)))/b a0313:= integrate(t0313,x) --R --R ---R (b x + a)sin(log(b x + a)) + (- b x - a)cos(log(b x + a)) ---R (29) --------------------------------------------------------- ---R 2b +--R (b x + a)sin(log(b x + a)) + (- b x - a)cos(log(b x + a)) +--R (3) --------------------------------------------------------- +--R 2b --R Type: Union(Expression(Integer),...) --E 68 @@ -727,7 +767,7 @@ a0313:= integrate(t0313,x) m0313:= a0313-r0313 --R --R ---R (30) 0 +--R (4) 0 --R Type: Expression(Integer) --E 69 @@ -735,18 +775,20 @@ m0313:= a0313-r0313 d0313:= D(m0313,x) --R --R ---R (31) 0 +--R (5) 0 --R Type: Expression(Integer) --E 70 +)clear all + --S 71 of 460 t0314:= tanh(a+b*log(c*x^n))^2/x --R --R ---R n 2 ---R tanh(b log(c x ) + a) ---R (32) ---------------------- ---R x +--R n 2 +--R tanh(b log(c x ) + a) +--R (1) ---------------------- +--R x --R Type: Expression(Integer) --E 71 @@ -754,10 +796,10 @@ t0314:= tanh(a+b*log(c*x^n))^2/x r0314:= 1/b/n*(b*log(c*x^n)-tanh(a+b*log(c*x^n))) --R --R ---R n n ---R - tanh(b log(c x ) + a) + b log(c x ) ---R (33) ------------------------------------- ---R b n +--R n n +--R - tanh(b log(c x ) + a) + b log(c x ) +--R (2) ------------------------------------- +--R b n --R Type: Expression(Integer) --E 72 @@ -765,7 +807,7 @@ r0314:= 1/b/n*(b*log(c*x^n)-tanh(a+b*log(c*x^n))) a0314:= integrate(t0314,x) --R --R ---R (34) +--R (3) --R - sinh(b n log(x) + b log(c) + a) --R + --R (b n log(x) + 1)cosh(b n log(x) + b log(c) + a) @@ -778,7 +820,7 @@ a0314:= integrate(t0314,x) m0314:= a0314-r0314 --R --R ---R (35) +--R (4) --R n --R cosh(b n log(x) + b log(c) + a)tanh(b log(c x ) + a) --R + @@ -797,7 +839,7 @@ m0314:= a0314-r0314 d0314:= D(m0314,x) --R --R ---R (36) +--R (5) --R n - 1 2 n 2 --R - x x cosh(b n log(x) + b log(c) + a) tanh(b log(c x ) + a) --R + @@ -809,14 +851,16 @@ d0314:= D(m0314,x) --R Type: Expression(Integer) --E 75 +)clear all + --S 76 of 460 t0315:= coth(a+b*log(c*x^n))^2/x --R --R ---R n 2 ---R coth(b log(c x ) + a) ---R (37) ---------------------- ---R x +--R n 2 +--R coth(b log(c x ) + a) +--R (1) ---------------------- +--R x --R Type: Expression(Integer) --E 76 @@ -824,10 +868,10 @@ t0315:= coth(a+b*log(c*x^n))^2/x r0315:= -1/b/n*(coth(a+b*log(c*x^n))-b*log(c*x^n)) --R --R ---R n n ---R - coth(b log(c x ) + a) + b log(c x ) ---R (38) ------------------------------------- ---R b n +--R n n +--R - coth(b log(c x ) + a) + b log(c x ) +--R (2) ------------------------------------- +--R b n --R Type: Expression(Integer) --E 77 @@ -835,7 +879,7 @@ r0315:= -1/b/n*(coth(a+b*log(c*x^n))-b*log(c*x^n)) a0315:= integrate(t0315,x) --R --R ---R (39) +--R (3) --R (b n log(x) + 1)sinh(b n log(x) + b log(c) + a) --R + --R - cosh(b n log(x) + b log(c) + a) @@ -848,7 +892,7 @@ a0315:= integrate(t0315,x) m0315:= a0315-r0315 --R --R ---R (40) +--R (4) --R n --R sinh(b n log(x) + b log(c) + a)coth(b log(c x ) + a) --R + @@ -865,7 +909,7 @@ m0315:= a0315-r0315 d0315:= D(m0315,x) --R --R ---R (41) +--R (5) --R n - 1 2 n 2 --R - x x sinh(b n log(x) + b log(c) + a) coth(b log(c x ) + a) --R + @@ -877,15 +921,17 @@ d0315:= D(m0315,x) --R Type: Expression(Integer) --E 80 +)clear all + --S 81 of 460 t0316:= sinh(a+b*log(c*x^n))^(1/2)/x --R --R ---R +---------------------+ ---R | n ---R \|sinh(b log(c x ) + a) ---R (42) ------------------------ ---R x +--R +---------------------+ +--R | n +--R \|sinh(b log(c x ) + a) +--R (1) ------------------------ +--R x --R Type: Expression(Integer) --E 81 @@ -899,6 +945,7 @@ r0316:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -912,11 +959,11 @@ r0316:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ a0316:= integrate(t0316,x) --R --R ---R +----------------------+ ---R x | n ---R ++ \|sinh(b log(c %R ) + a) ---R (43) | ------------------------- d%R ---R ++ %R +--R +----------------------+ +--R x | n +--R ++ \|sinh(b log(c %R ) + a) +--R (2) | ------------------------- d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 83 @@ -928,15 +975,17 @@ a0316:= integrate(t0316,x) --d0316:= D(m0316,x) --E 85 +)clear all + --S 86 of 460 t0317:= sinh(a+b*log(c*x^n))^(3/2)/x --R --R ---R +---------------------+ ---R n | n ---R sinh(b log(c x ) + a)\|sinh(b log(c x ) + a) ---R (44) --------------------------------------------- ---R x +--R +---------------------+ +--R n | n +--R sinh(b log(c x ) + a)\|sinh(b log(c x ) + a) +--R (1) --------------------------------------------- +--R x --R Type: Expression(Integer) --E 86 @@ -951,6 +1000,7 @@ r0317:= 2/3*%i*EllipticF(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -964,11 +1014,11 @@ r0317:= 2/3*%i*EllipticF(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ a0317:= integrate(t0317,x) --R --R ---R +----------------------+ ---R x n | n ---R ++ sinh(b log(c %R ) + a)\|sinh(b log(c %R ) + a) ---R (45) | ----------------------------------------------- d%R ---R ++ %R +--R +----------------------+ +--R x n | n +--R ++ sinh(b log(c %R ) + a)\|sinh(b log(c %R ) + a) +--R (2) | ----------------------------------------------- d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 88 @@ -980,15 +1030,17 @@ a0317:= integrate(t0317,x) --d0317:= D(m0317,x) --E 90 +)clear all + --S 91 of 460 t0318:= sinh(a+b*log(c*x^n))^(5/2)/x --R --R ---R +---------------------+ ---R n 2 | n ---R sinh(b log(c x ) + a) \|sinh(b log(c x ) + a) ---R (46) ---------------------------------------------- ---R x +--R +---------------------+ +--R n 2 | n +--R sinh(b log(c x ) + a) \|sinh(b log(c x ) + a) +--R (1) ---------------------------------------------- +--R x --R Type: Expression(Integer) --E 91 @@ -1003,6 +1055,7 @@ r0318:= 6/5*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1016,11 +1069,11 @@ r0318:= 6/5*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ a0318:= integrate(t0318,x) --R --R ---R +----------------------+ ---R x n 2 | n ---R ++ sinh(b log(c %R ) + a) \|sinh(b log(c %R ) + a) ---R (47) | ------------------------------------------------ d%R ---R ++ %R +--R +----------------------+ +--R x n 2 | n +--R ++ sinh(b log(c %R ) + a) \|sinh(b log(c %R ) + a) +--R (2) | ------------------------------------------------ d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 93 @@ -1032,15 +1085,17 @@ a0318:= integrate(t0318,x) --d0318:= D(m0318,x) --E 95 +)clear all + --S 96 of 460 t0319:= 1/x/sinh(a+b*log(c*x^n))^(1/2) --R --R ---R 1 ---R (48) ------------------------- ---R +---------------------+ ---R | n ---R x\|sinh(b log(c x ) + a) +--R 1 +--R (1) ------------------------- +--R +---------------------+ +--R | n +--R x\|sinh(b log(c x ) + a) --R Type: Expression(Integer) --E 96 @@ -1054,6 +1109,7 @@ r0319:= -2*%i*EllipticF(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1067,12 +1123,12 @@ r0319:= -2*%i*EllipticF(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)*_ a0319:= integrate(t0319,x) --R --R ---R x ---R ++ 1 ---R (49) | --------------------------- d%R ---R ++ +----------------------+ ---R | n ---R %R\|sinh(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | --------------------------- d%R +--R ++ +----------------------+ +--R | n +--R %R\|sinh(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 98 @@ -1084,15 +1140,17 @@ a0319:= integrate(t0319,x) --d0319:= D(m0319,x) --E 100 +)clear all + --S 101 of 460 t0320:= 1/x/sinh(a+b*log(c*x^n))^(3/2) --R --R ---R 1 ---R (50) ----------------------------------------------- ---R +---------------------+ ---R n | n ---R x sinh(b log(c x ) + a)\|sinh(b log(c x ) + a) +--R 1 +--R (1) ----------------------------------------------- +--R +---------------------+ +--R n | n +--R x sinh(b log(c x ) + a)\|sinh(b log(c x ) + a) --R Type: Expression(Integer) --E 101 @@ -1107,6 +1165,7 @@ r0320:= -2*cosh(a+b*log(c*x^n))/b/n/sinh(a+b*log(c*x^n))^(1/2)-_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1120,12 +1179,12 @@ r0320:= -2*cosh(a+b*log(c*x^n))/b/n/sinh(a+b*log(c*x^n))^(1/2)-_ a0320:= integrate(t0320,x) --R --R ---R x ---R ++ 1 ---R (51) | -------------------------------------------------- d%R ---R ++ +----------------------+ ---R n | n ---R %R sinh(b log(c %R ) + a)\|sinh(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | -------------------------------------------------- d%R +--R ++ +----------------------+ +--R n | n +--R %R sinh(b log(c %R ) + a)\|sinh(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 103 @@ -1137,15 +1196,17 @@ a0320:= integrate(t0320,x) --d0320:= D(m0320,x) --E 105 +)clear all + --S 106 of 460 t0321:= 1/x/sinh(a+b*log(c*x^n))^(5/2) --R --R ---R 1 ---R (52) ------------------------------------------------ ---R +---------------------+ ---R n 2 | n ---R x sinh(b log(c x ) + a) \|sinh(b log(c x ) + a) +--R 1 +--R (1) ------------------------------------------------ +--R +---------------------+ +--R n 2 | n +--R x sinh(b log(c x ) + a) \|sinh(b log(c x ) + a) --R Type: Expression(Integer) --E 106 @@ -1160,6 +1221,7 @@ r0321:= -2/3*cosh(a+b*log(c*x^n))/b/n/sinh(a+b*log(c*x^n))^(3/2)+_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1173,12 +1235,12 @@ r0321:= -2/3*cosh(a+b*log(c*x^n))/b/n/sinh(a+b*log(c*x^n))^(3/2)+_ a0321:= integrate(t0321,x) --R --R ---R x ---R ++ 1 ---R (53) | --------------------------------------------------- d%R ---R ++ +----------------------+ ---R n 2 | n ---R %R sinh(b log(c %R ) + a) \|sinh(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | --------------------------------------------------- d%R +--R ++ +----------------------+ +--R n 2 | n +--R %R sinh(b log(c %R ) + a) \|sinh(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 108 @@ -1190,15 +1252,17 @@ a0321:= integrate(t0321,x) --d0321:= D(m0321,x) --E 110 +)clear all + --S 111 of 460 t0322:= cosh(a+b*log(c*x^n))^(1/2)/x --R --R ---R +---------------------+ ---R | n ---R \|cosh(b log(c x ) + a) ---R (54) ------------------------ ---R x +--R +---------------------+ +--R | n +--R \|cosh(b log(c x ) + a) +--R (1) ------------------------ +--R x --R Type: Expression(Integer) --E 111 @@ -1211,6 +1275,7 @@ r0322:= -2*%i*EllipticE(1/2*%i*(a+b*log(c*x^n)),2)/b/n --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1224,11 +1289,11 @@ r0322:= -2*%i*EllipticE(1/2*%i*(a+b*log(c*x^n)),2)/b/n a0322:= integrate(t0322,x) --R --R ---R +----------------------+ ---R x | n ---R ++ \|cosh(b log(c %R ) + a) ---R (55) | ------------------------- d%R ---R ++ %R +--R +----------------------+ +--R x | n +--R ++ \|cosh(b log(c %R ) + a) +--R (2) | ------------------------- d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 113 @@ -1240,15 +1305,17 @@ a0322:= integrate(t0322,x) --d0322:= D(m0322,x) --E 115 +)clear all + --S 116 of 460 t0323:= cosh(a+b*log(c*x^n))^(3/2)/x --R --R ---R +---------------------+ ---R n | n ---R cosh(b log(c x ) + a)\|cosh(b log(c x ) + a) ---R (56) --------------------------------------------- ---R x +--R +---------------------+ +--R n | n +--R cosh(b log(c x ) + a)\|cosh(b log(c x ) + a) +--R (1) --------------------------------------------- +--R x --R Type: Expression(Integer) --E 116 @@ -1262,6 +1329,7 @@ r0323:= -2/3/b/n*(%i*EllipticF(1/2*%i*(a+b*log(c*x^n)),2)-_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1275,11 +1343,11 @@ r0323:= -2/3/b/n*(%i*EllipticF(1/2*%i*(a+b*log(c*x^n)),2)-_ a0323:= integrate(t0323,x) --R --R ---R +----------------------+ ---R x n | n ---R ++ cosh(b log(c %R ) + a)\|cosh(b log(c %R ) + a) ---R (57) | ----------------------------------------------- d%R ---R ++ %R +--R +----------------------+ +--R x n | n +--R ++ cosh(b log(c %R ) + a)\|cosh(b log(c %R ) + a) +--R (2) | ----------------------------------------------- d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 118 @@ -1291,15 +1359,17 @@ a0323:= integrate(t0323,x) --d0323:= D(m0323,x) --E 120 +)clear all + --S 121 of 460 t0324:= cosh(a+b*log(c*x^n))^(5/2)/x --R --R ---R +---------------------+ ---R n 2 | n ---R cosh(b log(c x ) + a) \|cosh(b log(c x ) + a) ---R (58) ---------------------------------------------- ---R x +--R +---------------------+ +--R n 2 | n +--R cosh(b log(c x ) + a) \|cosh(b log(c x ) + a) +--R (1) ---------------------------------------------- +--R x --R Type: Expression(Integer) --E 121 @@ -1313,6 +1383,7 @@ r0324:= 2/5/b/n*(-3*%i*EllipticE(1/2*%i*(a+b*log(c*x^n)),2)+_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1326,11 +1397,11 @@ r0324:= 2/5/b/n*(-3*%i*EllipticE(1/2*%i*(a+b*log(c*x^n)),2)+_ a0324:= integrate(t0324,x) --R --R ---R +----------------------+ ---R x n 2 | n ---R ++ cosh(b log(c %R ) + a) \|cosh(b log(c %R ) + a) ---R (59) | ------------------------------------------------ d%R ---R ++ %R +--R +----------------------+ +--R x n 2 | n +--R ++ cosh(b log(c %R ) + a) \|cosh(b log(c %R ) + a) +--R (2) | ------------------------------------------------ d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 123 @@ -1342,15 +1413,17 @@ a0324:= integrate(t0324,x) --d0324:= D(m0324,x) --E 125 +)clear all + --S 126 of 460 t0325:= 1/x/cosh(a+b*log(c*x^n))^(1/2) --R --R ---R 1 ---R (60) ------------------------- ---R +---------------------+ ---R | n ---R x\|cosh(b log(c x ) + a) +--R 1 +--R (1) ------------------------- +--R +---------------------+ +--R | n +--R x\|cosh(b log(c x ) + a) --R Type: Expression(Integer) --E 126 @@ -1363,6 +1436,7 @@ r0325:= -2*%i*EllipticF(1/2*%i*(a+b*log(c*x^n)),2)/b/n --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1376,12 +1450,12 @@ r0325:= -2*%i*EllipticF(1/2*%i*(a+b*log(c*x^n)),2)/b/n a0325:= integrate(t0325,x) --R --R ---R x ---R ++ 1 ---R (61) | --------------------------- d%R ---R ++ +----------------------+ ---R | n ---R %R\|cosh(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | --------------------------- d%R +--R ++ +----------------------+ +--R | n +--R %R\|cosh(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 128 @@ -1393,15 +1467,17 @@ a0325:= integrate(t0325,x) --d0325:= D(m0325,x) --E 130 +)clear all + --S 131 of 460 t0326:= 1/x/cosh(a+b*log(c*x^n))^(3/2) --R --R ---R 1 ---R (62) ----------------------------------------------- ---R +---------------------+ ---R n | n ---R x cosh(b log(c x ) + a)\|cosh(b log(c x ) + a) +--R 1 +--R (1) ----------------------------------------------- +--R +---------------------+ +--R n | n +--R x cosh(b log(c x ) + a)\|cosh(b log(c x ) + a) --R Type: Expression(Integer) --E 131 @@ -1415,6 +1491,7 @@ r0326:= 2*%i*EllipticE(1/2*%i*(a+b*log(c*x^n)),2)/b/n+_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1428,12 +1505,12 @@ r0326:= 2*%i*EllipticE(1/2*%i*(a+b*log(c*x^n)),2)/b/n+_ a0326:= integrate(t0326,x) --R --R ---R x ---R ++ 1 ---R (63) | -------------------------------------------------- d%R ---R ++ +----------------------+ ---R n | n ---R %R cosh(b log(c %R ) + a)\|cosh(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | -------------------------------------------------- d%R +--R ++ +----------------------+ +--R n | n +--R %R cosh(b log(c %R ) + a)\|cosh(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 133 @@ -1445,15 +1522,17 @@ a0326:= integrate(t0326,x) --d0326:= D(m0326,x) --E 135 +)clear all + --S 136 of 460 t0327:= 1/x/cosh(a+b*log(c*x^n))^(5/2) --R --R ---R 1 ---R (64) ------------------------------------------------ ---R +---------------------+ ---R n 2 | n ---R x cosh(b log(c x ) + a) \|cosh(b log(c x ) + a) +--R 1 +--R (1) ------------------------------------------------ +--R +---------------------+ +--R n 2 | n +--R x cosh(b log(c x ) + a) \|cosh(b log(c x ) + a) --R Type: Expression(Integer) --E 136 @@ -1467,6 +1546,7 @@ r0327:= -2/3*%i*EllipticF(1/2*%i*(a+b*log(c*x^n)),2)/b/n+_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1480,12 +1560,12 @@ r0327:= -2/3*%i*EllipticF(1/2*%i*(a+b*log(c*x^n)),2)/b/n+_ a0327:= integrate(t0327,x) --R --R ---R x ---R ++ 1 ---R (65) | --------------------------------------------------- d%R ---R ++ +----------------------+ ---R n 2 | n ---R %R cosh(b log(c %R ) + a) \|cosh(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | --------------------------------------------------- d%R +--R ++ +----------------------+ +--R n 2 | n +--R %R cosh(b log(c %R ) + a) \|cosh(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 138 @@ -1497,15 +1577,17 @@ a0327:= integrate(t0327,x) --d0327:= D(m0327,x) --E 140 +)clear all + --S 141 of 460 t0328:= sech(a+b*log(c*x^n))^(1/2)/x --R --R ---R +---------------------+ ---R | n ---R \|sech(b log(c x ) + a) ---R (66) ------------------------ ---R x +--R +---------------------+ +--R | n +--R \|sech(b log(c x ) + a) +--R (1) ------------------------ +--R x --R Type: Expression(Integer) --E 141 @@ -1519,6 +1601,7 @@ r0328:= -2*%i*cosh(a+b*log(c*x^n))^(1/2)*_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1532,11 +1615,11 @@ r0328:= -2*%i*cosh(a+b*log(c*x^n))^(1/2)*_ a0328:= integrate(t0328,x) --R --R ---R +----------------------+ ---R x | n ---R ++ \|sech(b log(c %R ) + a) ---R (67) | ------------------------- d%R ---R ++ %R +--R +----------------------+ +--R x | n +--R ++ \|sech(b log(c %R ) + a) +--R (2) | ------------------------- d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 143 @@ -1548,15 +1631,17 @@ a0328:= integrate(t0328,x) --d0328:= D(m0328,x) --E 145 +)clear all + --S 146 of 460 t0329:= sech(a+b*log(c*x^n))^(3/2)/x --R --R ---R +---------------------+ ---R n | n ---R sech(b log(c x ) + a)\|sech(b log(c x ) + a) ---R (68) --------------------------------------------- ---R x +--R +---------------------+ +--R n | n +--R sech(b log(c x ) + a)\|sech(b log(c x ) + a) +--R (1) --------------------------------------------- +--R x --R Type: Expression(Integer) --E 146 @@ -1571,6 +1656,7 @@ r0329:= 2*%i*cosh(a+b*log(c*x^n))^(1/2)*_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1584,11 +1670,11 @@ r0329:= 2*%i*cosh(a+b*log(c*x^n))^(1/2)*_ a0329:= integrate(t0329,x) --R --R ---R +----------------------+ ---R x n | n ---R ++ sech(b log(c %R ) + a)\|sech(b log(c %R ) + a) ---R (69) | ----------------------------------------------- d%R ---R ++ %R +--R +----------------------+ +--R x n | n +--R ++ sech(b log(c %R ) + a)\|sech(b log(c %R ) + a) +--R (2) | ----------------------------------------------- d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 148 @@ -1600,15 +1686,17 @@ a0329:= integrate(t0329,x) --d0329:= D(m0329,x) --E 150 +)clear all + --S 151 of 460 t0330:= sech(a+b*log(c*x^n))^(5/2)/x --R --R ---R +---------------------+ ---R n 2 | n ---R sech(b log(c x ) + a) \|sech(b log(c x ) + a) ---R (70) ---------------------------------------------- ---R x +--R +---------------------+ +--R n 2 | n +--R sech(b log(c x ) + a) \|sech(b log(c x ) + a) +--R (1) ---------------------------------------------- +--R x --R Type: Expression(Integer) --E 151 @@ -1623,6 +1711,7 @@ r0330:= -2/3*%i*cosh(a+b*log(c*x^n))^(1/2)*_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1636,11 +1725,11 @@ r0330:= -2/3*%i*cosh(a+b*log(c*x^n))^(1/2)*_ a0330:= integrate(t0330,x) --R --R ---R +----------------------+ ---R x n 2 | n ---R ++ sech(b log(c %R ) + a) \|sech(b log(c %R ) + a) ---R (71) | ------------------------------------------------ d%R ---R ++ %R +--R +----------------------+ +--R x n 2 | n +--R ++ sech(b log(c %R ) + a) \|sech(b log(c %R ) + a) +--R (2) | ------------------------------------------------ d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 153 @@ -1652,15 +1741,17 @@ a0330:= integrate(t0330,x) --d0330:= D(m0330,x) --E 155 +)clear all + --S 156 of 460 t0331:= 1/x/sech(a+b*log(c*x^n))^(1/2) --R --R ---R 1 ---R (72) ------------------------- ---R +---------------------+ ---R | n ---R x\|sech(b log(c x ) + a) +--R 1 +--R (1) ------------------------- +--R +---------------------+ +--R | n +--R x\|sech(b log(c x ) + a) --R Type: Expression(Integer) --E 156 @@ -1674,6 +1765,7 @@ r0331:= -2*%i*cosh(a+b*log(c*x^n))^(1/2)*_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1687,12 +1779,12 @@ r0331:= -2*%i*cosh(a+b*log(c*x^n))^(1/2)*_ a0331:= integrate(t0331,x) --R --R ---R x ---R ++ 1 ---R (73) | --------------------------- d%R ---R ++ +----------------------+ ---R | n ---R %R\|sech(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | --------------------------- d%R +--R ++ +----------------------+ +--R | n +--R %R\|sech(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 158 @@ -1704,15 +1796,17 @@ a0331:= integrate(t0331,x) --d0331:= D(m0331,x) --E 160 +)clear all + --S 161 of 460 t0332:= 1/x/sech(a+b*log(c*x^n))^(3/2) --R --R ---R 1 ---R (74) ----------------------------------------------- ---R +---------------------+ ---R n | n ---R x sech(b log(c x ) + a)\|sech(b log(c x ) + a) +--R 1 +--R (1) ----------------------------------------------- +--R +---------------------+ +--R n | n +--R x sech(b log(c x ) + a)\|sech(b log(c x ) + a) --R Type: Expression(Integer) --E 161 @@ -1727,6 +1821,7 @@ r0332:= -2/3*%i*cosh(a+b*log(c*x^n))^(1/2)*_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1740,12 +1835,12 @@ r0332:= -2/3*%i*cosh(a+b*log(c*x^n))^(1/2)*_ a0332:= integrate(t0332,x) --R --R ---R x ---R ++ 1 ---R (75) | -------------------------------------------------- d%R ---R ++ +----------------------+ ---R n | n ---R %R sech(b log(c %R ) + a)\|sech(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | -------------------------------------------------- d%R +--R ++ +----------------------+ +--R n | n +--R %R sech(b log(c %R ) + a)\|sech(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 163 @@ -1757,15 +1852,17 @@ a0332:= integrate(t0332,x) --d0332:= D(m0332,x) --E 165 +)clear all + --S 166 of 460 t0333:= 1/x/sech(a+b*log(c*x^n))^(5/2) --R --R ---R 1 ---R (76) ------------------------------------------------ ---R +---------------------+ ---R n 2 | n ---R x sech(b log(c x ) + a) \|sech(b log(c x ) + a) +--R 1 +--R (1) ------------------------------------------------ +--R +---------------------+ +--R n 2 | n +--R x sech(b log(c x ) + a) \|sech(b log(c x ) + a) --R Type: Expression(Integer) --E 166 @@ -1780,6 +1877,7 @@ r0333:= -6/5*%i*cosh(a+b*log(c*x^n))^(1/2)*_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1793,12 +1891,12 @@ r0333:= -6/5*%i*cosh(a+b*log(c*x^n))^(1/2)*_ a0333:= integrate(t0333,x) --R --R ---R x ---R ++ 1 ---R (77) | --------------------------------------------------- d%R ---R ++ +----------------------+ ---R n 2 | n ---R %R sech(b log(c %R ) + a) \|sech(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | --------------------------------------------------- d%R +--R ++ +----------------------+ +--R n 2 | n +--R %R sech(b log(c %R ) + a) \|sech(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 168 @@ -1810,15 +1908,17 @@ a0333:= integrate(t0333,x) --d0333:= D(m0333,x) --E 170 +)clear all + --S 171 of 460 t0334:= csch(a+b*log(c*x^n))^(1/2)/x --R --R ---R +---------------------+ ---R | n ---R \|csch(b log(c x ) + a) ---R (78) ------------------------ ---R x +--R +---------------------+ +--R | n +--R \|csch(b log(c x ) + a) +--R (1) ------------------------ +--R x --R Type: Expression(Integer) --E 171 @@ -1833,6 +1933,7 @@ r0334:= -2*%i*csch(a+b*log(c*x^n))^(1/2)*_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1846,11 +1947,11 @@ r0334:= -2*%i*csch(a+b*log(c*x^n))^(1/2)*_ a0334:= integrate(t0334,x) --R --R ---R +----------------------+ ---R x | n ---R ++ \|csch(b log(c %R ) + a) ---R (79) | ------------------------- d%R ---R ++ %R +--R +----------------------+ +--R x | n +--R ++ \|csch(b log(c %R ) + a) +--R (2) | ------------------------- d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 173 @@ -1862,15 +1963,17 @@ a0334:= integrate(t0334,x) --d0334:= D(m0334,x) --E 175 +)clear all + --S 176 of 460 t0335:= csch(a+b*log(c*x^n))^(3/2)/x --R --R ---R +---------------------+ ---R n | n ---R csch(b log(c x ) + a)\|csch(b log(c x ) + a) ---R (80) --------------------------------------------- ---R x +--R +---------------------+ +--R n | n +--R csch(b log(c x ) + a)\|csch(b log(c x ) + a) +--R (1) --------------------------------------------- +--R x --R Type: Expression(Integer) --E 176 @@ -1885,6 +1988,7 @@ r0335:= -2*cosh(a+b*log(c*x^n))*csch(a+b*log(c*x^n))^(1/2)/b/n-_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1898,11 +2002,11 @@ r0335:= -2*cosh(a+b*log(c*x^n))*csch(a+b*log(c*x^n))^(1/2)/b/n-_ a0335:= integrate(t0335,x) --R --R ---R +----------------------+ ---R x n | n ---R ++ csch(b log(c %R ) + a)\|csch(b log(c %R ) + a) ---R (81) | ----------------------------------------------- d%R ---R ++ %R +--R +----------------------+ +--R x n | n +--R ++ csch(b log(c %R ) + a)\|csch(b log(c %R ) + a) +--R (2) | ----------------------------------------------- d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 178 @@ -1914,15 +2018,17 @@ a0335:= integrate(t0335,x) --d0335:= D(m0335,x) --E 180 +)clear all + --S 181 of 460 t0336:= csch(a+b*log(c*x^n))^(5/2)/x --R --R ---R +---------------------+ ---R n 2 | n ---R csch(b log(c x ) + a) \|csch(b log(c x ) + a) ---R (82) ---------------------------------------------- ---R x +--R +---------------------+ +--R n 2 | n +--R csch(b log(c x ) + a) \|csch(b log(c x ) + a) +--R (1) ---------------------------------------------- +--R x --R Type: Expression(Integer) --E 181 @@ -1937,6 +2043,7 @@ r0336:= -2/3*cosh(a+b*log(c*x^n))*csch(a+b*log(c*x^n))^(3/2)/b/n+_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -1950,11 +2057,11 @@ r0336:= -2/3*cosh(a+b*log(c*x^n))*csch(a+b*log(c*x^n))^(3/2)/b/n+_ a0336:= integrate(t0336,x) --R --R ---R +----------------------+ ---R x n 2 | n ---R ++ csch(b log(c %R ) + a) \|csch(b log(c %R ) + a) ---R (83) | ------------------------------------------------ d%R ---R ++ %R +--R +----------------------+ +--R x n 2 | n +--R ++ csch(b log(c %R ) + a) \|csch(b log(c %R ) + a) +--R (2) | ------------------------------------------------ d%R +--R ++ %R --R Type: Union(Expression(Integer),...) --E 183 @@ -1966,15 +2073,17 @@ a0336:= integrate(t0336,x) --d0336:= D(m0336,x) --E 185 +)clear all + --S 186 of 460 t0337:= 1/x/csch(a+b*log(c*x^n))^(1/2) --R --R ---R 1 ---R (84) ------------------------- ---R +---------------------+ ---R | n ---R x\|csch(b log(c x ) + a) +--R 1 +--R (1) ------------------------- +--R +---------------------+ +--R | n +--R x\|csch(b log(c x ) + a) --R Type: Expression(Integer) --E 186 @@ -1988,6 +2097,7 @@ r0337:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)/b/n/_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -2001,12 +2111,12 @@ r0337:= -2*%i*EllipticE(-1/4*%pi+1/2*%i*(a+b*log(c*x^n)),2)/b/n/_ a0337:= integrate(t0337,x) --R --R ---R x ---R ++ 1 ---R (85) | --------------------------- d%R ---R ++ +----------------------+ ---R | n ---R %R\|csch(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | --------------------------- d%R +--R ++ +----------------------+ +--R | n +--R %R\|csch(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 188 @@ -2018,15 +2128,17 @@ a0337:= integrate(t0337,x) --d0337:= D(m0337,x) --E 190 +)clear all + --S 191 of 460 t0338:= 1/x/csch(a+b*log(c*x^n))^(3/2) --R --R ---R 1 ---R (86) ----------------------------------------------- ---R +---------------------+ ---R n | n ---R x csch(b log(c x ) + a)\|csch(b log(c x ) + a) +--R 1 +--R (1) ----------------------------------------------- +--R +---------------------+ +--R n | n +--R x csch(b log(c x ) + a)\|csch(b log(c x ) + a) --R Type: Expression(Integer) --E 191 @@ -2041,6 +2153,7 @@ r0338:= 2/3*cosh(a+b*log(c*x^n))/b/n/csch(a+b*log(c*x^n))^(1/2)+_ --R to learn if there is any operation containing " EllipticF " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticF with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -2054,12 +2167,12 @@ r0338:= 2/3*cosh(a+b*log(c*x^n))/b/n/csch(a+b*log(c*x^n))^(1/2)+_ a0338:= integrate(t0338,x) --R --R ---R x ---R ++ 1 ---R (87) | -------------------------------------------------- d%R ---R ++ +----------------------+ ---R n | n ---R %R csch(b log(c %R ) + a)\|csch(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | -------------------------------------------------- d%R +--R ++ +----------------------+ +--R n | n +--R %R csch(b log(c %R ) + a)\|csch(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 193 @@ -2071,15 +2184,17 @@ a0338:= integrate(t0338,x) --d0338:= D(m0338,x) --E 195 +)clear all + --S 196 of 460 t0339:= 1/x/csch(a+b*log(c*x^n))^(5/2) --R --R ---R 1 ---R (88) ------------------------------------------------ ---R +---------------------+ ---R n 2 | n ---R x csch(b log(c x ) + a) \|csch(b log(c x ) + a) +--R 1 +--R (1) ------------------------------------------------ +--R +---------------------+ +--R n 2 | n +--R x csch(b log(c x ) + a) \|csch(b log(c x ) + a) --R Type: Expression(Integer) --E 196 @@ -2094,6 +2209,7 @@ r0339:= 2/5*cosh(a+b*log(c*x^n))/b/n/csch(a+b*log(c*x^n))^(3/2)+_ --R to learn if there is any operation containing " EllipticE " in --R its name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R EllipticE with argument type(s) --R Expression(Complex(Fraction(Integer))) @@ -2107,12 +2223,12 @@ r0339:= 2/5*cosh(a+b*log(c*x^n))/b/n/csch(a+b*log(c*x^n))^(3/2)+_ a0339:= integrate(t0339,x) --R --R ---R x ---R ++ 1 ---R (89) | --------------------------------------------------- d%R ---R ++ +----------------------+ ---R n 2 | n ---R %R csch(b log(c %R ) + a) \|csch(b log(c %R ) + a) +--R x +--R ++ 1 +--R (2) | --------------------------------------------------- d%R +--R ++ +----------------------+ +--R n 2 | n +--R %R csch(b log(c %R ) + a) \|csch(b log(c %R ) + a) --R Type: Union(Expression(Integer),...) --E 198 @@ -2124,13 +2240,15 @@ a0339:= integrate(t0339,x) --d0339:= D(m0339,x) --E 200 +)clear all + --S 201 of 460 t0340:= 1/2*log(a+b*x) --R --R ---R log(b x + a) ---R (90) ------------ ---R 2 +--R log(b x + a) +--R (1) ------------ +--R 2 --R Type: Expression(Integer) --E 201 @@ -2138,9 +2256,9 @@ t0340:= 1/2*log(a+b*x) r0340:= -1/2*x+1/2*(a+b*x)*log(a+b*x)/b --R --R ---R (b x + a)log(b x + a) - b x ---R (91) --------------------------- ---R 2b +--R (b x + a)log(b x + a) - b x +--R (2) --------------------------- +--R 2b --R Type: Expression(Integer) --E 202 @@ -2148,9 +2266,9 @@ r0340:= -1/2*x+1/2*(a+b*x)*log(a+b*x)/b a0340:= integrate(t0340,x) --R --R ---R (b x + a)log(b x + a) - b x ---R (92) --------------------------- ---R 2b +--R (b x + a)log(b x + a) - b x +--R (3) --------------------------- +--R 2b --R Type: Union(Expression(Integer),...) --E 203 @@ -2158,7 +2276,7 @@ a0340:= integrate(t0340,x) m0340:= a0340-r0340 --R --R ---R (93) 0 +--R (4) 0 --R Type: Expression(Integer) --E 204 @@ -2166,16 +2284,18 @@ m0340:= a0340-r0340 d0340:= D(m0340,x) --R --R ---R (94) 0 +--R (5) 0 --R Type: Expression(Integer) --E 205 +)clear all + --S 206 of 460 t0341:= log(x^(1/2)+(1+x)^(1/2)) --R --R ---R +-----+ +-+ ---R (95) log(\|x + 1 + \|x ) +--R +-----+ +-+ +--R (1) log(\|x + 1 + \|x ) --R Type: Expression(Integer) --E 206 @@ -2184,45 +2304,66 @@ r0341:= -1/2*(x/(1+x))^(1/2)*(1+x)+1/2*atanh((x/(1+x))^(1/2))+_ x*log(x^(1/2)+(1+x)^(1/2)) --R --R ---R +-----+ +-----+ ---R +-----+ +-+ | x | x ---R 2x log(\|x + 1 + \|x ) + atanh( |----- ) + (- x - 1) |----- ---R \|x + 1 \|x + 1 ---R (96) ------------------------------------------------------------- ---R 2 +--R +-----+ +-----+ +--R +-----+ +-+ | x | x +--R 2x log(\|x + 1 + \|x ) + atanh( |----- ) + (- x - 1) |----- +--R \|x + 1 \|x + 1 +--R (2) ------------------------------------------------------------- +--R 2 --R Type: Expression(Integer) --E 207 ---S 208 of 460 +--S 208 of 460 random value, ok to fail a0341:= integrate(t0341,x) --R --R ---R (97) +--R (3) --R +-+ +-----+ 2 +-----+ +-+ ---R ((4x + 2)\|x \|x + 1 - 4x - 4x - 1)log(\|x + 1 + \|x ) +--R ((4x + 2)\|x \|x + 1 + 4x + 4x + 1)log(\|x + 1 + \|x ) --R + ---R +-+ +-----+ 2 ---R (2x + 1)\|x \|x + 1 - 2x - 2x +--R +-+ +-----+ 2 +--R (- 2x - 1)\|x \|x + 1 - 2x - 2x --R / --R +-+ +-----+ ---R 4\|x \|x + 1 - 4x - 2 +--R 4\|x \|x + 1 + 4x + 2 --R Type: Union(Expression(Integer),...) --E 208 --S 209 of 460 random value, ok to fail m0341:= a0341-r0341 +--R +--R +--R +-----+ +-----+ +--R +-----+ +-+ | x | x +--R - 2x log(\|x + 1 + \|x ) - atanh( |----- ) + (x + 1) |----- + 2a0341 +--R \|x + 1 \|x + 1 +--R (4) ---------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) --E 209 --S 210 of 460 random value, ok to fail d0341:= D(m0341,x) +--R +--R +--R +-----+ +--R +-+ +-----+ +-----+ +-+ | x +-+ +-----+ +--R - 2\|x \|x + 1 log(\|x + 1 + \|x ) + |----- \|x \|x + 1 - x +--R \|x + 1 +--R (5) -------------------------------------------------------------- +--R +-+ +-----+ +--R 2\|x \|x + 1 +--R Type: Expression(Integer) --E 210 +)clear all + --S 211 of 460 t0342:= log(abs(a^2-x^2)) --R --R ---R 2 2 ---R (100) log(abs(x - a )) +--R 2 2 +--R (1) log(abs(x - a )) --R Type: Expression(Integer) --E 211 @@ -2230,11 +2371,11 @@ t0342:= log(abs(a^2-x^2)) r0342:= -2*x+2*a*atanh(x/a)+1/2*x*log((a^2-x^2)^2) --R --R ---R 4 2 2 4 x ---R x log(x - 2a x + a ) + 4a atanh(-) - 4x ---R a ---R (101) ----------------------------------------- ---R 2 +--R 4 2 2 4 x +--R x log(x - 2a x + a ) + 4a atanh(-) - 4x +--R a +--R (2) ----------------------------------------- +--R 2 --R Type: Expression(Integer) --E 212 @@ -2242,16 +2383,16 @@ r0342:= -2*x+2*a*atanh(x/a)+1/2*x*log((a^2-x^2)^2) a0342:= integrate(t0342,x) --R --R ---R 2 2 ---R (102) x log(abs(x - a )) + a log(x + a) - a log(x - a) - 2x ---R Type: Expression(Integer) +--R 2 2 +--R (3) x log(abs(x - a )) + a log(x + a) - a log(x - a) - 2x +--R Type: Union(Expression(Integer),...) --E 213 --S 214 of 460 m0342:= a0342-r0342 --R --R ---R (103) +--R (4) --R 2 2 4 2 2 4 --R 2x log(abs(x - a )) - x log(x - 2a x + a ) + 2a log(x + a) --R + @@ -2260,27 +2401,29 @@ m0342:= a0342-r0342 --R a --R / --R 2 ---R Type: Union(Expression(Integer),...) +--R Type: Expression(Integer) --E 214 --S 215 of 460 d0342:= D(m0342,x) --R --R ---R 2 2 4 2 2 4 ---R 2log(abs(x - a )) - log(x - 2a x + a ) ---R (104) ----------------------------------------- ---R 2 +--R 2 2 4 2 2 4 +--R 2log(abs(x - a )) - log(x - 2a x + a ) +--R (5) ----------------------------------------- +--R 2 --R Type: Expression(Integer) --E 215 +)clear all + --S 216 of 460 t0343:= log((-11+5*x)/(5+76*x)) --R --R ---R 5x - 11 ---R (105) log(-------) ---R 76x + 5 +--R 5x - 11 +--R (1) log(-------) +--R 76x + 5 --R Type: Expression(Integer) --E 216 @@ -2288,11 +2431,11 @@ t0343:= log((-11+5*x)/(5+76*x)) r0343:= -11/5*log(11-5*x)+x*log((-11+5*x)/(5+76*x))-5/76*log(5+76*x) --R --R ---R 5x - 11 ---R - 25log(76x + 5) + 380x log(-------) - 836log(- 5x + 11) ---R 76x + 5 ---R (106) -------------------------------------------------------- ---R 380 +--R 5x - 11 +--R - 25log(76x + 5) + 380x log(-------) - 836log(- 5x + 11) +--R 76x + 5 +--R (2) -------------------------------------------------------- +--R 380 --R Type: Expression(Integer) --E 217 @@ -2300,42 +2443,44 @@ r0343:= -11/5*log(11-5*x)+x*log((-11+5*x)/(5+76*x))-5/76*log(5+76*x) a0343:= integrate(t0343,x) --R --R ---R 5x - 11 ---R - 25log(76x + 5) - 836log(5x - 11) + 380x log(-------) ---R 76x + 5 ---R (107) ------------------------------------------------------ ---R 380 ---R Type: Expression(Integer) +--R 5x - 11 +--R - 25log(76x + 5) - 836log(5x - 11) + 380x log(-------) +--R 76x + 5 +--R (3) ------------------------------------------------------ +--R 380 +--R Type: Union(Expression(Integer),...) --E 218 --S 219 of 460 m0343:= a0343-r0343 --R --R ---R - 11log(5x - 11) + 11log(- 5x + 11) ---R (108) ----------------------------------- ---R 5 ---R Type: Union(Expression(Integer),...) +--R - 11log(5x - 11) + 11log(- 5x + 11) +--R (4) ----------------------------------- +--R 5 +--R Type: Expression(Integer) --E 219 --S 220 of 460 d0343:= D(m0343,x) --R --R ---R (109) 0 +--R (5) 0 --R Type: Expression(Integer) --E 220 +)clear all + --S 221 of 460 t0344:= log((1+x)/(-1+x))/x^2 --R --R ---R x + 1 ---R log(-----) ---R x - 1 ---R (110) ---------- ---R 2 ---R x +--R x + 1 +--R log(-----) +--R x - 1 +--R (1) ---------- +--R 2 +--R x --R Type: Expression(Integer) --E 221 @@ -2343,11 +2488,11 @@ t0344:= log((1+x)/(-1+x))/x^2 r0344:= 2*log(x)-log(-(1+x)/(1-x))/x-log(1-x^2) --R --R ---R x + 1 2 ---R 2x log(x) - log(-----) - x log(- x + 1) ---R x - 1 ---R (111) ---------------------------------------- ---R x +--R x + 1 2 +--R 2x log(x) - log(-----) - x log(- x + 1) +--R x - 1 +--R (2) ---------------------------------------- +--R x --R Type: Expression(Integer) --E 222 @@ -2355,39 +2500,41 @@ r0344:= 2*log(x)-log(-(1+x)/(1-x))/x-log(1-x^2) a0344:= integrate(t0344,x) --R --R ---R 2 x + 1 ---R - x log(x - 1) + 2x log(x) - log(-----) ---R x - 1 ---R (112) ---------------------------------------- ---R x ---R Type: Expression(Integer) +--R 2 x + 1 +--R - x log(x - 1) + 2x log(x) - log(-----) +--R x - 1 +--R (3) ---------------------------------------- +--R x +--R Type: Union(Expression(Integer),...) --E 223 --S 224 of 460 m0344:= a0344-r0344 --R --R ---R 2 2 ---R (113) - log(x - 1) + log(- x + 1) ---R Type: Union(Expression(Integer),...) +--R 2 2 +--R (4) - log(x - 1) + log(- x + 1) +--R Type: Expression(Integer) --E 224 --S 225 of 460 d0344:= D(m0344,x) --R --R ---R (114) 0 +--R (5) 0 --R Type: Expression(Integer) --E 225 +)clear all + --S 226 of 460 t0345:= x*log((1+x)/x^2) --R --R ---R x + 1 ---R (115) x log(-----) ---R 2 ---R x +--R x + 1 +--R (1) x log(-----) +--R 2 +--R x --R Type: Expression(Integer) --E 226 @@ -2395,12 +2542,12 @@ t0345:= x*log((1+x)/x^2) r0345:= 1/2*x+1/4*x^2-1/2*log(1+x)+1/2*x^2*log((1+x)/x^2) --R --R ---R 2 x + 1 2 ---R - 2log(x + 1) + 2x log(-----) + x + 2x ---R 2 ---R x ---R (116) --------------------------------------- ---R 4 +--R 2 x + 1 2 +--R - 2log(x + 1) + 2x log(-----) + x + 2x +--R 2 +--R x +--R (2) --------------------------------------- +--R 4 --R Type: Expression(Integer) --E 227 @@ -2408,37 +2555,39 @@ r0345:= 1/2*x+1/4*x^2-1/2*log(1+x)+1/2*x^2*log((1+x)/x^2) a0345:= integrate(t0345,x) --R --R ---R 2 x + 1 2 ---R - 2log(x + 1) + 2x log(-----) + x + 2x ---R 2 ---R x ---R (117) --------------------------------------- ---R 4 ---R Type: Expression(Integer) +--R 2 x + 1 2 +--R - 2log(x + 1) + 2x log(-----) + x + 2x +--R 2 +--R x +--R (3) --------------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) --E 228 --S 229 of 460 m0345:= a0345-r0345 --R --R ---R (118) 0 ---R Type: Union(Expression(Integer),...) +--R (4) 0 +--R Type: Expression(Integer) --E 229 --S 230 of 460 d0345:= D(m0345,x) --R --R ---R (119) 0 +--R (5) 0 --R Type: Expression(Integer) --E 230 +)clear all + --S 231 of 460 t0346:= (a+b*x)^n*log(a+b*x) --R --R ---R n ---R (120) log(b x + a)(b x + a) +--R n +--R (1) log(b x + a)(b x + a) --R Type: Expression(Integer) --E 231 @@ -2446,11 +2595,11 @@ t0346:= (a+b*x)^n*log(a+b*x) r0346:= 1/b/(1+n)^2*(a+b*x)^(1+n)*(-1+log(a+b*x)+n*log(a+b*x)) --R --R ---R n + 1 ---R ((n + 1)log(b x + a) - 1)(b x + a) ---R (121) --------------------------------------- ---R 2 ---R b n + 2b n + b +--R n + 1 +--R ((n + 1)log(b x + a) - 1)(b x + a) +--R (2) --------------------------------------- +--R 2 +--R b n + 2b n + b --R Type: Expression(Integer) --E 232 @@ -2458,19 +2607,19 @@ r0346:= 1/b/(1+n)^2*(a+b*x)^(1+n)*(-1+log(a+b*x)+n*log(a+b*x)) a0346:= integrate(t0346,x) --R --R ---R n log(b x + a) ---R (((b n + b)x + a n + a)log(b x + a) - b x - a)%e ---R (122) -------------------------------------------------------------- ---R 2 ---R b n + 2b n + b ---R Type: Expression(Integer) +--R n log(b x + a) +--R (((b n + b)x + a n + a)log(b x + a) - b x - a)%e +--R (3) -------------------------------------------------------------- +--R 2 +--R b n + 2b n + b +--R Type: Union(Expression(Integer),...) --E 233 --S 234 of 460 m0346:= a0346-r0346 --R --R ---R (123) +--R (4) --R n log(b x + a) --R (((b n + b)x + a n + a)log(b x + a) - b x - a)%e --R + @@ -2479,14 +2628,14 @@ m0346:= a0346-r0346 --R / --R 2 --R b n + 2b n + b ---R Type: Union(Expression(Integer),...) +--R Type: Expression(Integer) --E 234 --S 235 of 460 d0346:= D(m0346,x) --R --R ---R (124) +--R (5) --R n log(b x + a) n + 1 --R ((b n + b)x + a n + a)log(b x + a)%e - (b x + a) --R + @@ -2497,15 +2646,17 @@ d0346:= D(m0346,x) --R Type: Expression(Integer) --E 235 +)clear all + --S 236 of 460 t0347:= log((a+b*x)/(c+d*x))/x --R --R ---R b x + a ---R log(-------) ---R d x + c ---R (125) ------------ ---R x +--R b x + a +--R log(-------) +--R d x + c +--R (1) ------------ +--R x --R Type: Expression(Integer) --E 236 @@ -2520,6 +2671,7 @@ r0347:= -log((b*c-a*d)/b/(c+d*x))*log((a+b*x)/(c+d*x))+_ --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -2533,12 +2685,12 @@ r0347:= -log((b*c-a*d)/b/(c+d*x))*log((a+b*x)/(c+d*x))+_ a0347:= integrate(t0347,x) --R --R ---R %R b + a ---R x log(--------) ---R ++ %R d + c ---R (126) | ------------- d%R ---R ++ %R ---R Type: Expression(Integer) +--R %R b + a +--R x log(--------) +--R ++ %R d + c +--R (2) | ------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) --E 238 --S 239 of 460 @@ -2549,16 +2701,18 @@ a0347:= integrate(t0347,x) --d0347:= D(m0347,x) --E 240 +)clear all + --S 241 of 460 t0348:= log((a+b*x)/(c+d*x))^2/x --R --R ---R b x + a 2 ---R log(-------) ---R d x + c ---R (127) ------------- ---R x ---R Type: Union(Expression(Integer),...) +--R b x + a 2 +--R log(-------) +--R d x + c +--R (1) ------------- +--R x +--R Type: Expression(Integer) --E 241 --S 242 of 460 @@ -2574,6 +2728,7 @@ r0348:= -log((b*c-a*d)/b/(c+d*x))*log((a+b*x)/(c+d*x))^2+_ --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -2587,12 +2742,12 @@ r0348:= -log((b*c-a*d)/b/(c+d*x))*log((a+b*x)/(c+d*x))^2+_ a0348:= integrate(t0348,x) --R --R ---R %R b + a 2 ---R x log(--------) ---R ++ %R d + c ---R (128) | -------------- d%R ---R ++ %R ---R Type: Expression(Integer) +--R %R b + a 2 +--R x log(--------) +--R ++ %R d + c +--R (2) | -------------- d%R +--R ++ %R +--R Type: Union(Expression(Integer),...) --E 243 --S 244 of 460 @@ -2603,29 +2758,31 @@ a0348:= integrate(t0348,x) --d0348:= D(m0348,x) --E 245 +)clear all + --S 246 of 460 t0349:= log(a*log(b*x^n)^p) --R --R ---R n p ---R (129) log(a log(b x ) ) ---R Type: Union(Expression(Integer),...) +--R n p +--R (1) log(a log(b x ) ) +--R Type: Expression(Integer) --E 246 --S 247 of 460 r0349:= -p*x*Ei(1/n*log(b*x^n))/((b*x^n)^(1/n))+x*log(a*log(b*x^n)^p) --R --R ---R 1 ---R - n ---R n n n p log(b x ) ---R x (b x ) log(a log(b x ) ) - p x Ei(---------) ---R n ---R (130) ---------------------------------------------- ---R 1 ---R - ---R n n ---R (b x ) +--R 1 +--R - n +--R n n n p log(b x ) +--R x (b x ) log(a log(b x ) ) - p x Ei(---------) +--R n +--R (2) ---------------------------------------------- +--R 1 +--R - +--R n n +--R (b x ) --R Type: Expression(Integer) --E 247 @@ -2633,11 +2790,11 @@ r0349:= -p*x*Ei(1/n*log(b*x^n))/((b*x^n)^(1/n))+x*log(a*log(b*x^n)^p) a0349:= integrate(t0349,x) --R --R ---R x ---R ++ n p ---R (131) | log(a log(b %R ) )d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ n p +--R (3) | log(a log(b %R ) )d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 248 --S 249 of 460 @@ -2648,13 +2805,15 @@ a0349:= integrate(t0349,x) --d0349:= D(m0349,x) --E 250 +)clear all + --S 251 of 460 t0350:= x^m*log(a*log(b*x)^p) --R --R ---R m p ---R (132) x log(a log(b x) ) ---R Type: Union(Expression(Integer),...) +--R m p +--R (1) x log(a log(b x) ) +--R Type: Expression(Integer) --E 251 --S 252 of 460 @@ -2662,10 +2821,10 @@ r0350:= -1/b/(1+m)*(p*x^m*(b*x)^(-m)*Ei((1+m)*log(b*x))-_ x^(1+m)*log(a*log(b*x)^p)*b) --R --R ---R m + 1 p m - m ---R b x log(a log(b x) ) - p x (b x) Ei((m + 1)log(b x)) ---R (133) ---------------------------------------------------------- ---R b m + b +--R m + 1 p m - m +--R b x log(a log(b x) ) - p x (b x) Ei((m + 1)log(b x)) +--R (2) ---------------------------------------------------------- +--R b m + b --R Type: Expression(Integer) --E 252 @@ -2673,11 +2832,11 @@ r0350:= -1/b/(1+m)*(p*x^m*(b*x)^(-m)*Ei((1+m)*log(b*x))-_ a0350:= integrate(t0350,x) --R --R ---R x ---R ++ m p ---R (134) | %R log(a log(%R b) )d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ m p +--R (3) | %R log(a log(%R b) )d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 253 --S 254 of 460 @@ -2688,13 +2847,15 @@ a0350:= integrate(t0350,x) --d0350:= D(m0350,x) --E 255 +)clear all + --S 256 of 460 t0351:= x^m*log(a*log(b*x^n)^p) --R --R ---R m n p ---R (135) x log(a log(b x ) ) ---R Type: Union(Expression(Integer),...) +--R m n p +--R (1) x log(a log(b x ) ) +--R Type: Expression(Integer) --E 256 --S 257 of 460 @@ -2702,13 +2863,13 @@ r0351:= 1/(1+m)*x^(1+m)*(-p*Ei((1+m)/n*log(b*x^n))*(b*x^n)^(-(1+m)/n)+_ log(a*log(b*x^n)^p)) --R --R ---R - m - 1 ---R ------- n ---R m + 1 n p m + 1 n n (m + 1)log(b x ) ---R x log(a log(b x ) ) - p x (b x ) Ei(----------------) ---R n ---R (136) ------------------------------------------------------------------- ---R m + 1 +--R - m - 1 +--R ------- n +--R m + 1 n p m + 1 n n (m + 1)log(b x ) +--R x log(a log(b x ) ) - p x (b x ) Ei(----------------) +--R n +--R (2) ------------------------------------------------------------------- +--R m + 1 --R Type: Expression(Integer) --E 257 @@ -2716,11 +2877,11 @@ r0351:= 1/(1+m)*x^(1+m)*(-p*Ei((1+m)/n*log(b*x^n))*(b*x^n)^(-(1+m)/n)+_ a0351:= integrate(t0351,x) --R --R ---R x ---R ++ m n p ---R (137) | %R log(a log(b %R ) )d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ m n p +--R (3) | %R log(a log(b %R ) )d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 258 --S 259 of 460 @@ -2731,15 +2892,17 @@ a0351:= integrate(t0351,x) --d0351:= D(m0351,x) --E 260 +)clear all + --S 261 of 460 t0352:= log(x)/(a+b*log(x))^(1/2) --R --R ---R log(x) ---R (138) --------------- ---R +------------+ ---R \|b log(x) + a ---R Type: Union(Expression(Integer),...) +--R log(x) +--R (1) --------------- +--R +------------+ +--R \|b log(x) + a +--R Type: Expression(Integer) --E 261 --S 262 of 460 @@ -2752,6 +2915,7 @@ r0352:= -1/2*(2*a+b)*%pi^(1/2)*erfi((a+b*log(x))^(1/2)/b^(1/2))/_ --R to learn if there is any operation containing " erfi " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named erfi --R with argument type(s) --R Expression(Integer) @@ -2764,6 +2928,7 @@ r0352:= -1/2*(2*a+b)*%pi^(1/2)*erfi((a+b*log(x))^(1/2)/b^(1/2))/_ a0352:= integrate(t0352,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R @@ -2779,14 +2944,16 @@ a0352:= integrate(t0352,x) --d0352:= D(m0352,x) --E 265 +)clear all + --S 266 of 460 t0353:= log(x)/(a-b*log(x))^(1/2) --R --R ---R log(x) ---R (139) ----------------- ---R +--------------+ ---R \|- b log(x) + a +--R log(x) +--R (1) ----------------- +--R +--------------+ +--R \|- b log(x) + a --R Type: Expression(Integer) --E 266 @@ -2795,15 +2962,15 @@ r0353:= -1/2*(2*a-b)*exp(1)^(a/b)*%pi^(1/2)*erf((a-b*log(x))^(1/2)/_ b^(1/2))/b^(3/2)-x*(a-b*log(x))^(1/2)/b --R --R ---R a ---R - +--------------+ ---R b +---+ \|- b log(x) + a +-+ +--------------+ ---R (b - 2a)%e \|%pi erf(-----------------) - 2x\|b \|- b log(x) + a ---R +-+ ---R \|b ---R (140) ----------------------------------------------------------------- ---R +-+ ---R 2b\|b +--R a +--R - +--------------+ +--R b +---+ \|- b log(x) + a +-+ +--------------+ +--R (b - 2a)%e \|%pi erf(-----------------) - 2x\|b \|- b log(x) + a +--R +-+ +--R \|b +--R (2) ----------------------------------------------------------------- +--R +-+ +--R 2b\|b --R Type: Expression(Integer) --E 267 @@ -2811,6 +2978,7 @@ r0353:= -1/2*(2*a-b)*exp(1)^(a/b)*%pi^(1/2)*erf((a-b*log(x))^(1/2)/_ a0353:= integrate(t0353,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R @@ -2826,14 +2994,16 @@ a0353:= integrate(t0353,x) --d0353:= D(m0353,x) --E 270 +)clear all + --S 271 of 460 t0354:= (A+B*log(x))/(a+b*log(x))^(1/2) --R --R ---R B log(x) + A ---R (141) --------------- ---R +------------+ ---R \|b log(x) + a +--R B log(x) + A +--R (1) --------------- +--R +------------+ +--R \|b log(x) + a --R Type: Expression(Integer) --E 271 @@ -2847,6 +3017,7 @@ r0354:= 1/2*(2*A*b-(2*a+b)*B)*%pi^(1/2)*erfi((a+b*log(x))^(1/2)/b^(1/2))/_ --R to learn if there is any operation containing " erfi " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named erfi --R with argument type(s) --R Expression(Integer) @@ -2859,6 +3030,7 @@ r0354:= 1/2*(2*A*b-(2*a+b)*B)*%pi^(1/2)*erfi((a+b*log(x))^(1/2)/b^(1/2))/_ a0354:= integrate(t0354,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R @@ -2874,14 +3046,16 @@ a0354:= integrate(t0354,x) --d0354:= D(m0354,x) --E 275 +)clear all + --S 276 of 460 t0355:= (A+B*log(x))/(a-b*log(x))^(1/2) --R --R ---R B log(x) + A ---R (142) ----------------- ---R +--------------+ ---R \|- b log(x) + a +--R B log(x) + A +--R (1) ----------------- +--R +--------------+ +--R \|- b log(x) + a --R Type: Expression(Integer) --E 276 @@ -2890,7 +3064,7 @@ r0355:= -1/2*(2*A*b+(2*a-b)*B)*exp(1)^(a/b)*%pi^(1/2)*_ erf((a-b*log(x))^(1/2)/b^(1/2))/b^(3/2)-B*x*(a-b*log(x))^(1/2)/b --R --R ---R (143) +--R (2) --R a --R - +--------------+ --R b +---+ \|- b log(x) + a +-+ +--------------+ @@ -2907,6 +3081,7 @@ r0355:= -1/2*(2*A*b+(2*a-b)*B)*exp(1)^(a/b)*%pi^(1/2)*_ a0355:= integrate(t0355,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R @@ -2922,11 +3097,13 @@ a0355:= integrate(t0355,x) --d0355:= D(m0355,x) --E 280 +)clear all + --S 281 of 460 t0356:= log(x)*sin(a+b*x) --R --R ---R (144) log(x)sin(b x + a) +--R (1) log(x)sin(b x + a) --R Type: Expression(Integer) --E 281 @@ -2934,9 +3111,9 @@ t0356:= log(x)*sin(a+b*x) r0356:= (cos(a)*Ci(b*x)-log(x)*cos(a+b*x)-sin(a)*Si(b*x))/b --R --R ---R - Si(b x)sin(a) - cos(b x + a)log(x) + Ci(b x)cos(a) ---R (145) ---------------------------------------------------- ---R b +--R - Si(b x)sin(a) - cos(b x + a)log(x) + Ci(b x)cos(a) +--R (2) ---------------------------------------------------- +--R b --R Type: Expression(Integer) --E 282 @@ -2944,11 +3121,11 @@ r0356:= (cos(a)*Ci(b*x)-log(x)*cos(a+b*x)-sin(a)*Si(b*x))/b a0356:= integrate(t0356,x) --R --R ---R x ---R ++ ---R (146) | log(%R)sin(%R b + a)d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ +--R (3) | log(%R)sin(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 283 --S 284 of 460 @@ -2959,13 +3136,15 @@ a0356:= integrate(t0356,x) --d0356:= D(m0356,x) --E 285 +)clear all + --S 286 of 460 t0357:= log(x)*sin(a+b*x)^2 --R --R ---R 2 ---R (147) log(x)sin(b x + a) ---R Type: Union(Expression(Integer),...) +--R 2 +--R (1) log(x)sin(b x + a) +--R Type: Expression(Integer) --E 286 --S 287 of 460 @@ -2973,7 +3152,7 @@ r0357:= -1/4*(2*b*x-Ci(2*b*x)*sin(2*a)-2*log(x)*b*x+2*log(x)*cos(a+b*x)*_ sin(a+b*x)-cos(2*a)*Si(2*b*x))/b --R --R ---R (148) +--R (2) --R - 2cos(b x + a)log(x)sin(b x + a) + Ci(2b x)sin(2a) + 2b x log(x) --R + --R Si(2b x)cos(2a) - 2b x @@ -2986,11 +3165,11 @@ r0357:= -1/4*(2*b*x-Ci(2*b*x)*sin(2*a)-2*log(x)*b*x+2*log(x)*cos(a+b*x)*_ a0357:= integrate(t0357,x) --R --R ---R x ---R ++ 2 ---R (149) | log(%R)sin(%R b + a) d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ 2 +--R (3) | log(%R)sin(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 288 --S 289 of 460 @@ -3001,13 +3180,15 @@ a0357:= integrate(t0357,x) --d0357:= D(m0357,x) --E 290 +)clear all + --S 291 of 460 t0358:= log(x)*sin(a+b*x)^3 --R --R ---R 3 ---R (150) log(x)sin(b x + a) ---R Type: Union(Expression(Integer),...) +--R 3 +--R (1) log(x)sin(b x + a) +--R Type: Expression(Integer) --E 291 --S 292 of 460 @@ -3015,7 +3196,7 @@ r0358:= 1/12*(9*cos(a)*Ci(b*x)-cos(3*a)*Ci(3*b*x)-12*log(x)*cos(a+b*x)+_ 4*log(x)*cos(a+b*x)^3-9*sin(a)*Si(b*x)+sin(3*a)*Si(3*b*x))/b --R --R ---R (151) +--R (2) --R Si(3b x)sin(3a) - 9Si(b x)sin(a) --R + --R 3 @@ -3029,11 +3210,11 @@ r0358:= 1/12*(9*cos(a)*Ci(b*x)-cos(3*a)*Ci(3*b*x)-12*log(x)*cos(a+b*x)+_ a0358:= integrate(t0358,x) --R --R ---R x ---R ++ 3 ---R (152) | log(%R)sin(%R b + a) d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ 3 +--R (3) | log(%R)sin(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 293 --S 294 of 460 @@ -3044,21 +3225,23 @@ a0358:= integrate(t0358,x) --d0358:= D(m0358,x) --E 295 +)clear all + --S 296 of 460 t0359:= log(x)*cos(a+b*x) --R --R ---R (153) cos(b x + a)log(x) ---R Type: Union(Expression(Integer),...) +--R (1) cos(b x + a)log(x) +--R Type: Expression(Integer) --E 296 --S 297 of 460 r0359:= -(Ci(b*x)*sin(a)-log(x)*sin(a+b*x)+cos(a)*Si(b*x))/b --R --R ---R log(x)sin(b x + a) - Ci(b x)sin(a) - Si(b x)cos(a) ---R (154) -------------------------------------------------- ---R b +--R log(x)sin(b x + a) - Ci(b x)sin(a) - Si(b x)cos(a) +--R (2) -------------------------------------------------- +--R b --R Type: Expression(Integer) --E 297 @@ -3066,11 +3249,11 @@ r0359:= -(Ci(b*x)*sin(a)-log(x)*sin(a+b*x)+cos(a)*Si(b*x))/b a0359:= integrate(t0359,x) --R --R ---R x ---R ++ ---R (155) | cos(%R b + a)log(%R)d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ +--R (3) | cos(%R b + a)log(%R)d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 298 --S 299 of 460 @@ -3081,13 +3264,15 @@ a0359:= integrate(t0359,x) --d0359:= D(m0359,x) --E 300 +)clear all + --S 301 of 460 t0360:= log(x)*cos(a+b*x)^2 --R --R ---R 2 ---R (156) cos(b x + a) log(x) ---R Type: Union(Expression(Integer),...) +--R 2 +--R (1) cos(b x + a) log(x) +--R Type: Expression(Integer) --E 301 --S 302 of 460 @@ -3095,7 +3280,7 @@ r0360:= 1/4*(-2*b*x-Ci(2*b*x)*sin(2*a)+2*log(x)*b*x+2*log(x)*cos(a+b*x)*_ sin(a+b*x)-cos(2*a)*Si(2*b*x))/b --R --R ---R (157) +--R (2) --R 2cos(b x + a)log(x)sin(b x + a) - Ci(2b x)sin(2a) + 2b x log(x) --R + --R - Si(2b x)cos(2a) - 2b x @@ -3108,11 +3293,11 @@ r0360:= 1/4*(-2*b*x-Ci(2*b*x)*sin(2*a)+2*log(x)*b*x+2*log(x)*cos(a+b*x)*_ a0360:= integrate(t0360,x) --R --R ---R x ---R ++ 2 ---R (158) | cos(%R b + a) log(%R)d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ 2 +--R (3) | cos(%R b + a) log(%R)d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 303 --S 304 of 460 @@ -3123,13 +3308,15 @@ a0360:= integrate(t0360,x) --d0360:= D(m0360,x) --E 305 +)clear all + --S 306 of 460 t0361:= log(x)*cos(a+b*x)^3 --R --R ---R 3 ---R (159) cos(b x + a) log(x) ---R Type: Union(Expression(Integer),...) +--R 3 +--R (1) cos(b x + a) log(x) +--R Type: Expression(Integer) --E 306 --S 307 of 460 @@ -3137,7 +3324,7 @@ r0361:= -1/12*(9*Ci(b*x)*sin(a)+Ci(3*b*x)*sin(3*a)-8*log(x)*sin(a+b*x)-_ 4*log(x)*sin(a+b*x)*cos(a+b*x)^2+9*cos(a)*Si(b*x)+cos(3*a)*Si(3*b*x))/b --R --R ---R (160) +--R (2) --R 2 --R (4cos(b x + a) + 8)log(x)sin(b x + a) - Ci(3b x)sin(3a) - 9Ci(b x)sin(a) --R + @@ -3151,11 +3338,11 @@ r0361:= -1/12*(9*Ci(b*x)*sin(a)+Ci(3*b*x)*sin(3*a)-8*log(x)*sin(a+b*x)-_ a0361:= integrate(t0361,x) --R --R ---R x ---R ++ 3 ---R (161) | cos(%R b + a) log(%R)d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ 3 +--R (3) | cos(%R b + a) log(%R)d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 308 --S 309 of 460 @@ -3166,12 +3353,14 @@ a0361:= integrate(t0361,x) --d0361:= D(m0361,x) --E 310 +)clear all + --S 311 of 460 t0362:= log(x)*sinh(a+b*x) --R --R ---R (162) log(x)sinh(b x + a) ---R Type: Union(Expression(Integer),...) +--R (1) log(x)sinh(b x + a) +--R Type: Expression(Integer) --E 311 --S 312 of 460 @@ -3183,6 +3372,7 @@ r0362:= (-cosh(a)*Chi(b*x)+log(x)*cosh(a+b*x)-sinh(a)*Shi(b*x))/b --R to learn if there is any operation containing " Chi " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named Chi --R with argument type(s) --R Polynomial(Integer) @@ -3195,11 +3385,11 @@ r0362:= (-cosh(a)*Chi(b*x)+log(x)*cosh(a+b*x)-sinh(a)*Shi(b*x))/b a0362:= integrate(t0362,x) --R --R ---R x ---R ++ ---R (163) | log(%R)sinh(%R b + a)d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ +--R (2) | log(%R)sinh(%R b + a)d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 313 --S 314 of 460 @@ -3210,13 +3400,15 @@ a0362:= integrate(t0362,x) --d0362:= D(m0362,x) --E 315 +)clear all + --S 316 of 460 t0363:= log(x)*sinh(a+b*x)^3 --R --R ---R 3 ---R (164) log(x)sinh(b x + a) ---R Type: Union(Expression(Integer),...) +--R 3 +--R (1) log(x)sinh(b x + a) +--R Type: Expression(Integer) --E 316 --S 317 of 460 @@ -3229,6 +3421,7 @@ r0363:= 1/12*(9*cosh(a)*Chi(b*x)-cosh(3*a)*Chi(3*b*x)-12*log(x)*cosh(a+b*x)+_ --R to learn if there is any operation containing " Chi " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named Chi --R with argument type(s) --R Polynomial(Integer) @@ -3241,11 +3434,11 @@ r0363:= 1/12*(9*cosh(a)*Chi(b*x)-cosh(3*a)*Chi(3*b*x)-12*log(x)*cosh(a+b*x)+_ a0363:= integrate(t0363,x) --R --R ---R x ---R ++ 3 ---R (165) | log(%R)sinh(%R b + a) d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ 3 +--R (2) | log(%R)sinh(%R b + a) d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 318 --S 319 of 460 @@ -3256,12 +3449,14 @@ a0363:= integrate(t0363,x) --d0363:= D(m0363,x) --E 320 +)clear all + --S 321 of 460 t0364:= log(x)*cosh(a+b*x) --R --R ---R (166) cosh(b x + a)log(x) ---R Type: Union(Expression(Integer),...) +--R (1) cosh(b x + a)log(x) +--R Type: Expression(Integer) --E 321 --S 322 of 460 @@ -3273,6 +3468,7 @@ r0364:= (-Chi(b*x)*sinh(a)+log(x)*sinh(a+b*x)-cosh(a)*Shi(b*x))/b --R to learn if there is any operation containing " Chi " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named Chi --R with argument type(s) --R Polynomial(Integer) @@ -3285,11 +3481,11 @@ r0364:= (-Chi(b*x)*sinh(a)+log(x)*sinh(a+b*x)-cosh(a)*Shi(b*x))/b a0364:= integrate(t0364,x) --R --R ---R x ---R ++ ---R (167) | cosh(%R b + a)log(%R)d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ +--R (2) | cosh(%R b + a)log(%R)d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 323 --S 324 of 460 @@ -3300,13 +3496,15 @@ a0364:= integrate(t0364,x) --d0364:= D(m0364,x) --E 325 +)clear all + --S 326 of 460 t0365:= log(x)*cosh(a+b*x)^3 --R --R ---R 3 ---R (168) cosh(b x + a) log(x) ---R Type: Union(Expression(Integer),...) +--R 3 +--R (1) cosh(b x + a) log(x) +--R Type: Expression(Integer) --E 326 --S 327 of 460 @@ -3320,6 +3518,7 @@ r0365:= 1/12/b*(-9*Chi(b*x)*sinh(a)-Chi(3*b*x)*sinh(3*a)+8*log(x)*_ --R to learn if there is any operation containing " Chi " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named Chi --R with argument type(s) --R Polynomial(Integer) @@ -3332,11 +3531,11 @@ r0365:= 1/12/b*(-9*Chi(b*x)*sinh(a)-Chi(3*b*x)*sinh(3*a)+8*log(x)*_ a0365:= integrate(t0365,x) --R --R ---R x ---R ++ 3 ---R (169) | cosh(%R b + a) log(%R)d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ 3 +--R (2) | cosh(%R b + a) log(%R)d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 328 --S 329 of 460 @@ -3347,14 +3546,16 @@ a0365:= integrate(t0365,x) --d0365:= D(m0365,x) --E 330 +)clear all + --S 331 of 460 t0366:= x*(4+x^2)^(1/2)*log(x) --R --R ---R +------+ ---R | 2 ---R (170) x log(x)\|x + 4 ---R Type: Union(Expression(Integer),...) +--R +------+ +--R | 2 +--R (1) x log(x)\|x + 4 +--R Type: Expression(Integer) --E 331 --S 332 of 460 @@ -3362,13 +3563,13 @@ r0366:= -4/3*(4+x^2)^(1/2)-1/9*(4+x^2)^(3/2)+8/3*atanh(1/2*(4+x^2)^(1/2))+_ 1/3*(4+x^2)^(3/2)*log(x) --R --R ---R +------+ ---R | 2 +------+ ---R \|x + 4 2 2 | 2 ---R 24atanh(---------) + ((3x + 12)log(x) - x - 16)\|x + 4 ---R 2 ---R (171) ---------------------------------------------------------- ---R 9 +--R +------+ +--R | 2 +------+ +--R \|x + 4 2 2 | 2 +--R 24atanh(---------) + ((3x + 12)log(x) - x - 16)\|x + 4 +--R 2 +--R (2) ---------------------------------------------------------- +--R 9 --R Type: Expression(Integer) --E 332 @@ -3376,7 +3577,7 @@ r0366:= -4/3*(4+x^2)^(1/2)-1/9*(4+x^2)^(3/2)+8/3*atanh(1/2*(4+x^2)^(1/2))+_ a0366:= integrate(t0366,x) --R --R ---R (172) +--R (3) --R +------+ +------+ --R 2 | 2 3 | 2 --R ((24x + 24)\|x + 4 - 24x - 72x)log(\|x + 4 - x + 2) @@ -3395,41 +3596,42 @@ a0366:= integrate(t0366,x) --R +------+ --R 2 | 2 3 --R (9x + 9)\|x + 4 - 9x - 27x ---R Type: Expression(Integer) +--R Type: Union(Expression(Integer),...) --E 333 --S 334 of 460 m0366:= a0366-r0366 --R --R ---R (173) ---R +------+ ---R +------+ +------+ | 2 ---R | 2 | 2 \|x + 4 ---R 8log(\|x + 4 - x + 2) - 8log(\|x + 4 - x - 2) - 8atanh(---------) ---R 2 ---R --------------------------------------------------------------------- ---R 3 ---R Type: Union(Expression(Integer),...) +--R +------+ +--R +------+ +------+ | 2 +--R | 2 | 2 \|x + 4 +--R 8log(\|x + 4 - x + 2) - 8log(\|x + 4 - x - 2) - 8atanh(---------) +--R 2 +--R (4) --------------------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) --E 334 --S 335 of 460 d0366:= D(m0366,x) --R --R ---R (174) 0 +--R (5) 0 --R Type: Expression(Integer) --E 335 +)clear all + --S 336 of 460 t0367:= x*log(x)/(-1+x^2)^(1/2) --R --R ---R x log(x) ---R (175) --------- ---R +------+ ---R | 2 ---R \|x - 1 +--R x log(x) +--R (1) --------- +--R +------+ +--R | 2 +--R \|x - 1 --R Type: Expression(Integer) --E 336 @@ -3437,9 +3639,9 @@ t0367:= x*log(x)/(-1+x^2)^(1/2) r0367:= -(-1+x^2)^(1/2)+atan((-1+x^2)^(1/2))+(-1+x^2)^(1/2)*log(x) --R --R ---R +------+ +------+ ---R | 2 | 2 ---R (176) atan(\|x - 1 ) + (log(x) - 1)\|x - 1 +--R +------+ +------+ +--R | 2 | 2 +--R (2) atan(\|x - 1 ) + (log(x) - 1)\|x - 1 --R Type: Expression(Integer) --E 337 @@ -3447,7 +3649,7 @@ r0367:= -(-1+x^2)^(1/2)+atan((-1+x^2)^(1/2))+(-1+x^2)^(1/2)*log(x) a0367:= integrate(t0367,x) --R --R ---R (177) +--R (3) --R +------+ +------+ +------+ --R | 2 | 2 | 2 --R (2\|x - 1 - 2x)atan(\|x - 1 - x) + (- x log(x) + x)\|x - 1 @@ -3458,32 +3660,34 @@ a0367:= integrate(t0367,x) --R +------+ --R | 2 --R \|x - 1 - x ---R Type: Expression(Integer) +--R Type: Union(Expression(Integer),...) --E 338 --S 339 of 460 m0367:= a0367-r0367 --R --R ---R +------+ +------+ ---R | 2 | 2 ---R (178) - atan(\|x - 1 ) + 2atan(\|x - 1 - x) ---R Type: Union(Expression(Integer),...) +--R +------+ +------+ +--R | 2 | 2 +--R (4) - atan(\|x - 1 ) + 2atan(\|x - 1 - x) +--R Type: Expression(Integer) --E 339 --S 340 of 460 d0367:= D(m0367,x) --R --R ---R (179) 0 +--R (5) 0 --R Type: Expression(Integer) --E 340 +)clear all + --S 341 of 460 t0368:= log(cos(x))*tan(x) --R --R ---R (180) tan(x)log(cos(x)) +--R (1) tan(x)log(cos(x)) --R Type: Expression(Integer) --E 341 @@ -3491,10 +3695,10 @@ t0368:= log(cos(x))*tan(x) r0368:= -1/2*log(cos(x))^2 --R --R ---R 2 ---R log(cos(x)) ---R (181) - ------------ ---R 2 +--R 2 +--R log(cos(x)) +--R (2) - ------------ +--R 2 --R Type: Expression(Integer) --E 342 @@ -3502,34 +3706,36 @@ r0368:= -1/2*log(cos(x))^2 a0368:= integrate(t0368,x) --R --R ---R 2 ---R log(cos(x)) ---R (182) - ------------ ---R 2 ---R Type: Expression(Integer) +--R 2 +--R log(cos(x)) +--R (3) - ------------ +--R 2 +--R Type: Union(Expression(Integer),...) --E 343 --S 344 of 460 m0368:= a0368-r0368 --R --R ---R (183) 0 ---R Type: Union(Expression(Integer),...) +--R (4) 0 +--R Type: Expression(Integer) --E 344 --S 345 of 460 d0368:= D(m0368,x) --R --R ---R (184) 0 +--R (5) 0 --R Type: Expression(Integer) --E 345 +)clear all + --S 346 of 460 t0369:= cos(x)*log(cos(x)) --R --R ---R (185) cos(x)log(cos(x)) +--R (1) cos(x)log(cos(x)) --R Type: Expression(Integer) --E 346 @@ -3537,7 +3743,7 @@ t0369:= cos(x)*log(cos(x)) r0369:= atanh(sin(x))-sin(x)+log(cos(x))*sin(x) --R --R ---R (186) sin(x)log(cos(x)) + atanh(sin(x)) - sin(x) +--R (2) sin(x)log(cos(x)) + atanh(sin(x)) - sin(x) --R Type: Expression(Integer) --E 347 @@ -3545,36 +3751,38 @@ r0369:= atanh(sin(x))-sin(x)+log(cos(x))*sin(x) a0369:= integrate(t0369,x) --R --R ---R log(sin(x) + 1) - log(sin(x) - 1) + 2sin(x)log(cos(x)) - 2sin(x) ---R (187) ---------------------------------------------------------------- ---R 2 ---R Type: Expression(Integer) +--R log(sin(x) + 1) - log(sin(x) - 1) + 2sin(x)log(cos(x)) - 2sin(x) +--R (3) ---------------------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) --E 348 --S 349 of 460 m0369:= a0369-r0369 --R --R ---R log(sin(x) + 1) - log(sin(x) - 1) - 2atanh(sin(x)) ---R (188) -------------------------------------------------- ---R 2 ---R Type: Union(Expression(Integer),...) +--R log(sin(x) + 1) - log(sin(x) - 1) - 2atanh(sin(x)) +--R (4) -------------------------------------------------- +--R 2 +--R Type: Expression(Integer) --E 349 --S 350 of 460 d0369:= D(m0369,x) --R --R ---R (189) 0 +--R (5) 0 --R Type: Expression(Integer) --E 350 +)clear all + --S 351 of 460 t0370:= log(sin(x))*sin(x)^2 --R --R ---R 2 ---R (190) sin(x) log(sin(x)) +--R 2 +--R (1) sin(x) log(sin(x)) --R Type: Expression(Integer) --E 351 @@ -3589,6 +3797,7 @@ r0370:= 1/4*x+1/4*%i*x^2-1/2*x*log(1-exp(1)^(2*%i*x))+_ --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -3602,11 +3811,11 @@ r0370:= 1/4*x+1/4*%i*x^2-1/2*x*log(1-exp(1)^(2*%i*x))+_ a0370:= integrate(t0370,x) --R --R ---R x ---R ++ 2 ---R (191) | sin(%R) log(sin(%R))d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ 2 +--R (2) | sin(%R) log(sin(%R))d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 353 --S 354 of 460 @@ -3617,13 +3826,15 @@ a0370:= integrate(t0370,x) --d0370:= D(m0370,x) --E 355 +)clear all + --S 356 of 460 t0371:= log(sin(x))*sin(x)^3 --R --R ---R 3 ---R (192) sin(x) log(sin(x)) ---R Type: Union(Expression(Integer),...) +--R 3 +--R (1) sin(x) log(sin(x)) +--R Type: Expression(Integer) --E 356 --S 357 of 460 @@ -3631,10 +3842,10 @@ r0371:= -2/3*atanh(cos(x))+2/3*cos(x)-1/9*cos(x)^3-_ 1/3*cos(x)*(3-cos(x)^2)*log(sin(x)) --R --R ---R 3 3 ---R (3cos(x) - 9cos(x))log(sin(x)) - 6atanh(cos(x)) - cos(x) + 6cos(x) ---R (193) -------------------------------------------------------------------- ---R 9 +--R 3 3 +--R (3cos(x) - 9cos(x))log(sin(x)) - 6atanh(cos(x)) - cos(x) + 6cos(x) +--R (2) -------------------------------------------------------------------- +--R 9 --R Type: Expression(Integer) --E 357 @@ -3642,7 +3853,7 @@ r0371:= -2/3*atanh(cos(x))+2/3*cos(x)-1/9*cos(x)^3-_ a0371:= integrate(t0371,x) --R --R ---R (194) +--R (3) --R 3 --R (3cos(x) - 9cos(x))log(sin(x)) - 3log(cos(x) + 1) + 3log(cos(x) - 1) --R + @@ -3650,7 +3861,7 @@ a0371:= integrate(t0371,x) --R - cos(x) + 6cos(x) --R / --R 9 ---R Type: Expression(Integer) +--R Type: Union(Expression(Integer),...) --E 358 --S 359 of 460 @@ -3661,13 +3872,15 @@ a0371:= integrate(t0371,x) --d0371:= D(m0371,x) --E 360 +)clear all + --S 361 of 460 t0372:= log(sin(x^(1/2))) --R --R ---R +-+ ---R (195) log(sin(\|x )) ---R Type: Union(Expression(Integer),...) +--R +-+ +--R (1) log(sin(\|x )) +--R Type: Expression(Integer) --E 361 --S 362 of 460 @@ -3681,6 +3894,7 @@ r0372:= 1/3*%i*x^(3/2)-x*log(1-exp(2*%i*x^(1/2)))+x*log(sin(x^(1/2)))+_ --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -3694,11 +3908,11 @@ r0372:= 1/3*%i*x^(3/2)-x*log(1-exp(2*%i*x^(1/2)))+x*log(sin(x^(1/2)))+_ a0372:= integrate(t0372,x) --R --R ---R x ---R ++ +--+ ---R (196) | log(sin(\|%R ))d%R ---R ++ ---R Type: Expression(Integer) +--R x +--R ++ +--+ +--R (2) | log(sin(\|%R ))d%R +--R ++ +--R Type: Union(Expression(Integer),...) --E 363 --S 364 of 460 @@ -3709,20 +3923,22 @@ a0372:= integrate(t0372,x) --d0372:= D(m0372,x) --E 365 +)clear all + --S 366 of 460 t0373:= log(sin(x))*csc(x)^2 --R --R ---R 2 ---R (197) csc(x) log(sin(x)) ---R Type: Union(Expression(Integer),...) +--R 2 +--R (1) csc(x) log(sin(x)) +--R Type: Expression(Integer) --E 366 --S 367 of 460 r0373:= -x-cot(x)-cot(x)*log(sin(x)) --R --R ---R (198) - cot(x)log(sin(x)) - cot(x) - x +--R (2) - cot(x)log(sin(x)) - cot(x) - x --R Type: Expression(Integer) --E 367 @@ -3730,19 +3946,19 @@ r0373:= -x-cot(x)-cot(x)*log(sin(x)) a0373:= integrate(t0373,x) --R --R ---R 2 ---R cos(x)sin(x)log(sin(x)) + cos(x)sin(x) - x cos(x) + x ---R (199) ------------------------------------------------------ ---R 2 ---R cos(x) - 1 ---R Type: Expression(Integer) +--R 2 +--R cos(x)sin(x)log(sin(x)) + cos(x)sin(x) - x cos(x) + x +--R (3) ------------------------------------------------------ +--R 2 +--R cos(x) - 1 +--R Type: Union(Expression(Integer),...) --E 368 --S 369 of 460 m0373:= a0373-r0373 --R --R ---R (200) +--R (4) --R 2 --R (cos(x)sin(x) + (cos(x) - 1)cot(x))log(sin(x)) + cos(x)sin(x) --R + @@ -3751,14 +3967,14 @@ m0373:= a0373-r0373 --R / --R 2 --R cos(x) - 1 ---R Type: Union(Expression(Integer),...) +--R Type: Expression(Integer) --E 369 --S 370 of 460 d0373:= D(m0373,x) --R --R ---R (201) +--R (5) --R 2 3 --R (cos(x) + 1)sin(x) --R + @@ -3781,14 +3997,16 @@ d0373:= D(m0373,x) --R Type: Expression(Integer) --E 370 +)clear all + --S 371 of 460 t0374:= x*log(x)/(a+b*x+c*x^2) --R --R ---R x log(x) ---R (202) -------------- ---R 2 ---R c x + b x + a +--R x log(x) +--R (1) -------------- +--R 2 +--R c x + b x + a --R Type: Expression(Integer) --E 371 @@ -3808,6 +4026,7 @@ r0374:= 1/2*(1-b/(b^2-4*a*c)^(1/2))*log(x)*_ --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -3821,12 +4040,12 @@ r0374:= 1/2*(1-b/(b^2-4*a*c)^(1/2))*log(x)*_ a0374:= integrate(t0374,x) --R --R ---R x ---R ++ %R log(%R) ---R (203) | --------------- d%R ---R ++ 2 ---R %R c + %R b + a ---R Type: Expression(Integer) +--R x +--R ++ %R log(%R) +--R (2) | --------------- d%R +--R ++ 2 +--R %R c + %R b + a +--R Type: Union(Expression(Integer),...) --E 373 --S 374 of 460 @@ -3837,16 +4056,18 @@ a0374:= integrate(t0374,x) --d0374:= D(m0374,x) --E 375 +)clear all + --S 376 of 460 t0375:= x^2*log(x)/(a+b*x+c*x^2) --R --R ---R 2 ---R x log(x) ---R (204) -------------- ---R 2 ---R c x + b x + a ---R Type: Union(Expression(Integer),...) +--R 2 +--R x log(x) +--R (1) -------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) --E 376 --S 377 of 460 @@ -3866,6 +4087,7 @@ r0375:= -x/c+x*log(x)/c+1/4*(b-(b^2-4*a*c)^(1/2))^2*log(x)*_ --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -3879,12 +4101,12 @@ r0375:= -x/c+x*log(x)/c+1/4*(b-(b^2-4*a*c)^(1/2))^2*log(x)*_ a0375:= integrate(t0375,x) --R --R ---R x 2 ---R ++ %R log(%R) ---R (205) | --------------- d%R ---R ++ 2 ---R %R c + %R b + a ---R Type: Expression(Integer) +--R x 2 +--R ++ %R log(%R) +--R (2) | --------------- d%R +--R ++ 2 +--R %R c + %R b + a +--R Type: Union(Expression(Integer),...) --E 378 --S 379 of 460 @@ -3895,15 +4117,17 @@ a0375:= integrate(t0375,x) --d0375:= D(m0375,x) --E 380 +)clear all + --S 381 of 460 t0376:= log(x)/x^2/(a+b*x+c*x^2) --R --R ---R log(x) ---R (206) ------------------ ---R 4 3 2 ---R c x + b x + a x ---R Type: Union(Expression(Integer),...) +--R log(x) +--R (1) ------------------ +--R 4 3 2 +--R c x + b x + a x +--R Type: Expression(Integer) --E 381 --S 382 of 460 @@ -3928,6 +4152,7 @@ r0376:= -2*c/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/x+_ --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -3941,12 +4166,12 @@ r0376:= -2*c/(b^2-4*a*c)^(1/2)/(b-(b^2-4*a*c)^(1/2))/x+_ a0376:= integrate(t0376,x) --R --R ---R x ---R ++ log(%R) ---R (207) | ------------------ d%R ---R ++ 4 3 2 ---R %R c + %R b + %R a ---R Type: Expression(Integer) +--R x +--R ++ log(%R) +--R (2) | ------------------ d%R +--R ++ 4 3 2 +--R %R c + %R b + %R a +--R Type: Union(Expression(Integer),...) --E 383 --S 384 of 460 @@ -3957,25 +4182,27 @@ a0376:= integrate(t0376,x) --d0376:= D(m0376,x) --E 385 +)clear all + --S 386 of 460 t0377:= (2-log(x))*(3+log(x))^2/x --R --R ---R 3 2 ---R - log(x) - 4log(x) + 3log(x) + 18 ---R (208) ----------------------------------- ---R x ---R Type: Union(Expression(Integer),...) +--R 3 2 +--R - log(x) - 4log(x) + 3log(x) + 18 +--R (1) ----------------------------------- +--R x +--R Type: Expression(Integer) --E 386 --S 387 of 460 r0377:= -1/12*(3+log(x))^3*(-11+3*log(x)) --R --R ---R 4 3 2 ---R - 3log(x) - 16log(x) + 18log(x) + 216log(x) + 297 ---R (209) ---------------------------------------------------- ---R 12 +--R 4 3 2 +--R - 3log(x) - 16log(x) + 18log(x) + 216log(x) + 297 +--R (2) ---------------------------------------------------- +--R 12 --R Type: Expression(Integer) --E 387 @@ -3983,39 +4210,41 @@ r0377:= -1/12*(3+log(x))^3*(-11+3*log(x)) a0377:= integrate(t0377,x) --R --R ---R 4 3 2 ---R - 3log(x) - 16log(x) + 18log(x) + 216log(x) ---R (210) ---------------------------------------------- ---R 12 ---R Type: Expression(Integer) +--R 4 3 2 +--R - 3log(x) - 16log(x) + 18log(x) + 216log(x) +--R (3) ---------------------------------------------- +--R 12 +--R Type: Union(Expression(Integer),...) --E 388 --S 389 of 460 m0377:= a0377-r0377 --R --R ---R 99 ---R (211) - -- ---R 4 ---R Type: Union(Expression(Integer),...) +--R 99 +--R (4) - -- +--R 4 +--R Type: Expression(Integer) --E 389 --S 390 of 460 d0377:= D(m0377,x) --R --R ---R (212) 0 +--R (5) 0 --R Type: Expression(Integer) --E 390 +)clear all + --S 391 of 460 t0378:= (1+log(x))^(1/2)/x/log(x) --R --R ---R +----------+ ---R \|log(x) + 1 ---R (213) ------------- ---R x log(x) +--R +----------+ +--R \|log(x) + 1 +--R (1) ------------- +--R x log(x) --R Type: Expression(Integer) --E 391 @@ -4023,8 +4252,8 @@ t0378:= (1+log(x))^(1/2)/x/log(x) r0378:= -2*atanh((1+log(x))^(1/2))+2*(1+log(x))^(1/2) --R --R ---R +----------+ +----------+ ---R (214) - 2atanh(\|log(x) + 1 ) + 2\|log(x) + 1 +--R +----------+ +----------+ +--R (2) - 2atanh(\|log(x) + 1 ) + 2\|log(x) + 1 --R Type: Expression(Integer) --E 392 @@ -4032,37 +4261,39 @@ r0378:= -2*atanh((1+log(x))^(1/2))+2*(1+log(x))^(1/2) a0378:= integrate(t0378,x) --R --R ---R +----------+ +----------+ +----------+ ---R (215) - log(\|log(x) + 1 + 1) + log(\|log(x) + 1 - 1) + 2\|log(x) + 1 ---R Type: Expression(Integer) +--R +----------+ +----------+ +----------+ +--R (3) - log(\|log(x) + 1 + 1) + log(\|log(x) + 1 - 1) + 2\|log(x) + 1 +--R Type: Union(Expression(Integer),...) --E 393 --S 394 of 460 m0378:= a0378-r0378 --R --R ---R (216) +--R (4) --R +----------+ +----------+ +----------+ --R - log(\|log(x) + 1 + 1) + log(\|log(x) + 1 - 1) + 2atanh(\|log(x) + 1 ) ---R Type: Union(Expression(Integer),...) +--R Type: Expression(Integer) --E 394 --S 395 of 460 d0378:= D(m0378,x) --R --R ---R (217) 0 +--R (5) 0 --R Type: Expression(Integer) --E 395 +)clear all + --S 396 of 460 t0379:= (log(a*x^n)^2)^p/x --R --R ---R n 2p ---R log(a x ) ---R (218) ----------- ---R x +--R n 2p +--R log(a x ) +--R (1) ----------- +--R x --R Type: Expression(Integer) --E 396 @@ -4070,10 +4301,10 @@ t0379:= (log(a*x^n)^2)^p/x r0379:= log(a*x^n)*(log(a*x^n)^2)^p/n/(1+2*p) --R --R ---R n n 2p ---R log(a x )log(a x ) ---R (219) -------------------- ---R 2n p + n +--R n n 2p +--R log(a x )log(a x ) +--R (2) -------------------- +--R 2n p + n --R Type: Expression(Integer) --E 397 @@ -4081,30 +4312,30 @@ r0379:= log(a*x^n)*(log(a*x^n)^2)^p/n/(1+2*p) a0379:= integrate(t0379,x) --R --R ---R 2p log(n log(x) + log(a)) ---R (n log(x) + log(a))%e ---R (220) ---------------------------------------------- ---R 2n p + n ---R Type: Expression(Integer) +--R 2p log(n log(x) + log(a)) +--R (n log(x) + log(a))%e +--R (3) ---------------------------------------------- +--R 2n p + n +--R Type: Union(Expression(Integer),...) --E 398 --S 399 of 460 m0379:= a0379-r0379 --R --R ---R (221) +--R (4) --R n n 2p 2p log(n log(x) + log(a)) --R - log(a x )log(a x ) + (n log(x) + log(a))%e --R ----------------------------------------------------------------------- --R 2n p + n ---R Type: Union(Expression(Integer),...) +--R Type: Expression(Integer) --E 399 --S 400 of 460 d0379:= D(m0379,x) --R --R ---R (222) +--R (5) --R n - 1 n 2p n - 1 n n 2p - 1 --R - x x log(a x ) - 2p x x log(a x )log(a x ) --R + @@ -4116,14 +4347,16 @@ d0379:= D(m0379,x) --R Type: Expression(Integer) --E 400 +)clear all + --S 401 of 460 t0380:= (log(a*x^n)^m)^p/x --R --R ---R n m p ---R log(a x ) ---R (223) ------------ ---R x +--R n m p +--R log(a x ) +--R (1) ------------ +--R x --R Type: Expression(Integer) --E 401 @@ -4131,10 +4364,10 @@ t0380:= (log(a*x^n)^m)^p/x r0380:= log(a*x^n)*(log(a*x^n)^m)^p/n/(1+m*p) --R --R ---R n n m p ---R log(a x )log(a x ) ---R (224) --------------------- ---R m n p + n +--R n n m p +--R log(a x )log(a x ) +--R (2) --------------------- +--R m n p + n --R Type: Expression(Integer) --E 402 @@ -4142,30 +4375,30 @@ r0380:= log(a*x^n)*(log(a*x^n)^m)^p/n/(1+m*p) a0380:= integrate(t0380,x) --R --R ---R m p log(n log(x) + log(a)) ---R (n log(x) + log(a))%e ---R (225) ----------------------------------------------- ---R m n p + n ---R Type: Expression(Integer) +--R m p log(n log(x) + log(a)) +--R (n log(x) + log(a))%e +--R (3) ----------------------------------------------- +--R m n p + n +--R Type: Union(Expression(Integer),...) --E 403 --S 404 of 460 m0380:= a0380-r0380 --R --R ---R (226) +--R (4) --R n n m p m p log(n log(x) + log(a)) --R - log(a x )log(a x ) + (n log(x) + log(a))%e --R ------------------------------------------------------------------------- --R m n p + n ---R Type: Union(Expression(Integer),...) +--R Type: Expression(Integer) --E 404 --S 405 of 460 d0380:= D(m0380,x) --R --R ---R (227) +--R (5) --R n - 1 n m p n - 1 n n m p - 1 --R - x x log(a x ) - m p x x log(a x )log(a x ) --R + @@ -4177,15 +4410,17 @@ d0380:= D(m0380,x) --R Type: Expression(Integer) --E 405 +)clear all + --S 406 of 460 t0381:= (log(a*x^n)^2)^(1/2)/x --R --R ---R +----------+ ---R | n 2 ---R \|log(a x ) ---R (228) ------------- ---R x +--R +----------+ +--R | n 2 +--R \|log(a x ) +--R (1) ------------- +--R x --R Type: Expression(Integer) --E 406 @@ -4198,6 +4433,7 @@ r0381:= 1/2*log(a*x^n)^2*csgn(log(a*x^n))/n --R to learn if there is any operation containing " csgn " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named csgn --R with argument type(s) --R Expression(Integer) @@ -4210,42 +4446,44 @@ r0381:= 1/2*log(a*x^n)^2*csgn(log(a*x^n))/n a0381:= integrate(t0381,x) --R --R ---R 2 ---R n log(x) + 2log(a)log(x) ---R (229) ------------------------- ---R 2 ---R Type: Expression(Integer) +--R 2 +--R n log(x) + 2log(a)log(x) +--R (2) ------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) --E 408 --S 409 of 460 m0381:= a0381-r0381 --R --R ---R 2 ---R n log(x) + 2log(a)log(x) - 2r0381 ---R (230) ---------------------------------- ---R 2 ---R Type: Union(Expression(Integer),...) +--R 2 +--R n log(x) + 2log(a)log(x) - 2r0381 +--R (3) ---------------------------------- +--R 2 +--R Type: Expression(Integer) --E 409 --S 410 of 460 d0381:= D(m0381,x) --R --R ---R n log(x) + log(a) ---R (231) ----------------- ---R x +--R n log(x) + log(a) +--R (4) ----------------- +--R x --R Type: Expression(Integer) --E 410 +)clear all + --S 411 of 460 t0382:= (b*log(a*x^n)^m)^p/x --R --R ---R n m p ---R (b log(a x ) ) ---R (232) --------------- ---R x +--R n m p +--R (b log(a x ) ) +--R (1) --------------- +--R x --R Type: Expression(Integer) --E 411 @@ -4253,10 +4491,10 @@ t0382:= (b*log(a*x^n)^m)^p/x r0382:= log(a*x^n)*(b*log(a*x^n)^m)^p/n/(1+m*p) --R --R ---R n n m p ---R log(a x )(b log(a x ) ) ---R (233) ------------------------ ---R m n p + n +--R n n m p +--R log(a x )(b log(a x ) ) +--R (2) ------------------------ +--R m n p + n --R Type: Expression(Integer) --E 412 @@ -4264,18 +4502,18 @@ r0382:= log(a*x^n)*(b*log(a*x^n)^m)^p/n/(1+m*p) a0382:= integrate(t0382,x) --R --R ---R m p log(n log(x) + log(a)) + p log(b) ---R (n log(x) + log(a))%e ---R (234) ---------------------------------------------------------- ---R m n p + n ---R Type: Expression(Integer) +--R m p log(n log(x) + log(a)) + p log(b) +--R (n log(x) + log(a))%e +--R (3) ---------------------------------------------------------- +--R m n p + n +--R Type: Union(Expression(Integer),...) --E 413 --S 414 of 460 m0382:= a0382-r0382 --R --R ---R (235) +--R (4) --R n n m p --R - log(a x )(b log(a x ) ) --R + @@ -4283,14 +4521,14 @@ m0382:= a0382-r0382 --R (n log(x) + log(a))%e --R / --R m n p + n ---R Type: Union(Expression(Integer),...) +--R Type: Expression(Integer) --E 414 --S 415 of 460 d0382:= D(m0382,x) --R --R ---R (236) +--R (5) --R n - 1 n m p --R - x x (b log(a x ) ) --R + @@ -4305,15 +4543,17 @@ d0382:= D(m0382,x) --R Type: Expression(Integer) --E 415 +)clear all + --S 416 of 460 t0383:= 1/(-log(a*x^2))^(1/2) --R --R ---R 1 ---R (237) -------------- ---R +-----------+ ---R | 2 ---R \|- log(a x ) +--R 1 +--R (1) -------------- +--R +-----------+ +--R | 2 +--R \|- log(a x ) --R Type: Expression(Integer) --E 416 @@ -4322,15 +4562,15 @@ r0383:= -1/2*2^(1/2)*%pi^(1/2)*x*erf(1/2*(-log(a*x^2))^(1/2)*2^(1/2))/_ (a*x^2)^(1/2) --R --R ---R +-----------+ ---R +-+ | 2 ---R +-+ +---+ \|2 \|- log(a x ) ---R x\|2 \|%pi erf(------------------) ---R 2 ---R (238) - ---------------------------------- ---R +----+ ---R | 2 ---R 2\|a x +--R +-----------+ +--R +-+ | 2 +--R +-+ +---+ \|2 \|- log(a x ) +--R x\|2 \|%pi erf(------------------) +--R 2 +--R (2) - ---------------------------------- +--R +----+ +--R | 2 +--R 2\|a x --R Type: Expression(Integer) --E 417 @@ -4338,6 +4578,7 @@ r0383:= -1/2*2^(1/2)*%pi^(1/2)*x*erf(1/2*(-log(a*x^2))^(1/2)*2^(1/2))/_ a0383:= integrate(t0383,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R @@ -4353,17 +4594,19 @@ a0383:= integrate(t0383,x) --d0383:= D(m0383,x) --E 420 +)clear all + --S 421 of 460 t0384:= 1/(-log(a/x^2))^(1/2) --R --R ---R 1 ---R (239) ------------ ---R +---------+ ---R | a ---R |- log(--) ---R | 2 ---R \| x +--R 1 +--R (1) ------------ +--R +---------+ +--R | a +--R |- log(--) +--R | 2 +--R \| x --R Type: Expression(Integer) --E 421 @@ -4377,6 +4620,7 @@ r0384:= 1/2*2^(1/2)*%pi^(1/2)*(a/x^2)^(1/2)*x*_ --R to learn if there is any operation containing " erfi " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named erfi --R with argument type(s) --R Expression(Integer) @@ -4389,6 +4633,7 @@ r0384:= 1/2*2^(1/2)*%pi^(1/2)*(a/x^2)^(1/2)*x*_ a0384:= integrate(t0384,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R @@ -4404,15 +4649,17 @@ a0384:= integrate(t0384,x) --d0384:= D(m0384,x) --E 425 +)clear all + --S 426 of 460 t0385:= 1/(-log(a*x^n))^(1/2) --R --R ---R 1 ---R (240) -------------- ---R +-----------+ ---R | n ---R \|- log(a x ) +--R 1 +--R (1) -------------- +--R +-----------+ +--R | n +--R \|- log(a x ) --R Type: Expression(Integer) --E 426 @@ -4420,17 +4667,17 @@ t0385:= 1/(-log(a*x^n))^(1/2) r0385:= -%pi^(1/2)*x*erf((-log(a*x^n))^(1/2)/n^(1/2))/n^(1/2)/((a*x^n)^(1/n)) --R --R ---R +-----------+ ---R | n ---R +---+ \|- log(a x ) ---R x\|%pi erf(--------------) ---R +-+ ---R \|n ---R (241) - -------------------------- ---R 1 ---R - ---R +-+ n n ---R \|n (a x ) +--R +-----------+ +--R | n +--R +---+ \|- log(a x ) +--R x\|%pi erf(--------------) +--R +-+ +--R \|n +--R (2) - -------------------------- +--R 1 +--R - +--R +-+ n n +--R \|n (a x ) --R Type: Expression(Integer) --E 427 @@ -4438,6 +4685,7 @@ r0385:= -%pi^(1/2)*x*erf((-log(a*x^n))^(1/2)/n^(1/2))/n^(1/2)/((a*x^n)^(1/n)) a0385:= integrate(t0385,x) --R --R +--RDaly Bug --R >> Error detected within library code: --R integrate: implementation incomplete (constant residues) --R @@ -4453,14 +4701,16 @@ a0385:= integrate(t0385,x) --d0385:= D(m0385,x) --E 430 +)clear all + --S 431 of 460 t0386:= log(x^n)/(a+b*x) --R --R ---R n ---R log(x ) ---R (242) ------- ---R b x + a +--R n +--R log(x ) +--R (1) ------- +--R b x + a --R Type: Expression(Integer) --E 431 @@ -4473,6 +4723,7 @@ r0386:= 1/b*(log(x^n)*log((a+b*x)/a)+n*polylog(2,-b*x/a)) --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -4486,11 +4737,11 @@ r0386:= 1/b*(log(x^n)*log((a+b*x)/a)+n*polylog(2,-b*x/a)) a0386:= integrate(t0386,x) --R --R ---R x n ---R ++ log(%R ) ---R (243) | -------- d%R ---R ++ %R b + a ---R Type: Expression(Integer) +--R x n +--R ++ log(%R ) +--R (2) | -------- d%R +--R ++ %R b + a +--R Type: Union(Expression(Integer),...) --E 433 --S 434 of 460 @@ -4501,19 +4752,21 @@ a0386:= integrate(t0386,x) --d0386:= D(m0386,x) --E 435 +)clear all + --S 436 of 460 t0387:= sin(x*log(x))+log(x)*sin(x*log(x)) --R --R ---R (244) (log(x) + 1)sin(x log(x)) ---R Type: Union(Expression(Integer),...) +--R (1) (log(x) + 1)sin(x log(x)) +--R Type: Expression(Integer) --E 436 --S 437 of 460 r0387:= -cos(x*log(x)) --R --R ---R (245) - cos(x log(x)) +--R (2) - cos(x log(x)) --R Type: Expression(Integer) --E 437 @@ -4521,38 +4774,40 @@ r0387:= -cos(x*log(x)) a0387:= integrate(t0387,x) --R --R ---R (246) - cos(x log(x)) ---R Type: Expression(Integer) +--R (3) - cos(x log(x)) +--R Type: Union(Expression(Integer),...) --E 438 --S 439 of 460 m0387:= a0387-r0387 --R --R ---R (247) 0 ---R Type: Union(Expression(Integer),...) +--R (4) 0 +--R Type: Expression(Integer) --E 439 --S 440 of 460 d0387:= D(m0387,x) --R --R ---R (248) 0 +--R (5) 0 --R Type: Expression(Integer) --E 440 +)clear all + --S 441 of 460 t0388:= log((1-x^2)/(1+x^2))/(1+x)^2 --R --R ---R 2 ---R - x + 1 ---R log(--------) ---R 2 ---R x + 1 ---R (249) ------------- ---R 2 ---R x + 2x + 1 +--R 2 +--R - x + 1 +--R log(--------) +--R 2 +--R x + 1 +--R (1) ------------- +--R 2 +--R x + 2x + 1 --R Type: Expression(Integer) --E 441 @@ -4561,7 +4816,7 @@ r0388:= -1/(1+x)-atan(x)+1/2*log(1-x)+1/2*log(1+x)-_ log((1-x^2)/(1+x^2))/(1+x)-1/2*log(1+x^2) --R --R ---R (250) +--R (2) --R 2 --R 2 - x + 1 --R (- x - 1)log(x + 1) + (x + 1)log(x + 1) - 2log(--------) @@ -4578,7 +4833,7 @@ r0388:= -1/(1+x)-atan(x)+1/2*log(1-x)+1/2*log(1+x)-_ a0388:= integrate(t0388,x) --R --R ---R (251) +--R (3) --R 2 --R 2 2 - x + 1 --R (- x - 1)log(x + 1) + (x + 1)log(x - 1) - 2log(--------) @@ -4588,35 +4843,37 @@ a0388:= integrate(t0388,x) --R (- 2x - 2)atan(x) - 2 --R / --R 2x + 2 ---R Type: Expression(Integer) +--R Type: Union(Expression(Integer),...) --E 443 --S 444 of 460 m0388:= a0388-r0388 --R --R ---R 2 ---R log(x - 1) - log(x + 1) - log(- x + 1) ---R (252) --------------------------------------- ---R 2 ---R Type: Union(Expression(Integer),...) +--R 2 +--R log(x - 1) - log(x + 1) - log(- x + 1) +--R (4) --------------------------------------- +--R 2 +--R Type: Expression(Integer) --E 444 --S 445 of 460 d0388:= D(m0388,x) --R --R ---R (253) 0 +--R (5) 0 --R Type: Expression(Integer) --E 445 +)clear all + --S 446 of 460 t0389:= log((-1+x)/(1+x)) --R --R ---R x - 1 ---R (254) log(-----) ---R x + 1 +--R x - 1 +--R (1) log(-----) +--R x + 1 --R Type: Expression(Integer) --E 446 @@ -4624,9 +4881,9 @@ t0389:= log((-1+x)/(1+x)) r0389:= x*log((-1+x)/(1+x))-log(-(-1+x)*(1+x)) --R --R ---R x - 1 2 ---R (255) x log(-----) - log(- x + 1) ---R x + 1 +--R x - 1 2 +--R (2) x log(-----) - log(- x + 1) +--R x + 1 --R Type: Expression(Integer) --E 447 @@ -4634,36 +4891,38 @@ r0389:= x*log((-1+x)/(1+x))-log(-(-1+x)*(1+x)) a0389:= integrate(t0389,x) --R --R ---R 2 x - 1 ---R (256) - log(x - 1) + x log(-----) ---R x + 1 ---R Type: Expression(Integer) +--R 2 x - 1 +--R (3) - log(x - 1) + x log(-----) +--R x + 1 +--R Type: Union(Expression(Integer),...) --E 448 --S 449 of 460 m0389:= a0389-r0389 --R --R ---R 2 2 ---R (257) - log(x - 1) + log(- x + 1) ---R Type: Union(Expression(Integer),...) +--R 2 2 +--R (4) - log(x - 1) + log(- x + 1) +--R Type: Expression(Integer) --E 449 --S 450 of 460 d0389:= D(m0389,x) --R --R ---R (258) 0 +--R (5) 0 --R Type: Expression(Integer) --E 450 +)clear all + --S 451 of 460 t0390:= log(x)/(-1+x) --R --R ---R log(x) ---R (259) ------ ---R x - 1 +--R log(x) +--R (1) ------ +--R x - 1 --R Type: Expression(Integer) --E 451 @@ -4676,6 +4935,7 @@ r0390:= -polylog(2,1-x) --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -4689,8 +4949,8 @@ r0390:= -polylog(2,1-x) a0390:= integrate(t0390,x) --R --R ---R (260) - dilog(x) ---R Type: Expression(Integer) +--R (2) - dilog(x) +--R Type: Union(Expression(Integer),...) --E 453 --S 454 of 460 @@ -4701,14 +4961,16 @@ a0390:= integrate(t0390,x) --d0390:= D(m0390,x) --E 455 +)clear all + --S 456 of 460 t0391:= x*log(1-a-b*x)/(a+b*x) --R --R ---R x log(- b x - a + 1) ---R (261) -------------------- ---R b x + a ---R Type: Union(Expression(Integer),...) +--R x log(- b x - a + 1) +--R (1) -------------------- +--R b x + a +--R Type: Expression(Integer) --E 456 --S 457 of 460 @@ -4720,6 +4982,7 @@ r0391:= -x/b-(1-a-b*x)*log(1-a-b*x)/b^2+a*polylog(2,a+b*x)/b^2 --R to learn if there is any operation containing " polylog " in its --R name. --R +--RDaly Bug --R Cannot find a definition or applicable library operation named --R polylog with argument type(s) --R PositiveInteger @@ -4733,11 +4996,11 @@ r0391:= -x/b-(1-a-b*x)*log(1-a-b*x)/b^2+a*polylog(2,a+b*x)/b^2 a0391:= integrate(t0391,x) --R --R ---R x ---R ++ %R log(- %R b - a + 1) ---R (262) | ---------------------- d%R ---R ++ %R b + a ---R Type: Expression(Integer) +--R x +--R ++ %R log(- %R b - a + 1) +--R (2) | ---------------------- d%R +--R ++ %R b + a +--R Type: Union(Expression(Integer),...) --E 458 --S 459 of 460 diff --git a/src/input/richtrig800-899.input.pamphlet b/src/input/richtrig800-899.input.pamphlet index 9790f76..e9d0244 100644 --- a/src/input/richtrig800-899.input.pamphlet +++ b/src/input/richtrig800-899.input.pamphlet @@ -129,12 +129,15 @@ d0800:= D(m0800,x) --R Type: Expression(Integer) --E 5 +)clear all + + --S 6 of 526 t0801:= cos(a+b*x)*csc(c+b*x)^3 --R --R --R 3 ---R (6) cos(b x + a)csc(b x + c) +--R (1) cos(b x + a)csc(b x + c) --R Type: Expression(Integer) --E 6 @@ -144,7 +147,7 @@ r0801:= -1/2*cos(a-c)*csc(c+b*x)^2/b+cot(c+b*x)*sin(a-c)/b --R --R 2 --R - 2cot(b x + c)sin(c - a) - cos(c - a)csc(b x + c) ---R (7) --------------------------------------------------- +--R (2) --------------------------------------------------- --R 2b --R Type: Expression(Integer) --E 7 @@ -153,7 +156,7 @@ r0801:= -1/2*cos(a-c)*csc(c+b*x)^2/b+cot(c+b*x)*sin(a-c)/b a0801:= integrate(t0801,x) --R --R ---R (8) +--R (3) --R 2 c - a 2 c - a --R (- cos(b x + c) - 1)tan(-----) + 8cos(b x + c)sin(b x + c)tan(-----) --R 2 2 @@ -171,7 +174,7 @@ a0801:= integrate(t0801,x) m0801:= a0801-r0801 --R --R ---R (9) +--R (4) --R 2 --R (4cos(b x + c) - 4)cot(b x + c)sin(c - a) --R + @@ -204,7 +207,7 @@ m0801:= a0801-r0801 d0801:= D(m0801,x) --R --R ---R (10) +--R (5) --R - cos(b x + c)sin(b x + c) --R + --R 4 2 2 @@ -257,14 +260,17 @@ d0801:= D(m0801,x) --R Type: Expression(Integer) --E 10 +)clear all + + --S 11 of 526 t0802:= sin(x)^2/(a+b*sin(2*x)) --R --R ---R 2 ---R sin(x) ---R (11) ------------- ---R b sin(2x) + a +--R 2 +--R sin(x) +--R (1) ------------- +--R b sin(2x) + a --R Type: Expression(Integer) --E 11 @@ -273,16 +279,16 @@ r0802:= 1/2*atan((b+a*tan(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(1/2)-_ 1/4*log(a+b*sin(2*x))/b --R --R ---R +---------+ ---R | 2 2 a tan(x) + b ---R - \|- b + a log(b sin(2x) + a) + 2b atan(------------) ---R +---------+ ---R | 2 2 ---R \|- b + a ---R (12) -------------------------------------------------------- ---R +---------+ ---R | 2 2 ---R 4b\|- b + a +--R +---------+ +--R | 2 2 a tan(x) + b +--R - \|- b + a log(b sin(2x) + a) + 2b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) -------------------------------------------------------- +--R +---------+ +--R | 2 2 +--R 4b\|- b + a --R Type: Expression(Integer) --E 12 @@ -290,7 +296,7 @@ r0802:= 1/2*atan((b+a*tan(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(1/2)-_ a0802:= integrate(t0802,x) --R --R ---R (13) +--R (3) --R [ --R b --R * @@ -349,7 +355,7 @@ a0802:= integrate(t0802,x) m0802a:= a0802.1-r0802 --R --R ---R (14) +--R (4) --R +---------+ --R | 2 2 --R b\|- b + a @@ -391,7 +397,7 @@ m0802a:= a0802.1-r0802 d0802a:= D(m0802a,x) --R --R ---R (15) +--R (5) --R 2 2 3 --R 2a b cos(x)sin(x) --R + @@ -753,7 +759,7 @@ d0802a:= D(m0802a,x) m0802b:= a0802.2-r0802 --R --R ---R (16) +--R (6) --R +---------+ +---------+ --R | 2 2 | 2 2 8b cos(x)sin(x) + 4a --R \|- b + a log(b sin(2x) + a) - \|- b + a log(---------------------) @@ -795,7 +801,7 @@ m0802b:= a0802.2-r0802 d0802b:= D(m0802b,x) --R --R ---R (17) +--R (7) --R 4 2 4 4 6 --R (a b cos(x) + 4a b cos(x) + 4a b)sin(x) --R + @@ -1792,14 +1798,17 @@ d0802b:= D(m0802b,x) --R Type: Expression(Integer) --E 17 +)clear all + + --S 18 of 526 t0803:= cos(x)^2/(a+b*sin(2*x)) --R --R ---R 2 ---R cos(x) ---R (18) ------------- ---R b sin(2x) + a +--R 2 +--R cos(x) +--R (1) ------------- +--R b sin(2x) + a --R Type: Expression(Integer) --E 18 @@ -1808,16 +1817,16 @@ r0803:= 1/2*atan((b+a*tan(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(1/2)+_ 1/4*log(a+b*sin(2*x))/b --R --R ---R +---------+ ---R | 2 2 a tan(x) + b ---R \|- b + a log(b sin(2x) + a) + 2b atan(------------) ---R +---------+ ---R | 2 2 ---R \|- b + a ---R (19) ------------------------------------------------------ ---R +---------+ ---R | 2 2 ---R 4b\|- b + a +--R +---------+ +--R | 2 2 a tan(x) + b +--R \|- b + a log(b sin(2x) + a) + 2b atan(------------) +--R +---------+ +--R | 2 2 +--R \|- b + a +--R (2) ------------------------------------------------------ +--R +---------+ +--R | 2 2 +--R 4b\|- b + a --R Type: Expression(Integer) --E 19 @@ -1825,7 +1834,7 @@ r0803:= 1/2*atan((b+a*tan(x))/(a^2-b^2)^(1/2))/(a^2-b^2)^(1/2)+_ a0803:= integrate(t0803,x) --R --R ---R (20) +--R (3) --R [ --R b --R * @@ -1884,7 +1893,7 @@ a0803:= integrate(t0803,x) m0803a:= a0803.1-r0803 --R --R ---R (21) +--R (4) --R +---------+ --R | 2 2 --R b\|- b + a @@ -1926,7 +1935,7 @@ m0803a:= a0803.1-r0803 d0803a:= D(m0803a,x) --R --R ---R (22) +--R (5) --R 2 2 3 3 2 2 --R - 2a b cos(x)sin(x) - 2a b cos(x) sin(x) --R + @@ -2243,7 +2252,7 @@ d0803a:= D(m0803a,x) m0803b:= a0803.2-r0803 --R --R ---R (23) +--R (6) --R +---------+ +---------+ --R | 2 2 | 2 2 8b cos(x)sin(x) + 4a --R - \|- b + a log(b sin(2x) + a) + \|- b + a log(---------------------) @@ -2285,7 +2294,7 @@ m0803b:= a0803.2-r0803 d0803b:= D(m0803b,x) --R --R ---R (24) +--R (7) --R 4 2 4 4 6 --R (- a b cos(x) - 4a b cos(x) - 4a b)sin(x) --R + @@ -3270,11 +3279,14 @@ d0803b:= D(m0803b,x) --R Type: Expression(Integer) --E 24 +)clear all + + --S 25 of 526 t0804:= csc(2*x)*sin(x) --R --R ---R (25) csc(2x)sin(x) +--R (1) csc(2x)sin(x) --R Type: Expression(Integer) --E 25 @@ -3282,9 +3294,9 @@ t0804:= csc(2*x)*sin(x) r0804:= 1/2*atanh(sin(x)) --R --R ---R atanh(sin(x)) ---R (26) ------------- ---R 2 +--R atanh(sin(x)) +--R (2) ------------- +--R 2 --R Type: Expression(Integer) --E 26 @@ -3292,11 +3304,11 @@ r0804:= 1/2*atanh(sin(x)) a0804:= integrate(t0804,x) --R --R ---R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 ---R log(-------------------) - log(-------------------) ---R cos(x) + 1 cos(x) + 1 ---R (27) --------------------------------------------------- ---R 2 +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) +--R cos(x) + 1 cos(x) + 1 +--R (3) --------------------------------------------------- +--R 2 --R Type: Union(Expression(Integer),...) --E 27 @@ -3304,11 +3316,11 @@ a0804:= integrate(t0804,x) m0804:= a0804-r0804 --R --R ---R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 ---R log(-------------------) - log(-------------------) - atanh(sin(x)) ---R cos(x) + 1 cos(x) + 1 ---R (28) ------------------------------------------------------------------- ---R 2 +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 +--R (4) ------------------------------------------------------------------- +--R 2 --R Type: Expression(Integer) --E 28 @@ -3316,19 +3328,22 @@ m0804:= a0804-r0804 d0804:= D(m0804,x) --R --R ---R 4 2 2 3 ---R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) ---R (29) --------------------------------------------------------------------- ---R 4 2 2 2 ---R 2sin(x) + (- 2cos(x) - 4cos(x) - 4)sin(x) + 2cos(x) + 4cos(x) + 2 +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R (5) --------------------------------------------------------------------- +--R 4 2 2 2 +--R 2sin(x) + (- 2cos(x) - 4cos(x) - 4)sin(x) + 2cos(x) + 4cos(x) + 2 --R Type: Expression(Integer) --E 29 +)clear all + + --S 30 of 526 t0805:= cos(4*x)*sec(2*x) --R --R ---R (30) cos(4x)sec(2x) +--R (1) cos(4x)sec(2x) --R Type: Expression(Integer) --E 30 @@ -3336,9 +3351,9 @@ t0805:= cos(4*x)*sec(2*x) r0805:= -1/2*atanh(sin(2*x))+sin(2*x) --R --R ---R - atanh(sin(2x)) + 2sin(2x) ---R (31) --------------------------- ---R 2 +--R - atanh(sin(2x)) + 2sin(2x) +--R (2) --------------------------- +--R 2 --R Type: Expression(Integer) --E 31 @@ -3346,11 +3361,11 @@ r0805:= -1/2*atanh(sin(2*x))+sin(2*x) a0805:= integrate(t0805,x) --R --R ---R sin(2x) + cos(2x) + 1 sin(2x) - cos(2x) - 1 ---R - log(---------------------) + log(---------------------) + 2sin(2x) ---R cos(2x) + 1 cos(2x) + 1 ---R (32) -------------------------------------------------------------------- ---R 2 +--R sin(2x) + cos(2x) + 1 sin(2x) - cos(2x) - 1 +--R - log(---------------------) + log(---------------------) + 2sin(2x) +--R cos(2x) + 1 cos(2x) + 1 +--R (3) -------------------------------------------------------------------- +--R 2 --R Type: Union(Expression(Integer),...) --E 32 @@ -3358,7 +3373,7 @@ a0805:= integrate(t0805,x) m0805:= a0805-r0805 --R --R ---R (33) +--R (4) --R sin(2x) + cos(2x) + 1 sin(2x) - cos(2x) - 1 --R - log(---------------------) + log(---------------------) + atanh(sin(2x)) --R cos(2x) + 1 cos(2x) + 1 @@ -3371,7 +3386,7 @@ m0805:= a0805-r0805 d0805:= D(m0805,x) --R --R ---R (34) +--R (5) --R 4 2 2 3 --R 2sin(2x) + (2cos(2x) + cos(2x) - 2)sin(2x) + cos(2x) - cos(2x) --R ------------------------------------------------------------------------ @@ -3380,12 +3395,15 @@ d0805:= D(m0805,x) --R Type: Expression(Integer) --E 34 +)clear all + + --S 35 of 526 t0806:= x*cos(2*x)*sec(x)^3 --R --R ---R 3 ---R (35) x cos(2x)sec(x) +--R 3 +--R (1) x cos(2x)sec(x) --R Type: Expression(Integer) --E 35 @@ -3412,10 +3430,10 @@ r0806:= -3*%i*x*atan(exp(1)^(%i*x))+3/2*%i*polylog(2,-%i*exp(1)^(%i*x))-_ a0806:= integrate(t0806,x) --R --R ---R x ---R ++ 3 ---R (36) | %J cos(2%J)sec(%J) d%J ---R ++ +--R x +--R ++ 3 +--R (2) | %J cos(2%J)sec(%J) d%J +--R ++ --R Type: Union(Expression(Integer),...) --E 37 @@ -3423,10 +3441,10 @@ a0806:= integrate(t0806,x) m0806:= a0806-r0806 --R --R ---R x ---R ++ 3 ---R (37) | %J cos(2%J)sec(%J) d%J - r0806 ---R ++ +--R x +--R ++ 3 +--R (3) | %J cos(2%J)sec(%J) d%J - r0806 +--R ++ --R Type: Expression(Integer) --E 38 @@ -3434,20 +3452,23 @@ m0806:= a0806-r0806 d0806:= D(m0806,x) --R --R ---R 3 ---R (38) x cos(2x)sec(x) +--R 3 +--R (4) x cos(2x)sec(x) --R Type: Expression(Integer) --E 39 +)clear all + + --S 40 of 526 t0807:= sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2) --R --R ---R +------------+ ---R \|sin(b x + a) ---R (39) --------------- ---R +------------+ ---R \|cos(b x + a) +--R +------------+ +--R \|sin(b x + a) +--R (1) --------------- +--R +------------+ +--R \|cos(b x + a) --R Type: Expression(Integer) --E 40 @@ -3459,7 +3480,7 @@ r0807:= -1/2*atan(1-2^(1/2)*sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2))*2^(1/2)/b+_ log(1+2^(1/2)*sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2)+tan(a+b*x))*2^(1/2)/b --R --R ---R (40) +--R (2) --R +-+ +------------+ +------------+ --R +-+ \|2 \|sin(b x + a) + (tan(b x + a) + 1)\|cos(b x + a) --R - \|2 log(-------------------------------------------------------) @@ -3492,11 +3513,11 @@ r0807:= -1/2*atan(1-2^(1/2)*sin(a+b*x)^(1/2)/cos(a+b*x)^(1/2))*2^(1/2)/b+_ a0807:= integrate(t0807,x) --R --R ---R x +-------------+ ---R ++ \|sin(%J b + a) ---R (41) | ---------------- d%J ---R ++ +-------------+ ---R \|cos(%J b + a) +--R x +-------------+ +--R ++ \|sin(%J b + a) +--R (3) | ---------------- d%J +--R ++ +-------------+ +--R \|cos(%J b + a) --R Type: Union(Expression(Integer),...) --E 42 @@ -3504,7 +3525,7 @@ a0807:= integrate(t0807,x) m0807:= a0807-r0807 --R --R ---R (42) +--R (4) --R x +-------------+ --R ++ \|sin(%J b + a) --R 4b | ---------------- d%J @@ -3543,7 +3564,7 @@ m0807:= a0807-r0807 d0807:= D(m0807,x) --R --R ---R (43) +--R (5) --R 2 2 --R (- cos(b x + a)sin(b x + a) - cos(b x + a) )tan(b x + a) --R + @@ -3569,15 +3590,18 @@ d0807:= D(m0807,x) --R Type: Expression(Integer) --E 44 +)clear all + + --S 45 of 526 t0808:= cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2) --R --R ---R +------------+ ---R \|cos(b x + a) ---R (44) --------------- ---R +------------+ ---R \|sin(b x + a) +--R +------------+ +--R \|cos(b x + a) +--R (1) --------------- +--R +------------+ +--R \|sin(b x + a) --R Type: Expression(Integer) --E 45 @@ -3589,7 +3613,7 @@ r0808:= -1/2*atan(-1+2^(1/2)*cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2))*2^(1/2)/b-_ cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2))*2^(1/2)/b --R --R ---R (45) +--R (2) --R +------------+ +-+ +------------+ --R +-+ (cot(b x + a) + 1)\|sin(b x + a) + \|2 \|cos(b x + a) --R \|2 log(-------------------------------------------------------) @@ -3622,11 +3646,11 @@ r0808:= -1/2*atan(-1+2^(1/2)*cos(a+b*x)^(1/2)/sin(a+b*x)^(1/2))*2^(1/2)/b-_ a0808:= integrate(t0808,x) --R --R ---R x +-------------+ ---R ++ \|cos(%J b + a) ---R (46) | ---------------- d%J ---R ++ +-------------+ ---R \|sin(%J b + a) +--R x +-------------+ +--R ++ \|cos(%J b + a) +--R (3) | ---------------- d%J +--R ++ +-------------+ +--R \|sin(%J b + a) --R Type: Union(Expression(Integer),...) --E 47 @@ -3634,7 +3658,7 @@ a0808:= integrate(t0808,x) m0808:= a0808-r0808 --R --R ---R (47) +--R (4) --R x +-------------+ --R ++ \|cos(%J b + a) --R 4b | ---------------- d%J @@ -3673,7 +3697,7 @@ m0808:= a0808-r0808 d0808:= D(m0808,x) --R --R ---R (48) +--R (5) --R 2 2 --R (- cot(b x + a) - cot(b x + a))sin(b x + a) --R + @@ -3705,15 +3729,18 @@ d0808:= D(m0808,x) --R Type: Expression(Integer) --E 49 +)clear all + + --S 50 of 526 t0809:= sin(a+b*x)^(1/3)/cos(a+b*x)^(1/3) --R --R ---R 3+------------+ ---R \|sin(b x + a) ---R (49) --------------- ---R 3+------------+ ---R \|cos(b x + a) +--R 3+------------+ +--R \|sin(b x + a) +--R (1) --------------- +--R 3+------------+ +--R \|cos(b x + a) --R Type: Expression(Integer) --E 50 @@ -3724,7 +3751,7 @@ r0809:= -1/2*3^(1/2)*atan(1/3*(1-2*sin(a+b*x)^(2/3)/cos(a+b*x)^(2/3))*_ sin(a+b*x)^(4/3)/cos(a+b*x)^(4/3))/b --R --R ---R (50) +--R (2) --R 3+------------+2 3+------------+2 --R \|sin(b x + a) + \|cos(b x + a) --R - 2log(-----------------------------------) @@ -3766,15 +3793,18 @@ r0809:= -1/2*3^(1/2)*atan(1/3*(1-2*sin(a+b*x)^(2/3)/cos(a+b*x)^(2/3))*_ --d0809:= D(m0809,x) --E 54 +)clear all + + --S 55 of 526 t0810:= cos(a+b*x)^(1/3)/sin(a+b*x)^(1/3) --R --R ---R 3+------------+ ---R \|cos(b x + a) ---R (51) --------------- ---R 3+------------+ ---R \|sin(b x + a) +--R 3+------------+ +--R \|cos(b x + a) +--R (1) --------------- +--R 3+------------+ +--R \|sin(b x + a) --R Type: Expression(Integer) --E 55 @@ -3785,7 +3815,7 @@ r0810:= 1/2*3^(1/2)*atan(1/3*(1-2*cos(a+b*x)^(2/3)/sin(a+b*x)^(2/3))*_ 1/2*log(1+cos(a+b*x)^(2/3)/sin(a+b*x)^(2/3))/b --R --R ---R (52) +--R (2) --R - --R log --R 3+------------+2 @@ -3828,12 +3858,15 @@ r0810:= 1/2*3^(1/2)*atan(1/3*(1-2*cos(a+b*x)^(2/3)/sin(a+b*x)^(2/3))*_ --d0810:= D(m0810,x) --E 59 +)clear all + + --S 60 of 526 t0811:= x*sin(x)*sec(x)^(1/2) --R --R ---R +------+ ---R (53) x sin(x)\|sec(x) +--R +------+ +--R (1) x sin(x)\|sec(x) --R Type: Expression(Integer) --E 60 @@ -3870,7 +3903,7 @@ a0811:= integrate(t0811,x) m0811:= a0811-r0811 --R --R ---R (54) - r0811 + a0811 +--R (2) - r0811 + a0811 --R Type: Polynomial(Integer) --E 63 @@ -3878,16 +3911,19 @@ m0811:= a0811-r0811 d0811:= D(m0811,x) --R --R ---R (55) 0 +--R (3) 0 --R Type: Polynomial(Integer) --E 64 +)clear all + + --S 65 of 526 t0812:= x*cos(x)*csc(x)^(1/2) --R --R ---R +------+ ---R (56) x cos(x)\|csc(x) +--R +------+ +--R (1) x cos(x)\|csc(x) --R Type: Expression(Integer) --E 65 @@ -3925,7 +3961,7 @@ a0812:= integrate(t0812,x) m0812:= a0812-r0812 --R --R ---R (57) - r0812 + a0812 +--R (2) - r0812 + a0812 --R Type: Polynomial(Integer) --E 68 @@ -3933,18 +3969,21 @@ m0812:= a0812-r0812 d0812:= D(m0812,x) --R --R ---R (58) 0 +--R (3) 0 --R Type: Polynomial(Integer) --E 69 +)clear all + + --S 70 of 526 t0813:= cos(x)/(cos(x)+1)^(1/2) --R --R ---R cos(x) ---R (59) ------------- ---R +----------+ ---R \|cos(x) + 1 +--R cos(x) +--R (1) ------------- +--R +----------+ +--R \|cos(x) + 1 --R Type: Expression(Integer) --E 70 @@ -3952,12 +3991,12 @@ t0813:= cos(x)/(cos(x)+1)^(1/2) r0813:= -2*(atanh(sin(1/2*x))*cos(1/2*x)-sin(x))/(cos(x)+1)^(1/2) --R --R ---R x x ---R - 2cos(-)atanh(sin(-)) + 2sin(x) ---R 2 2 ---R (60) -------------------------------- ---R +----------+ ---R \|cos(x) + 1 +--R x x +--R - 2cos(-)atanh(sin(-)) + 2sin(x) +--R 2 2 +--R (2) -------------------------------- +--R +----------+ +--R \|cos(x) + 1 --R Type: Expression(Integer) --E 71 @@ -3965,7 +4004,7 @@ r0813:= -2*(atanh(sin(1/2*x))*cos(1/2*x)-sin(x))/(cos(x)+1)^(1/2) a0813:= integrate(t0813,x) --R --R ---R (61) +--R (3) --R +-+ +-+ --R (\|2 cos(x) + \|2 ) --R * @@ -3986,7 +4025,7 @@ a0813:= integrate(t0813,x) m0813:= a0813-r0813 --R --R ---R (62) +--R (4) --R +-+ +----------+ 2 --R +-+ +----------+ - 2\|2 sin(x)\|cos(x) + 1 - cos(x) + 2cos(x) + 3 --R \|2 \|cos(x) + 1 log(--------------------------------------------------) @@ -4006,7 +4045,7 @@ m0813:= a0813-r0813 d0813:= D(m0813,x) --R --R ---R (63) +--R (5) --R +-+ x x 2 +-+ x 2 --R (2\|2 cos(-)sin(-) - 2\|2 cos(-))sin(x) --R 2 2 2 @@ -4088,14 +4127,17 @@ d0813:= D(m0813,x) --R Type: Expression(Integer) --E 74 +)clear all + + --S 75 of 526 t0814:= cos(x)/(1-cos(2*x))^(1/2) --R --R ---R cos(x) ---R (64) ---------------- ---R +-------------+ ---R \|- cos(2x) + 1 +--R cos(x) +--R (1) ---------------- +--R +-------------+ +--R \|- cos(2x) + 1 --R Type: Expression(Integer) --E 75 @@ -4103,10 +4145,10 @@ t0814:= cos(x)/(1-cos(2*x))^(1/2) r0814:= 1/2*log(sin(x))*2^(1/2)*cos(sin(x)) --R --R ---R +-+ ---R \|2 cos(sin(x))log(sin(x)) ---R (65) -------------------------- ---R 2 +--R +-+ +--R \|2 cos(sin(x))log(sin(x)) +--R (2) -------------------------- +--R 2 --R Type: Expression(Integer) --E 76 @@ -4114,11 +4156,11 @@ r0814:= 1/2*log(sin(x))*2^(1/2)*cos(sin(x)) a0814:= integrate(t0814,x) --R --R ---R +-+ sin(x) +-+ 2 ---R \|2 log(----------) - \|2 log(----------) ---R cos(x) + 1 cos(x) + 1 ---R (66) ----------------------------------------- ---R 2 +--R +-+ sin(x) +-+ 2 +--R \|2 log(----------) - \|2 log(----------) +--R cos(x) + 1 cos(x) + 1 +--R (3) ----------------------------------------- +--R 2 --R Type: Union(Expression(Integer),...) --E 77 @@ -4126,7 +4168,7 @@ a0814:= integrate(t0814,x) m0814:= a0814-r0814 --R --R ---R (67) +--R (4) --R +-+ +-+ sin(x) +-+ 2 --R - \|2 cos(sin(x))log(sin(x)) + \|2 log(----------) - \|2 log(----------) --R cos(x) + 1 cos(x) + 1 @@ -4139,7 +4181,7 @@ m0814:= a0814-r0814 d0814:= D(m0814,x) --R --R ---R (68) +--R (5) --R +-+ +-+ +-+ --R \|2 cos(x)sin(x)log(sin(x))sin(sin(x)) - \|2 cos(x)cos(sin(x)) + \|2 cos(x) --R --------------------------------------------------------------------------- @@ -4147,12 +4189,15 @@ d0814:= D(m0814,x) --R Type: Expression(Integer) --E 79 +)clear all + + --S 80 of 526 t0815:= tan(x)*(2+3*cos(x))^(1/2) --R --R ---R +-----------+ ---R (69) tan(x)\|3cos(x) + 2 +--R +-----------+ +--R (1) tan(x)\|3cos(x) + 2 --R Type: Expression(Integer) --E 80 @@ -4160,10 +4205,10 @@ t0815:= tan(x)*(2+3*cos(x))^(1/2) r0815:= 2*2^(1/2)*atanh(1/2*(2+3*cos(x))^(1/2)*2^(1/2))-2*(2+3*cos(x))^(1/2) --R --R ---R +-+ +-----------+ ---R +-+ \|2 \|3cos(x) + 2 +-----------+ ---R (70) 2\|2 atanh(------------------) - 2\|3cos(x) + 2 ---R 2 +--R +-+ +-----------+ +--R +-+ \|2 \|3cos(x) + 2 +-----------+ +--R (2) 2\|2 atanh(------------------) - 2\|3cos(x) + 2 +--R 2 --R Type: Expression(Integer) --E 81 @@ -4171,7 +4216,7 @@ r0815:= 2*2^(1/2)*atanh(1/2*(2+3*cos(x))^(1/2)*2^(1/2))-2*(2+3*cos(x))^(1/2) a0815:= integrate(t0815,x) --R --R ---R (71) +--R (3) --R - --R +-+ --R \|2 @@ -4196,7 +4241,7 @@ a0815:= integrate(t0815,x) m0815:= a0815-r0815 --R --R ---R (72) +--R (4) --R - --R +-+ --R \|2 @@ -4223,16 +4268,19 @@ m0815:= a0815-r0815 d0815:= D(m0815,x) --R --R ---R (73) 0 +--R (5) 0 --R Type: Expression(Integer) --E 84 +)clear all + + --S 85 of 526 t0816:= cot(x)*(1+sin(x))^(1/2) --R --R ---R +----------+ ---R (74) cot(x)\|sin(x) + 1 +--R +----------+ +--R (1) cot(x)\|sin(x) + 1 --R Type: Expression(Integer) --E 85 @@ -4240,8 +4288,8 @@ t0816:= cot(x)*(1+sin(x))^(1/2) r0816:= -2*atanh((1+sin(x))^(1/2))+2*(1+sin(x))^(1/2) --R --R ---R +----------+ +----------+ ---R (75) - 2atanh(\|sin(x) + 1 ) + 2\|sin(x) + 1 +--R +----------+ +----------+ +--R (2) - 2atanh(\|sin(x) + 1 ) + 2\|sin(x) + 1 --R Type: Expression(Integer) --E 86 @@ -4249,7 +4297,7 @@ r0816:= -2*atanh((1+sin(x))^(1/2))+2*(1+sin(x))^(1/2) a0816:= integrate(t0816,x) --R --R ---R (76) +--R (3) --R +---------------------+ --R | 4 --R (- cos(x) - 1) |--------------------- @@ -4302,7 +4350,7 @@ a0816:= integrate(t0816,x) m0816:= a0816-r0816 --R --R ---R (77) +--R (4) --R +---------------------+ --R | 4 --R (- cos(x) - 1) |--------------------- @@ -4367,7 +4415,7 @@ m0816:= a0816-r0816 d0816:= D(m0816,x) --R --R ---R (78) +--R (5) --R 5 4 2 3 --R 2sin(x) + (cos(x) + 1)sin(x) + (3cos(x) + cos(x) - 2)sin(x) --R + @@ -4457,14 +4505,17 @@ d0816:= D(m0816,x) --R Type: Expression(Integer) --E 89 +)clear all + + --S 90 of 526 t0817:= cot(x)/(3-cos(x))^(1/2) --R --R ---R cot(x) ---R (79) --------------- ---R +------------+ ---R \|- cos(x) + 3 +--R cot(x) +--R (1) --------------- +--R +------------+ +--R \|- cos(x) + 3 --R Type: Expression(Integer) --E 90 @@ -4473,12 +4524,12 @@ r0817:= -1/2*atanh(1/2*(3-cos(x))^(1/2))-_ 1/2*atanh(1/2*(3-cos(x))^(1/2)*2^(1/2))*2^(1/2) --R --R ---R +-+ +------------+ +------------+ ---R +-+ \|2 \|- cos(x) + 3 \|- cos(x) + 3 ---R - \|2 atanh(-------------------) - atanh(---------------) ---R 2 2 ---R (80) --------------------------------------------------------- ---R 2 +--R +-+ +------------+ +------------+ +--R +-+ \|2 \|- cos(x) + 3 \|- cos(x) + 3 +--R - \|2 atanh(-------------------) - atanh(---------------) +--R 2 2 +--R (2) --------------------------------------------------------- +--R 2 --R Type: Expression(Integer) --E 91 @@ -4486,7 +4537,7 @@ r0817:= -1/2*atanh(1/2*(3-cos(x))^(1/2))-_ a0817:= integrate(t0817,x) --R --R ---R (81) +--R (3) --R log --R 3 2 +------------+ 2 --R (16cos(x) - 112cos(x) - 8cos(x) + 56)\|- cos(x) + 3 + cos(x) @@ -4521,7 +4572,7 @@ a0817:= integrate(t0817,x) m0817:= a0817-r0817 --R --R ---R (82) +--R (4) --R log --R 3 2 +------------+ 2 --R (16cos(x) - 112cos(x) - 8cos(x) + 56)\|- cos(x) + 3 + cos(x) @@ -4561,7 +4612,7 @@ m0817:= a0817-r0817 d0817:= D(m0817,x) --R --R ---R (83) +--R (5) --R +-+ 6 +-+ 5 +-+ 4 --R 128\|2 cos(x) + (- 1920\|2 + 6)cos(x) + (9024\|2 - 168)cos(x) --R + @@ -4614,15 +4665,18 @@ d0817:= D(m0817,x) --R Type: Expression(Integer) --E 94 +)clear all + + --S 95 of 526 t0818:= sin(x)/(1+sin(x)^2)^(1/2) --R --R ---R sin(x) ---R (84) -------------- ---R +-----------+ ---R | 2 ---R \|sin(x) + 1 +--R sin(x) +--R (1) -------------- +--R +-----------+ +--R | 2 +--R \|sin(x) + 1 --R Type: Expression(Integer) --E 95 @@ -4630,10 +4684,10 @@ t0818:= sin(x)/(1+sin(x)^2)^(1/2) r0818:= -asin(1/2*cos(x)*2^(1/2)) --R --R ---R +-+ ---R \|2 cos(x) ---R (85) - asin(----------) ---R 2 +--R +-+ +--R \|2 cos(x) +--R (2) - asin(----------) +--R 2 --R Type: Expression(Integer) --E 96 @@ -4641,7 +4695,7 @@ r0818:= -asin(1/2*cos(x)*2^(1/2)) a0818:= integrate(t0818,x) --R --R ---R (86) +--R (3) --R +---------------------+ --R | 2 --R | - 4cos(x) + 8 2 @@ -4692,7 +4746,7 @@ a0818:= integrate(t0818,x) m0818:= a0818-r0818 --R --R ---R (87) +--R (4) --R +---------------------+ --R | 2 --R | - 4cos(x) + 8 2 @@ -4748,7 +4802,7 @@ m0818:= a0818-r0818 d0818:= D(m0818,x) --R --R ---R (88) +--R (5) --R 7 6 5 4 3 --R - 16cos(x) - 16cos(x) + 48cos(x) + 48cos(x) - 36cos(x) --R + @@ -5027,13 +5081,16 @@ d0818:= D(m0818,x) --R Type: Expression(Integer) --E 99 +)clear all + + --S 100 of 526 t0819:= sin(x)*(1+sin(x)^2)^(1/2) --R --R ---R +-----------+ ---R | 2 ---R (89) sin(x)\|sin(x) + 1 +--R +-----------+ +--R | 2 +--R (1) sin(x)\|sin(x) + 1 --R Type: Expression(Integer) --E 100 @@ -5041,12 +5098,12 @@ t0819:= sin(x)*(1+sin(x)^2)^(1/2) r0819:= -asin(1/2*cos(x)*2^(1/2))-1/2*cos(x)*(2-cos(x)^2)^(1/2) --R --R ---R +-------------+ +-+ ---R | 2 \|2 cos(x) ---R - cos(x)\|- cos(x) + 2 - 2asin(----------) ---R 2 ---R (90) -------------------------------------------- ---R 2 +--R +-------------+ +-+ +--R | 2 \|2 cos(x) +--R - cos(x)\|- cos(x) + 2 - 2asin(----------) +--R 2 +--R (2) -------------------------------------------- +--R 2 --R Type: Expression(Integer) --E 101 @@ -5054,7 +5111,7 @@ r0819:= -asin(1/2*cos(x)*2^(1/2))-1/2*cos(x)*(2-cos(x)^2)^(1/2) a0819:= integrate(t0819,x) --R --R ---R (91) +--R (3) --R +---------------------+ --R | 2 --R 3 2 | - 4cos(x) + 8 @@ -5142,7 +5199,7 @@ a0819:= integrate(t0819,x) m0819:= a0819-r0819 --R --R ---R (92) +--R (4) --R +---------------------+ --R | 2 --R 3 2 | - 4cos(x) + 8 @@ -5248,7 +5305,7 @@ m0819:= a0819-r0819 d0819:= D(m0819,x) --R --R ---R (93) +--R (5) --R 13 12 11 10 --R 1024cos(x) + 1024cos(x) - 8192cos(x) - 8192cos(x) --R + @@ -5781,15 +5838,18 @@ d0819:= D(m0819,x) --R Type: Expression(Integer) --E 104 +)clear all + + --S 105 of 526 t0820:= sin(7+3*x)/(3+sin(7+3*x)^2)^(1/2) --R --R ---R sin(3x + 7) ---R (94) ------------------- ---R +----------------+ ---R | 2 ---R \|sin(3x + 7) + 3 +--R sin(3x + 7) +--R (1) ------------------- +--R +----------------+ +--R | 2 +--R \|sin(3x + 7) + 3 --R Type: Expression(Integer) --E 105 @@ -5797,11 +5857,11 @@ t0820:= sin(7+3*x)/(3+sin(7+3*x)^2)^(1/2) r0820:= -1/3*asin(1/2*cos(7+3*x)) --R --R ---R cos(3x + 7) ---R asin(-----------) ---R 2 ---R (95) - ----------------- ---R 3 +--R cos(3x + 7) +--R asin(-----------) +--R 2 +--R (2) - ----------------- +--R 3 --R Type: Expression(Integer) --E 106 @@ -5809,7 +5869,7 @@ r0820:= -1/3*asin(1/2*cos(7+3*x)) a0820:= integrate(t0820,x) --R --R ---R (96) +--R (3) --R - --R atan --R +-------------------------------+ @@ -5869,7 +5929,7 @@ a0820:= integrate(t0820,x) m0820:= a0820-r0820 --R --R ---R (97) +--R (4) --R - --R atan --R +-------------------------------+ @@ -5933,7 +5993,7 @@ m0820:= a0820-r0820 d0820:= D(m0820,x) --R --R ---R (98) +--R (5) --R 7 6 5 --R - 64cos(3x + 7) - 64cos(3x + 7) + 384cos(3x + 7) --R + @@ -6298,15 +6358,18 @@ d0820:= D(m0820,x) --R Type: Expression(Integer) --E 109 +)clear all + + --S 110 of 526 t0821:= cos(x)/(1+cos(x)^2)^(1/2) --R --R ---R cos(x) ---R (99) -------------- ---R +-----------+ ---R | 2 ---R \|cos(x) + 1 +--R cos(x) +--R (1) -------------- +--R +-----------+ +--R | 2 +--R \|cos(x) + 1 --R Type: Expression(Integer) --E 110 @@ -6314,10 +6377,10 @@ t0821:= cos(x)/(1+cos(x)^2)^(1/2) r0821:= asin(1/2*sin(x)*2^(1/2)) --R --R ---R +-+ ---R \|2 sin(x) ---R (100) asin(----------) ---R 2 +--R +-+ +--R \|2 sin(x) +--R (2) asin(----------) +--R 2 --R Type: Expression(Integer) --E 111 @@ -6325,7 +6388,7 @@ r0821:= asin(1/2*sin(x)*2^(1/2)) a0821:= integrate(t0821,x) --R --R ---R (101) +--R (3) --R - --R atan --R +---------------------+ @@ -6363,7 +6426,7 @@ a0821:= integrate(t0821,x) m0821:= a0821-r0821 --R --R ---R (102) +--R (4) --R - --R atan --R +---------------------+ @@ -6402,7 +6465,7 @@ m0821:= a0821-r0821 d0821:= D(m0821,x) --R --R ---R (103) +--R (5) --R 13 12 11 10 --R - 64cos(x) - 64cos(x) - 112cos(x) - 112cos(x) --R + @@ -6539,15 +6602,18 @@ d0821:= D(m0821,x) --R Type: Expression(Integer) --E 114 +)clear all + + --S 115 of 526 t0822:= cos(5+3*x)/(3+cos(5+3*x)^2)^(1/2) --R --R ---R cos(3x + 5) ---R (104) ------------------- ---R +----------------+ ---R | 2 ---R \|cos(3x + 5) + 3 +--R cos(3x + 5) +--R (1) ------------------- +--R +----------------+ +--R | 2 +--R \|cos(3x + 5) + 3 --R Type: Expression(Integer) --E 115 @@ -6555,11 +6621,11 @@ t0822:= cos(5+3*x)/(3+cos(5+3*x)^2)^(1/2) r0822:= 1/3*asin(1/2*sin(5+3*x)) --R --R ---R sin(3x + 5) ---R asin(-----------) ---R 2 ---R (105) ----------------- ---R 3 +--R sin(3x + 5) +--R asin(-----------) +--R 2 +--R (2) ----------------- +--R 3 --R Type: Expression(Integer) --E 116 @@ -6567,7 +6633,7 @@ r0822:= 1/3*asin(1/2*sin(5+3*x)) a0822:= integrate(t0822,x) --R --R ---R (106) +--R (3) --R - --R atan --R 3 2 @@ -6608,7 +6674,7 @@ a0822:= integrate(t0822,x) m0822:= a0822-r0822 --R --R ---R (107) +--R (4) --R - --R atan --R 3 2 @@ -6649,7 +6715,7 @@ m0822:= a0822-r0822 d0822:= D(m0822,x) --R --R ---R (108) +--R (5) --R 13 12 11 --R - 64cos(3x + 5) - 64cos(3x + 5) - 496cos(3x + 5) --R + @@ -6842,15 +6908,18 @@ d0822:= D(m0822,x) --R Type: Expression(Integer) --E 119 +)clear all + + --S 120 of 526 t0823:= cos(x)/(4-cos(x)^2)^(1/2) --R --R ---R cos(x) ---R (109) ---------------- ---R +-------------+ ---R | 2 ---R \|- cos(x) + 4 +--R cos(x) +--R (1) ---------------- +--R +-------------+ +--R | 2 +--R \|- cos(x) + 4 --R Type: Expression(Integer) --E 120 @@ -6858,10 +6927,10 @@ t0823:= cos(x)/(4-cos(x)^2)^(1/2) r0823:= asinh(1/3*sin(x)*3^(1/2)) --R --R ---R +-+ ---R \|3 sin(x) ---R (110) asinh(----------) ---R 3 +--R +-+ +--R \|3 sin(x) +--R (2) asinh(----------) +--R 3 --R Type: Expression(Integer) --E 121 @@ -6869,7 +6938,7 @@ r0823:= asinh(1/3*sin(x)*3^(1/2)) a0823:= integrate(t0823,x) --R --R ---R (111) +--R (3) --R log --R +---------------------+ --R | 2 @@ -6889,7 +6958,7 @@ a0823:= integrate(t0823,x) m0823:= a0823-r0823 --R --R ---R (112) +--R (4) --R log --R 3 2 --R (- 4cos(x) - 4cos(x) + 10cos(x) + 10)sin(x) @@ -6917,7 +6986,7 @@ m0823:= a0823-r0823 d0823:= D(m0823,x) --R --R ---R (113) +--R (5) --R 4 3 2 --R (- 8cos(x) - 8cos(x) + 20cos(x) + 20cos(x))sin(x) --R * @@ -6967,13 +7036,16 @@ d0823:= D(m0823,x) --R Type: Expression(Integer) --E 124 +)clear all + + --S 125 of 526 t0824:= sin(x)/(a*cos(x)+b*sin(x)) --R --R ---R sin(x) ---R (114) ------------------- ---R b sin(x) + a cos(x) +--R sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) --R Type: Expression(Integer) --E 125 @@ -6981,10 +7053,10 @@ t0824:= sin(x)/(a*cos(x)+b*sin(x)) r0824:= -(-b*x+a*log(a*cos(x)+b*sin(x)))/(a^2+b^2) --R --R ---R - a log(b sin(x) + a cos(x)) + b x ---R (115) ---------------------------------- ---R 2 2 ---R b + a +--R - a log(b sin(x) + a cos(x)) + b x +--R (2) ---------------------------------- +--R 2 2 +--R b + a --R Type: Expression(Integer) --E 126 @@ -6992,12 +7064,12 @@ r0824:= -(-b*x+a*log(a*cos(x)+b*sin(x)))/(a^2+b^2) a0824:= integrate(t0824,x) --R --R ---R 2 - 2b sin(x) - 2a cos(x) ---R a log(----------) - a log(-----------------------) + b x ---R cos(x) + 1 cos(x) + 1 ---R (116) -------------------------------------------------------- ---R 2 2 ---R b + a +--R 2 - 2b sin(x) - 2a cos(x) +--R a log(----------) - a log(-----------------------) + b x +--R cos(x) + 1 cos(x) + 1 +--R (3) -------------------------------------------------------- +--R 2 2 +--R b + a --R Type: Union(Expression(Integer),...) --E 127 @@ -7005,7 +7077,7 @@ a0824:= integrate(t0824,x) m0824:= a0824-r0824 --R --R ---R (117) +--R (4) --R 2 --R a log(b sin(x) + a cos(x)) + a log(----------) --R cos(x) + 1 @@ -7023,18 +7095,21 @@ m0824:= a0824-r0824 d0824:= D(m0824,x) --R --R ---R (118) 0 +--R (5) 0 --R Type: Expression(Integer) --E 129 +)clear all + + --S 130 of 526 t0825:= sin(x)^2/(a*cos(x)+b*sin(x)) --R --R ---R 2 ---R sin(x) ---R (119) ------------------- ---R b sin(x) + a cos(x) +--R 2 +--R sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) --R Type: Expression(Integer) --E 130 @@ -7043,16 +7118,16 @@ r0825:= -a^2*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ b*cos(x)/(a^2+b^2)-a*sin(x)/(a^2+b^2) --R --R ---R +-------+ ---R 2 a sin(x) - b cos(x) | 2 2 ---R a atanh(-------------------) + (- a sin(x) - b cos(x))\|b + a ---R +-------+ ---R | 2 2 ---R \|b + a ---R (120) ---------------------------------------------------------------- ---R +-------+ ---R 2 2 | 2 2 ---R (b + a )\|b + a +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R a atanh(-------------------) + (- a sin(x) - b cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (2) ---------------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a --R Type: Expression(Integer) --E 131 @@ -7060,7 +7135,7 @@ r0825:= -a^2*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ a0825:= integrate(t0825,x) --R --R ---R (121) +--R (3) --R 2 --R a --R * @@ -7088,7 +7163,7 @@ a0825:= integrate(t0825,x) m0825:= a0825-r0825 --R --R ---R (122) +--R (4) --R 2 --R a --R * @@ -7118,7 +7193,7 @@ m0825:= a0825-r0825 d0825:= D(m0825,x) --R --R ---R (123) +--R (5) --R 3 3 2 2 3 2 3 2 3 --R a sin(x) - a b cos(x)sin(x) + (a cos(x) - a )sin(x) - a b cos(x) --R + @@ -7140,14 +7215,17 @@ d0825:= D(m0825,x) --R Type: Expression(Integer) --E 134 +)clear all + + --S 135 of 526 t0826:= sin(x)^3/(a*cos(x)+b*sin(x)) --R --R ---R 3 ---R sin(x) ---R (124) ------------------- ---R b sin(x) + a cos(x) +--R 3 +--R sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) --R Type: Expression(Integer) --E 135 @@ -7157,7 +7235,7 @@ r0826:= 1/2/(a^2+b^2)^2*(3*a^2*b*x+b^3*x-2*a^3*log(a*cos(x)+b*sin(x))-_ b^2*a+b^2*a*cos(x)^2) --R --R ---R (125) +--R (2) --R 3 3 2 --R - 2a log(b sin(x) + a cos(x)) + (- b - a b)cos(x)sin(x) --R + @@ -7173,7 +7251,7 @@ r0826:= 1/2/(a^2+b^2)^2*(3*a^2*b*x+b^3*x-2*a^3*log(a*cos(x)+b*sin(x))-_ a0826:= integrate(t0826,x) --R --R ---R (126) +--R (3) --R 3 2 3 - 2b sin(x) - 2a cos(x) --R 2a log(----------) - 2a log(-----------------------) --R cos(x) + 1 cos(x) + 1 @@ -7190,7 +7268,7 @@ a0826:= integrate(t0826,x) m0826:= a0826-r0826 --R --R ---R (127) +--R (4) --R 3 3 2 --R 2a log(b sin(x) + a cos(x)) + 2a log(----------) --R cos(x) + 1 @@ -7208,18 +7286,21 @@ m0826:= a0826-r0826 d0826:= D(m0826,x) --R --R ---R (128) 0 +--R (5) 0 --R Type: Expression(Integer) --E 139 +)clear all + + --S 140 of 526 t0827:= sin(x)/(a*cos(x)+b*sin(x))^2 --R --R ---R sin(x) ---R (129) ----------------------------------------- ---R 2 2 2 2 ---R b sin(x) + 2a b cos(x)sin(x) + a cos(x) +--R sin(x) +--R (1) ----------------------------------------- +--R 2 2 2 2 +--R b sin(x) + 2a b cos(x)sin(x) + a cos(x) --R Type: Expression(Integer) --E 140 @@ -7228,16 +7309,16 @@ r0827:= -b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)+_ a/(a^2+b^2)/(a*cos(x)+b*sin(x)) --R --R ---R +-------+ ---R 2 a sin(x) - b cos(x) | 2 2 ---R (b sin(x) + a b cos(x))atanh(-------------------) + a\|b + a ---R +-------+ ---R | 2 2 ---R \|b + a ---R (130) --------------------------------------------------------------- ---R +-------+ ---R 3 2 2 3 | 2 2 ---R ((b + a b)sin(x) + (a b + a )cos(x))\|b + a +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R (b sin(x) + a b cos(x))atanh(-------------------) + a\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (2) --------------------------------------------------------------- +--R +-------+ +--R 3 2 2 3 | 2 2 +--R ((b + a b)sin(x) + (a b + a )cos(x))\|b + a --R Type: Expression(Integer) --E 141 @@ -7245,7 +7326,7 @@ r0827:= -b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)+_ a0827:= integrate(t0827,x) --R --R ---R (131) +--R (3) --R 2 --R (b sin(x) + a b cos(x)) --R * @@ -7273,7 +7354,7 @@ a0827:= integrate(t0827,x) m0827:= a0827-r0827 --R --R ---R (132) +--R (4) --R b --R * --R log @@ -7303,7 +7384,7 @@ m0827:= a0827-r0827 d0827:= D(m0827,x) --R --R ---R (133) +--R (5) --R 3 2 2 2 2 3 --R a b sin(x) - b cos(x)sin(x) + (a b cos(x) - a b)sin(x) - b cos(x) --R + @@ -7325,15 +7406,18 @@ d0827:= D(m0827,x) --R Type: Expression(Integer) --E 144 +)clear all + + --S 145 of 526 t0828:= sin(x)^2/(a*cos(x)+b*sin(x))^2 --R --R ---R 2 ---R sin(x) ---R (134) ----------------------------------------- ---R 2 2 2 2 ---R b sin(x) + 2a b cos(x)sin(x) + a cos(x) +--R 2 +--R sin(x) +--R (1) ----------------------------------------- +--R 2 2 2 2 +--R b sin(x) + 2a b cos(x)sin(x) + a cos(x) --R Type: Expression(Integer) --E 145 @@ -7342,7 +7426,7 @@ r0828:= -(a^2-b^2)*x/(a^2+b^2)^2+a/(a^2+b^2)/(b+a*cot(x))-_ 2*a*b*log(a*cos(x)+b*sin(x))/(a^2+b^2)^2 --R --R ---R (135) +--R (2) --R 2 2 2 3 --R (- 2a b cot(x) - 2a b )log(b sin(x) + a cos(x)) + (a b - a )x cot(x) --R + @@ -7358,7 +7442,7 @@ r0828:= -(a^2-b^2)*x/(a^2+b^2)^2+a/(a^2+b^2)/(b+a*cot(x))-_ a0828:= integrate(t0828,x) --R --R ---R (136) +--R (3) --R 2 2 2 --R (2a b sin(x) + 2a b cos(x))log(----------) --R cos(x) + 1 @@ -7379,7 +7463,7 @@ a0828:= integrate(t0828,x) m0828:= a0828-r0828 --R --R ---R (137) +--R (4) --R 2 2 3 3 2 2 --R ((2a b cot(x) + 2a b )sin(x) + 2a b cos(x)cot(x) + 2a b cos(x)) --R * @@ -7414,7 +7498,7 @@ m0828:= a0828-r0828 d0828:= D(m0828,x) --R --R ---R (138) +--R (5) --R 2 2 4 2 3 2 --R ((- a b + a )cot(x) + 2a b cot(x))sin(x) --R + @@ -7443,14 +7527,17 @@ d0828:= D(m0828,x) --R Type: Expression(Integer) --E 149 +)clear all + + --S 150 of 526 t0829:= sin(x)/(a*cos(x)+b*sin(x))^3 --R --R ---R sin(x) ---R (139) --------------------------------------------------------------- ---R 3 3 2 2 2 2 3 3 ---R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) +--R sin(x) +--R (1) --------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) --R Type: Expression(Integer) --E 150 @@ -7459,7 +7546,7 @@ r0829:= 1/2*a/(a^2+b^2)/(a*cos(x)+b*sin(x))^2+_ b*sin(x)/a/(a^2+b^2)/(a*cos(x)+b*sin(x)) --R --R ---R (140) +--R (2) --R 2 2 2 --R 2b sin(x) + 2a b cos(x)sin(x) + a --R -------------------------------------------------------------------------- @@ -7472,11 +7559,11 @@ r0829:= 1/2*a/(a^2+b^2)/(a*cos(x)+b*sin(x))^2+_ a0829:= integrate(t0829,x) --R --R ---R 2 ---R - cos(x) + 1 ---R (141) -------------------------------------------------- ---R 2 2 3 2 2 ---R 4a b cos(x)sin(x) + (- 2a b + 2a )cos(x) + 2a b +--R 2 +--R - cos(x) + 1 +--R (3) -------------------------------------------------- +--R 2 2 3 2 2 +--R 4a b cos(x)sin(x) + (- 2a b + 2a )cos(x) + 2a b --R Type: Union(Expression(Integer),...) --E 152 @@ -7484,7 +7571,7 @@ a0829:= integrate(t0829,x) m0829:= a0829-r0829 --R --R ---R (142) +--R (4) --R 3 3 4 2 2 2 4 2 2 2 --R - 4a b cos(x)sin(x) + ((b - 7a b )cos(x) - b + a b )sin(x) --R + @@ -7509,7 +7596,7 @@ m0829:= a0829-r0829 d0829:= D(m0829,x) --R --R ---R (143) +--R (5) --R 6 2 4 2 6 2 4 5 --R ((b - 3a b )cos(x) + b + a b )sin(x) --R + @@ -7582,15 +7669,18 @@ d0829:= D(m0829,x) --R Type: Expression(Integer) --E 154 +)clear all + + --S 155 of 526 t0830:= sin(x)^3/(a*cos(x)+b*sin(x))^3 --R --R ---R 3 ---R sin(x) ---R (144) --------------------------------------------------------------- ---R 3 3 2 2 2 2 3 3 ---R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) +--R 3 +--R sin(x) +--R (1) --------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) --R Type: Expression(Integer) --E 155 @@ -7600,7 +7690,7 @@ r0830:= -b*(3*a^2-b^2)*x/(a^2+b^2)^3+1/2*a/(a^2+b^2)/(b+a*cot(x))^2+_ log(a*cos(x)+b*sin(x))/(a^2+b^2)^3 --R --R ---R (145) +--R (2) --R 3 2 5 2 2 3 4 4 3 2 --R ((- 6a b + 2a )cot(x) + (- 12a b + 4a b)cot(x) - 6a b + 2a b ) --R * @@ -7624,7 +7714,7 @@ r0830:= -b*(3*a^2-b^2)*x/(a^2+b^2)^3+1/2*a/(a^2+b^2)/(b+a*cot(x))^2+_ a0830:= integrate(t0830,x) --R --R ---R (146) +--R (3) --R 2 3 4 4 3 2 5 2 4 --R (12a b - 4a b)cos(x)sin(x) + (- 6a b + 8a b - 2a )cos(x) + 6a b --R + @@ -7666,7 +7756,7 @@ a0830:= integrate(t0830,x) m0830:= a0830-r0830 --R --R ---R (147) +--R (4) --R 4 3 6 2 3 4 5 2 --R (12a b - 4a b)cos(x)cot(x) + (24a b - 8a b )cos(x)cot(x) --R + @@ -7777,7 +7867,7 @@ m0830:= a0830-r0830 d0830:= D(m0830,x) --R --R ---R (148) +--R (5) --R 5 3 7 2 5 3 7 3 --R ((- 5a b + 3a b)cos(x) + 3a b + a b)cot(x) --R + @@ -7914,13 +8004,16 @@ d0830:= D(m0830,x) --R Type: Expression(Integer) --E 159 +)clear all + + --S 160 of 526 t0831:= cos(x)/(a*cos(x)+b*sin(x)) --R --R ---R cos(x) ---R (149) ------------------- ---R b sin(x) + a cos(x) +--R cos(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) --R Type: Expression(Integer) --E 160 @@ -7928,10 +8021,10 @@ t0831:= cos(x)/(a*cos(x)+b*sin(x)) r0831:= (a*x+b*log(a*cos(x)+b*sin(x)))/(a^2+b^2) --R --R ---R b log(b sin(x) + a cos(x)) + a x ---R (150) -------------------------------- ---R 2 2 ---R b + a +--R b log(b sin(x) + a cos(x)) + a x +--R (2) -------------------------------- +--R 2 2 +--R b + a --R Type: Expression(Integer) --E 161 @@ -7939,12 +8032,12 @@ r0831:= (a*x+b*log(a*cos(x)+b*sin(x)))/(a^2+b^2) a0831:= integrate(t0831,x) --R --R ---R 2 - 2b sin(x) - 2a cos(x) ---R - b log(----------) + b log(-----------------------) + a x ---R cos(x) + 1 cos(x) + 1 ---R (151) ---------------------------------------------------------- ---R 2 2 ---R b + a +--R 2 - 2b sin(x) - 2a cos(x) +--R - b log(----------) + b log(-----------------------) + a x +--R cos(x) + 1 cos(x) + 1 +--R (3) ---------------------------------------------------------- +--R 2 2 +--R b + a --R Type: Union(Expression(Integer),...) --E 162 @@ -7952,7 +8045,7 @@ a0831:= integrate(t0831,x) m0831:= a0831-r0831 --R --R ---R (152) +--R (4) --R 2 --R - b log(b sin(x) + a cos(x)) - b log(----------) --R cos(x) + 1 @@ -7970,18 +8063,21 @@ m0831:= a0831-r0831 d0831:= D(m0831,x) --R --R ---R (153) 0 +--R (5) 0 --R Type: Expression(Integer) --E 164 +)clear all + + --S 165 of 526 t0832:= cos(x)^2/(a*cos(x)+b*sin(x)) --R --R ---R 2 ---R cos(x) ---R (154) ------------------- ---R b sin(x) + a cos(x) +--R 2 +--R cos(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) --R Type: Expression(Integer) --E 165 @@ -7990,16 +8086,16 @@ r0832:= -b^2*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)+_ b*cos(x)/(a^2+b^2)+a*sin(x)/(a^2+b^2) --R --R ---R +-------+ ---R 2 a sin(x) - b cos(x) | 2 2 ---R b atanh(-------------------) + (a sin(x) + b cos(x))\|b + a ---R +-------+ ---R | 2 2 ---R \|b + a ---R (155) -------------------------------------------------------------- ---R +-------+ ---R 2 2 | 2 2 ---R (b + a )\|b + a +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R b atanh(-------------------) + (a sin(x) + b cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (2) -------------------------------------------------------------- +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a --R Type: Expression(Integer) --E 166 @@ -8007,7 +8103,7 @@ r0832:= -b^2*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)+_ a0832:= integrate(t0832,x) --R --R ---R (156) +--R (3) --R 2 --R b --R * @@ -8035,7 +8131,7 @@ a0832:= integrate(t0832,x) m0832:= a0832-r0832 --R --R ---R (157) +--R (4) --R 2 --R b --R * @@ -8065,7 +8161,7 @@ m0832:= a0832-r0832 d0832:= D(m0832,x) --R --R ---R (158) +--R (5) --R 2 3 3 2 2 2 2 3 3 --R a b sin(x) - b cos(x)sin(x) + (a b cos(x) - a b )sin(x) - b cos(x) --R + @@ -8087,14 +8183,17 @@ d0832:= D(m0832,x) --R Type: Expression(Integer) --E 169 +)clear all + + --S 170 of 526 t0833:= cos(x)^3/(a*cos(x)+b*sin(x)) --R --R ---R 3 ---R cos(x) ---R (159) ------------------- ---R b sin(x) + a cos(x) +--R 3 +--R cos(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) --R Type: Expression(Integer) --E 170 @@ -8104,7 +8203,7 @@ r0833:= 1/2/(a^2+b^2)^2*(3*a*b^2*x+a^3*x+2*b^3*log(a*cos(x)+_ a^2*b+b*cos(x)^2*a^2-b^3+b^3*cos(x)^2) --R --R ---R (160) +--R (2) --R 3 2 3 3 2 2 --R 2b log(b sin(x) + a cos(x)) + (a b + a )cos(x)sin(x) + (b + a b)cos(x) --R + @@ -8120,7 +8219,7 @@ r0833:= 1/2/(a^2+b^2)^2*(3*a*b^2*x+a^3*x+2*b^3*log(a*cos(x)+_ a0833:= integrate(t0833,x) --R --R ---R (161) +--R (3) --R 3 2 3 - 2b sin(x) - 2a cos(x) --R - 2b log(----------) + 2b log(-----------------------) --R cos(x) + 1 cos(x) + 1 @@ -8137,7 +8236,7 @@ a0833:= integrate(t0833,x) m0833:= a0833-r0833 --R --R ---R (162) +--R (4) --R 3 3 2 --R - 2b log(b sin(x) + a cos(x)) - 2b log(----------) --R cos(x) + 1 @@ -8155,18 +8254,21 @@ m0833:= a0833-r0833 d0833:= D(m0833,x) --R --R ---R (163) 0 +--R (5) 0 --R Type: Expression(Integer) --E 174 +)clear all + + --S 175 of 526 t0834:= cos(x)/(a*cos(x)+b*sin(x))^2 --R --R ---R cos(x) ---R (164) ----------------------------------------- ---R 2 2 2 2 ---R b sin(x) + 2a b cos(x)sin(x) + a cos(x) +--R cos(x) +--R (1) ----------------------------------------- +--R 2 2 2 2 +--R b sin(x) + 2a b cos(x)sin(x) + a cos(x) --R Type: Expression(Integer) --E 175 @@ -8175,16 +8277,16 @@ r0834:= -a*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ b/(a^2+b^2)/(a*cos(x)+b*sin(x)) --R --R ---R +-------+ ---R 2 a sin(x) - b cos(x) | 2 2 ---R (a b sin(x) + a cos(x))atanh(-------------------) - b\|b + a ---R +-------+ ---R | 2 2 ---R \|b + a ---R (165) --------------------------------------------------------------- ---R +-------+ ---R 3 2 2 3 | 2 2 ---R ((b + a b)sin(x) + (a b + a )cos(x))\|b + a +--R +-------+ +--R 2 a sin(x) - b cos(x) | 2 2 +--R (a b sin(x) + a cos(x))atanh(-------------------) - b\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (2) --------------------------------------------------------------- +--R +-------+ +--R 3 2 2 3 | 2 2 +--R ((b + a b)sin(x) + (a b + a )cos(x))\|b + a --R Type: Expression(Integer) --E 176 @@ -8192,7 +8294,7 @@ r0834:= -a*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ a0834:= integrate(t0834,x) --R --R ---R (166) +--R (3) --R 2 3 --R (a b sin(x) + a cos(x)) --R * @@ -8220,7 +8322,7 @@ a0834:= integrate(t0834,x) m0834:= a0834-r0834 --R --R ---R (167) +--R (4) --R 2 --R a --R * @@ -8251,7 +8353,7 @@ m0834:= a0834-r0834 d0834:= D(m0834,x) --R --R ---R (168) +--R (5) --R 2 3 2 2 2 2 3 --R a sin(x) - a b cos(x)sin(x) + (a cos(x) - a )sin(x) - a b cos(x) --R + @@ -8272,15 +8374,18 @@ d0834:= D(m0834,x) --R Type: Expression(Integer) --E 179 +)clear all + + --S 180 of 526 t0835:= cos(x)^2/(a*cos(x)+b*sin(x))^2 --R --R ---R 2 ---R cos(x) ---R (169) ----------------------------------------- ---R 2 2 2 2 ---R b sin(x) + 2a b cos(x)sin(x) + a cos(x) +--R 2 +--R cos(x) +--R (1) ----------------------------------------- +--R 2 2 2 2 +--R b sin(x) + 2a b cos(x)sin(x) + a cos(x) --R Type: Expression(Integer) --E 180 @@ -8289,7 +8394,7 @@ r0835:= (a^2-b^2)*x/(a^2+b^2)^2+2*a*b*log(a*cos(x)+b*sin(x))/(a^2+b^2)^2-_ b/(a^2+b^2)/(a+b*tan(x)) --R --R ---R (170) +--R (2) --R 2 2 3 2 --R (2a b tan(x) + 2a b)log(b sin(x) + a cos(x)) + (- b + a b)x tan(x) --R + @@ -8305,7 +8410,7 @@ r0835:= (a^2-b^2)*x/(a^2+b^2)^2+2*a*b*log(a*cos(x)+b*sin(x))/(a^2+b^2)^2-_ a0835:= integrate(t0835,x) --R --R ---R (171) +--R (3) --R 2 2 3 2 --R (- 2a b sin(x) - 2a b cos(x))log(----------) --R cos(x) + 1 @@ -8326,7 +8431,7 @@ a0835:= integrate(t0835,x) m0835:= a0835-r0835 --R --R ---R (172) +--R (4) --R 2 3 3 2 3 2 4 --R ((- 2a b sin(x) - 2a b cos(x))tan(x) - 2a b sin(x) - 2a b cos(x)) --R * @@ -8361,7 +8466,7 @@ m0835:= a0835-r0835 d0835:= D(m0835,x) --R --R ---R (173) +--R (5) --R 3 4 2 2 2 2 --R (- 2a b cos(x)sin(x) + (b - a b )cos(x) )tan(x) --R + @@ -8393,14 +8498,17 @@ d0835:= D(m0835,x) --R Type: Expression(Integer) --E 184 +)clear all + + --S 185 of 526 t0836:= cos(x)/(a*cos(x)+b*sin(x))^3 --R --R ---R cos(x) ---R (174) --------------------------------------------------------------- ---R 3 3 2 2 2 2 3 3 ---R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) +--R cos(x) +--R (1) --------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) --R Type: Expression(Integer) --E 185 @@ -8409,7 +8517,7 @@ r0836:= -1/2*b/(a^2+b^2)/(a*cos(x)+b*sin(x))^2+_ sin(x)/(a^2+b^2)/(a*cos(x)+b*sin(x)) --R --R ---R (175) +--R (2) --R 2 --R 2b sin(x) + 2a cos(x)sin(x) - b --R ------------------------------------------------------------------------ @@ -8422,11 +8530,11 @@ r0836:= -1/2*b/(a^2+b^2)/(a*cos(x)+b*sin(x))^2+_ a0836:= integrate(t0836,x) --R --R ---R 2 ---R 2a cos(x)sin(x) - b cos(x) + b ---R (176) -------------------------------------------------- ---R 3 2 2 4 2 2 2 ---R 4a b cos(x)sin(x) + (- 2a b + 2a )cos(x) + 2a b +--R 2 +--R 2a cos(x)sin(x) - b cos(x) + b +--R (3) -------------------------------------------------- +--R 3 2 2 4 2 2 2 +--R 4a b cos(x)sin(x) + (- 2a b + 2a )cos(x) + 2a b --R Type: Union(Expression(Integer),...) --E 187 @@ -8434,7 +8542,7 @@ a0836:= integrate(t0836,x) m0836:= a0836-r0836 --R --R ---R (177) +--R (4) --R 4 3 2 3 --R (2a b - 2a b )cos(x)sin(x) --R + @@ -8465,7 +8573,7 @@ m0836:= a0836-r0836 d0836:= D(m0836,x) --R --R ---R (178) +--R (5) --R 5 3 3 2 5 --R (a b - 3a b )cos(x) sin(x) --R + @@ -8532,15 +8640,18 @@ d0836:= D(m0836,x) --R Type: Expression(Integer) --E 189 +)clear all + + --S 190 of 526 t0837:= cos(x)^3/(a*cos(x)+b*sin(x))^3 --R --R ---R 3 ---R cos(x) ---R (179) --------------------------------------------------------------- ---R 3 3 2 2 2 2 3 3 ---R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) +--R 3 +--R cos(x) +--R (1) --------------------------------------------------------------- +--R 3 3 2 2 2 2 3 3 +--R b sin(x) + 3a b cos(x)sin(x) + 3a b cos(x) sin(x) + a cos(x) --R Type: Expression(Integer) --E 190 @@ -8550,7 +8661,7 @@ r0837:= (a^3*x-3*a*b^2*x)/(a^2+b^2)^3+b*(3*a^2-b^2)*_ 2*a*b/(a^2+b^2)^2/(a+b*tan(x)) --R --R ---R (180) +--R (2) --R 5 2 3 2 4 3 2 2 3 4 --R ((- 2b + 6a b )tan(x) + (- 4a b + 12a b )tan(x) - 2a b + 6a b) --R * @@ -8574,7 +8685,7 @@ r0837:= (a^3*x-3*a*b^2*x)/(a^2+b^2)^3+b*(3*a^2-b^2)*_ a0837:= integrate(t0837,x) --R --R ---R (181) +--R (3) --R 3 4 5 2 2 5 4 3 6 2 --R (4a b - 12a b )cos(x)sin(x) + (- 2a b + 8a b - 6a b)cos(x) --R + @@ -8616,7 +8727,7 @@ a0837:= integrate(t0837,x) m0837:= a0837-r0837 --R --R ---R (182) +--R (4) --R 3 6 5 4 2 7 4 5 6 3 2 --R (4a b - 12a b )cos(x)sin(x) + (- 2a b + 8a b - 6a b )cos(x) --R + @@ -8754,7 +8865,7 @@ m0837:= a0837-r0837 d0837:= D(m0837,x) --R --R ---R (183) +--R (5) --R 7 3 5 2 7 2 --R ((3a b - 5a b )cos(x) + 2a b )sin(x) --R + @@ -8882,13 +8993,16 @@ d0837:= D(m0837,x) --R Type: Expression(Integer) --E 194 +)clear all + + --S 195 of 526 t0838:= tan(x)/(b*cos(x)+a*sin(x)) --R --R ---R tan(x) ---R (184) ------------------- ---R a sin(x) + b cos(x) +--R tan(x) +--R (1) ------------------- +--R a sin(x) + b cos(x) --R Type: Expression(Integer) --E 195 @@ -8897,16 +9011,16 @@ r0838:= atanh(sin(x))/a+b*atanh((a*cos(x)-b*sin(x))/(a^2+b^2)^(1/2))/_ a/(a^2+b^2)^(1/2) --R --R ---R +-------+ ---R | 2 2 b sin(x) - a cos(x) ---R \|b + a atanh(sin(x)) - b atanh(-------------------) ---R +-------+ ---R | 2 2 ---R \|b + a ---R (185) ------------------------------------------------------ ---R +-------+ ---R | 2 2 ---R a\|b + a +--R +-------+ +--R | 2 2 b sin(x) - a cos(x) +--R \|b + a atanh(sin(x)) - b atanh(-------------------) +--R +-------+ +--R | 2 2 +--R \|b + a +--R (2) ------------------------------------------------------ +--R +-------+ +--R | 2 2 +--R a\|b + a --R Type: Expression(Integer) --E 196 @@ -8914,7 +9028,7 @@ r0838:= atanh(sin(x))/a+b*atanh((a*cos(x)-b*sin(x))/(a^2+b^2)^(1/2))/_ a0838:= integrate(t0838,x) --R --R ---R (186) +--R (3) --R b --R * --R log @@ -8942,7 +9056,7 @@ a0838:= integrate(t0838,x) m0838:= a0838-r0838 --R --R ---R (187) +--R (4) --R b --R * --R log @@ -8977,7 +9091,7 @@ m0838:= a0838-r0838 d0838:= D(m0838,x) --R --R ---R (188) +--R (5) --R 5 2 3 8 4 3 2 4 3 2 7 --R (b - a b )sin(x) + ((- 4a b + 4a b )cos(x) + a b + a b )sin(x) --R + @@ -9326,13 +9440,16 @@ d0838:= D(m0838,x) --R Type: Expression(Integer) --E 199 +)clear all + + --S 200 of 526 t0839:= sec(x)/(sec(x)-tan(x)) --R --R ---R sec(x) ---R (189) - --------------- ---R tan(x) - sec(x) +--R sec(x) +--R (1) - --------------- +--R tan(x) - sec(x) --R Type: Expression(Integer) --E 200 @@ -9340,9 +9457,9 @@ t0839:= sec(x)/(sec(x)-tan(x)) r0839:= (1+sin(x))/cos(x) --R --R ---R sin(x) + 1 ---R (190) ---------- ---R cos(x) +--R sin(x) + 1 +--R (2) ---------- +--R cos(x) --R Type: Expression(Integer) --E 201 @@ -9350,9 +9467,9 @@ r0839:= (1+sin(x))/cos(x) a0839:= integrate(t0839,x) --R --R ---R - 2cos(x) - 2 ---R (191) ------------------- ---R sin(x) - cos(x) - 1 +--R - 2cos(x) - 2 +--R (3) ------------------- +--R sin(x) - cos(x) - 1 --R Type: Union(Expression(Integer),...) --E 202 @@ -9360,11 +9477,11 @@ a0839:= integrate(t0839,x) m0839:= a0839-r0839 --R --R ---R 2 2 ---R - sin(x) + cos(x)sin(x) - 2cos(x) - cos(x) + 1 ---R (192) ------------------------------------------------ ---R 2 ---R cos(x)sin(x) - cos(x) - cos(x) +--R 2 2 +--R - sin(x) + cos(x)sin(x) - 2cos(x) - cos(x) + 1 +--R (4) ------------------------------------------------ +--R 2 +--R cos(x)sin(x) - cos(x) - cos(x) --R Type: Expression(Integer) --E 203 @@ -9372,7 +9489,7 @@ m0839:= a0839-r0839 d0839:= D(m0839,x) --R --R ---R (193) +--R (5) --R 4 3 2 --R - sin(x) + (2cos(x) + 1)sin(x) + sin(x) --R + @@ -9387,13 +9504,16 @@ d0839:= D(m0839,x) --R Type: Expression(Integer) --E 204 +)clear all + + --S 205 of 526 t0840:= tan(x)/(csc(x)+cot(x)) --R --R ---R tan(x) ---R (194) --------------- ---R csc(x) + cot(x) +--R tan(x) +--R (1) --------------- +--R csc(x) + cot(x) --R Type: Expression(Integer) --E 205 @@ -9401,7 +9521,7 @@ t0840:= tan(x)/(csc(x)+cot(x)) r0840:= -x+atanh(sin(x)) --R --R ---R (195) atanh(sin(x)) - x +--R (2) atanh(sin(x)) - x --R Type: Expression(Integer) --E 206 @@ -9409,9 +9529,9 @@ r0840:= -x+atanh(sin(x)) a0840:= integrate(t0840,x) --R --R ---R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 ---R (196) log(-------------------) - log(-------------------) - x ---R cos(x) + 1 cos(x) + 1 +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (3) log(-------------------) - log(-------------------) - x +--R cos(x) + 1 cos(x) + 1 --R Type: Union(Expression(Integer),...) --E 207 @@ -9419,9 +9539,9 @@ a0840:= integrate(t0840,x) m0840:= a0840-r0840 --R --R ---R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 ---R (197) log(-------------------) - log(-------------------) - atanh(sin(x)) ---R cos(x) + 1 cos(x) + 1 +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (4) log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 --R Type: Expression(Integer) --E 208 @@ -9429,21 +9549,24 @@ m0840:= a0840-r0840 d0840:= D(m0840,x) --R --R ---R 4 2 2 3 ---R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) ---R (198) ------------------------------------------------------------------ ---R 4 2 2 2 ---R sin(x) + (- cos(x) - 2cos(x) - 2)sin(x) + cos(x) + 2cos(x) + 1 +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R (5) ------------------------------------------------------------------ +--R 4 2 2 2 +--R sin(x) + (- cos(x) - 2cos(x) - 2)sin(x) + cos(x) + 2cos(x) + 1 --R Type: Expression(Integer) --E 209 +)clear all + + --S 210 of 526 t0841:= tan(x)/(csc(x)-cot(x)) --R --R ---R tan(x) ---R (199) --------------- ---R csc(x) - cot(x) +--R tan(x) +--R (1) --------------- +--R csc(x) - cot(x) --R Type: Expression(Integer) --E 210 @@ -9451,7 +9574,7 @@ t0841:= tan(x)/(csc(x)-cot(x)) r0841:= x+atanh(sin(x)) --R --R ---R (200) atanh(sin(x)) + x +--R (2) atanh(sin(x)) + x --R Type: Expression(Integer) --E 211 @@ -9459,9 +9582,9 @@ r0841:= x+atanh(sin(x)) a0841:= integrate(t0841,x) --R --R ---R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 ---R (201) log(-------------------) - log(-------------------) + x ---R cos(x) + 1 cos(x) + 1 +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (3) log(-------------------) - log(-------------------) + x +--R cos(x) + 1 cos(x) + 1 --R Type: Union(Expression(Integer),...) --E 212 @@ -9469,9 +9592,9 @@ a0841:= integrate(t0841,x) m0841:= a0841-r0841 --R --R ---R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 ---R (202) log(-------------------) - log(-------------------) - atanh(sin(x)) ---R cos(x) + 1 cos(x) + 1 +--R sin(x) + cos(x) + 1 sin(x) - cos(x) - 1 +--R (4) log(-------------------) - log(-------------------) - atanh(sin(x)) +--R cos(x) + 1 cos(x) + 1 --R Type: Expression(Integer) --E 213 @@ -9479,21 +9602,24 @@ m0841:= a0841-r0841 d0841:= D(m0841,x) --R --R ---R 4 2 2 3 ---R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) ---R (203) ------------------------------------------------------------------ ---R 4 2 2 2 ---R sin(x) + (- cos(x) - 2cos(x) - 2)sin(x) + cos(x) + 2cos(x) + 1 +--R 4 2 2 3 +--R - 2sin(x) + (- 2cos(x) - cos(x) + 2)sin(x) - cos(x) + cos(x) +--R (5) ------------------------------------------------------------------ +--R 4 2 2 2 +--R sin(x) + (- cos(x) - 2cos(x) - 2)sin(x) + cos(x) + 2cos(x) + 1 --R Type: Expression(Integer) --E 214 +)clear all + + --S 215 of 526 t0842:= cos(x)*sin(x)/(a*cos(x)+b*sin(x)) --R --R ---R cos(x)sin(x) ---R (204) ------------------- ---R b sin(x) + a cos(x) +--R cos(x)sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) --R Type: Expression(Integer) --E 215 @@ -9502,16 +9628,16 @@ r0842:= a*b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ a*cos(x)/(a^2+b^2)+b*sin(x)/(a^2+b^2) --R --R ---R +-------+ ---R a sin(x) - b cos(x) | 2 2 ---R - a b atanh(-------------------) + (b sin(x) - a cos(x))\|b + a ---R +-------+ ---R | 2 2 ---R \|b + a ---R (205) ------------------------------------------------------------------ ---R +-------+ ---R 2 2 | 2 2 ---R (b + a )\|b + a +--R +-------+ +--R a sin(x) - b cos(x) | 2 2 +--R - a b atanh(-------------------) + (b sin(x) - a cos(x))\|b + a +--R +-------+ +--R | 2 2 +--R \|b + a +--R (2) ------------------------------------------------------------------ +--R +-------+ +--R 2 2 | 2 2 +--R (b + a )\|b + a --R Type: Expression(Integer) --E 216 @@ -9519,7 +9645,7 @@ r0842:= a*b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(3/2)-_ a0842:= integrate(t0842,x) --R --R ---R (206) +--R (3) --R a b --R * --R log @@ -9546,7 +9672,7 @@ a0842:= integrate(t0842,x) m0842:= a0842-r0842 --R --R ---R (207) +--R (4) --R a b --R * --R log @@ -9575,7 +9701,7 @@ m0842:= a0842-r0842 d0842:= D(m0842,x) --R --R ---R (208) +--R (5) --R 2 3 2 2 2 2 2 --R a b sin(x) - a b cos(x)sin(x) + (a b cos(x) - a b)sin(x) --R + @@ -9597,14 +9723,17 @@ d0842:= D(m0842,x) --R Type: Expression(Integer) --E 291 +)clear all + + --S 220 of 526 t0843:= cos(x)*sin(x)^2/(a*cos(x)+b*sin(x)) --R --R ---R 2 ---R cos(x)sin(x) ---R (209) ------------------- ---R b sin(x) + a cos(x) +--R 2 +--R cos(x)sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) --R Type: Expression(Integer) --E 220 @@ -9614,7 +9743,7 @@ r0843:= 1/2/(a^2+b^2)^2*(a^3*x-a*b^2*x+2*a^2*b*_ cos(x)*sin(x)*b^2*a-b*cos(x)^2*a^2+a^2*b-b^3*cos(x)^2+b^3) --R --R ---R (210) +--R (2) --R 2 2 3 --R 2a b log(b sin(x) + a cos(x)) + (- a b - a )cos(x)sin(x) --R + @@ -9630,7 +9759,7 @@ r0843:= 1/2/(a^2+b^2)^2*(a^3*x-a*b^2*x+2*a^2*b*_ a0843:= integrate(t0843,x) --R --R ---R (211) +--R (3) --R 2 2 2 - 2b sin(x) - 2a cos(x) --R - 2a b log(----------) + 2a b log(-----------------------) --R cos(x) + 1 cos(x) + 1 @@ -9647,7 +9776,7 @@ a0843:= integrate(t0843,x) m0843:= a0843-r0843 --R --R ---R (212) +--R (4) --R 2 2 2 --R - 2a b log(b sin(x) + a cos(x)) - 2a b log(----------) --R cos(x) + 1 @@ -9665,18 +9794,21 @@ m0843:= a0843-r0843 d0843:= D(m0843,x) --R --R ---R (213) 0 +--R (5) 0 --R Type: Expression(Integer) --E 224 +)clear all + + --S 225 of 526 t0844:= cos(x)*sin(x)^3/(a*cos(x)+b*sin(x)) --R --R ---R 3 ---R cos(x)sin(x) ---R (214) ------------------- ---R b sin(x) + a cos(x) +--R 3 +--R cos(x)sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) --R Type: Expression(Integer) --E 225 @@ -9687,7 +9819,7 @@ r0844:= a^3*b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)-_ b*sin(x)^3/(3*a^2+3*b^2) --R --R ---R (215) +--R (2) --R 3 a sin(x) - b cos(x) --R - 3a b atanh(-------------------) --R +-------+ @@ -9711,7 +9843,7 @@ r0844:= a^3*b*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)-_ a0844:= integrate(t0844,x) --R --R ---R (216) +--R (3) --R 3 --R 3a b --R * @@ -9745,7 +9877,7 @@ a0844:= integrate(t0844,x) m0844:= a0844-r0844 --R --R ---R (217) +--R (4) --R 3 --R 3a b --R * @@ -9779,7 +9911,7 @@ m0844:= a0844-r0844 d0844:= D(m0844,x) --R --R ---R (218) +--R (5) --R 4 3 3 2 2 4 2 4 --R 3a b sin(x) - 3a b cos(x)sin(x) + (3a b cos(x) - 3a b)sin(x) --R + @@ -9824,14 +9956,17 @@ d0844:= D(m0844,x) --R Type: Expression(Integer) --E 229 +)clear all + + --S 230 of 526 t0845:= sin(x)*cos(x)^2/(a*cos(x)+b*sin(x)) --R --R ---R 2 ---R cos(x) sin(x) ---R (219) ------------------- ---R b sin(x) + a cos(x) +--R 2 +--R cos(x) sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) --R Type: Expression(Integer) --E 230 @@ -9841,7 +9976,7 @@ r0845:= -1/2*(-b^3*x+a^2*b*x+2*a*b^2*log(a*cos(x)+b*sin(x))-_ a^3+b^2*a*cos(x)^2-b^2*a)/(a^2+b^2)^2 --R --R ---R (220) +--R (2) --R 2 3 2 --R - 2a b log(b sin(x) + a cos(x)) + (b + a b)cos(x)sin(x) --R + @@ -9857,7 +9992,7 @@ r0845:= -1/2*(-b^3*x+a^2*b*x+2*a*b^2*log(a*cos(x)+b*sin(x))-_ a0845:= integrate(t0845,x) --R --R ---R (221) +--R (3) --R 2 2 2 - 2b sin(x) - 2a cos(x) --R 2a b log(----------) - 2a b log(-----------------------) --R cos(x) + 1 cos(x) + 1 @@ -9874,7 +10009,7 @@ a0845:= integrate(t0845,x) m0845:= a0845-r0845 --R --R ---R (222) +--R (4) --R 2 2 2 --R 2a b log(b sin(x) + a cos(x)) + 2a b log(----------) --R cos(x) + 1 @@ -9892,18 +10027,21 @@ m0845:= a0845-r0845 d0845:= D(m0845,x) --R --R ---R (223) 0 +--R (5) 0 --R Type: Expression(Integer) --E 234 +)clear all + + --S 235 of 526 t0846:= sin(x)*cos(x)^3/(a*cos(x)+b*sin(x)) --R --R ---R 3 ---R cos(x) sin(x) ---R (224) ------------------- ---R b sin(x) + a cos(x) +--R 3 +--R cos(x) sin(x) +--R (1) ------------------- +--R b sin(x) + a cos(x) --R Type: Expression(Integer) --E 235 @@ -9913,7 +10051,7 @@ r0846:= a*b^3*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)-_ a^2*b*sin(x)/(a^2+b^2)^2+b*sin(x)/(a^2+b^2)-b*sin(x)^3/(3*a^2+3*b^2) --R --R ---R (225) +--R (2) --R 3 a sin(x) - b cos(x) --R - 3a b atanh(-------------------) --R +-------+ @@ -9937,7 +10075,7 @@ r0846:= a*b^3*atanh((b*cos(x)-a*sin(x))/(a^2+b^2)^(1/2))/(a^2+b^2)^(5/2)-_ a0846:= integrate(t0846,x) --R --R ---R (226) +--R (3) --R 3 --R 3a b --R * @@ -9971,7 +10109,7 @@ a0846:= integrate(t0846,x) m0846:= a0846-r0846 --R --R ---R (227) +--R (4) --R 3 --R 3a b --R * @@ -10005,7 +10143,7 @@ m0846:= a0846-r0846 d0846:= D(m0846,x) --R --R ---R (228) +--R (5) --R 2 3 3 4 2 2 3 2 2 3 --R 3a b sin(x) - 3a b cos(x)sin(x) + (3a b cos(x) - 3a b )sin(x) --R + @@ -10050,14 +10188,17 @@ d0846:= D(m0846,x) --R Type: Expression(Integer) --E 239 +)clear all + + --S 240 of 526 t0847:= sec(x)^2/(a+b*tan(x)+c*sec(x)) --R --R ---R 2 ---R sec(x) ---R (229) ----------------------- ---R b tan(x) + c sec(x) + a +--R 2 +--R sec(x) +--R (1) ----------------------- +--R b tan(x) + c sec(x) + a --R Type: Expression(Integer) --E 240 @@ -10068,7 +10209,7 @@ r0847:= -2*a*c*atanh((b-(a-c)*tan(1/2*x))/(a^2+b^2-c^2)^(1/2))/_ tan(1/2*x)^2)/(b^2-c^2) --R --R ---R (230) +--R (2) --R +--------------+ --R | 2 2 2 x 2 x --R - b\|- c + b + a log((c - a)tan(-) + 2b tan(-) + c + a) @@ -10097,7 +10238,7 @@ r0847:= -2*a*c*atanh((b-(a-c)*tan(1/2*x))/(a^2+b^2-c^2)^(1/2))/_ a0847:= integrate(t0847,x) --R --R ---R (231) +--R (3) --R [ --R a c --R * @@ -10173,7 +10314,7 @@ a0847:= integrate(t0847,x) m0847a:= a0847.1-r0847 --R --R ---R (232) +--R (4) --R a c --R * --R log @@ -10235,7 +10376,7 @@ m0847a:= a0847.1-r0847 d0847a:= D(m0847a,x) --R --R ---R (233) +--R (5) --R 3 2 3 2 3 5 --R (b c - 2a b c + a b )sin(x) --R + @@ -13199,7 +13340,7 @@ d0847a:= D(m0847a,x) m0847b:= a0847.2-r0847 --R --R ---R (234) +--R (6) --R +--------------+ +------------+ --R | 2 2 2 | 2 2 2 x 2 x --R b\|- c + b + a \|c - b - a log((c - a)tan(-) + 2b tan(-) + c + a) @@ -13255,7 +13396,7 @@ m0847b:= a0847.2-r0847 d0847b:= D(m0847b,x) --R --R ---R (235) +--R (7) --R 2 2 2 2 2 6 --R (b c - 2a b c + a b )sin(x) --R + @@ -14301,14 +14442,17 @@ d0847b:= D(m0847b,x) --R Type: Expression(Integer) --E 246 +)clear all + + --S 247 of 526 t0848:= csc(x)^2/(a+b*cot(x)+c*csc(x)) --R --R ---R 2 ---R csc(x) ---R (236) ----------------------- ---R c csc(x) + b cot(x) + a +--R 2 +--R csc(x) +--R (1) ----------------------- +--R c csc(x) + b cot(x) + a --R Type: Expression(Integer) --E 247 @@ -14318,7 +14462,7 @@ r0848:= -2*a*c*atanh((a-(b-c)*tan(1/2*x))/(a^2+b^2-c^2)^(1/2))/_ b*log(b+c+2*a*tan(1/2*x)-(b-c)*tan(1/2*x)^2)/(b^2-c^2) --R --R ---R (237) +--R (2) --R +--------------+ --R | 2 2 2 x 2 x --R b\|- c + b + a log((c - b)tan(-) + 2a tan(-) + c + b) @@ -14342,7 +14486,7 @@ r0848:= -2*a*c*atanh((a-(b-c)*tan(1/2*x))/(a^2+b^2-c^2)^(1/2))/_ a0848:= integrate(t0848,x) --R --R ---R (238) +--R (3) --R [ --R a c --R * @@ -14408,7 +14552,7 @@ a0848:= integrate(t0848,x) m0848a:= a0848.1-r0848 --R --R ---R (239) +--R (4) --R a c --R * --R log @@ -14460,7 +14604,7 @@ m0848a:= a0848.1-r0848 d0848a:= D(m0848a,x) --R --R ---R (240) +--R (5) --R 2 2 2 2 2 2 2 2 3 --R ((- a c + a b )cos(x) - a c + a b )sin(x) --R + @@ -15375,7 +15519,7 @@ d0848a:= D(m0848a,x) m0848b:= a0848.2-r0848 --R --R ---R (241) +--R (6) --R - --R +--------------+ +------------+ --R | 2 2 2 | 2 2 2 @@ -15425,7 +15569,7 @@ m0848b:= a0848.2-r0848 d0848b:= D(m0848b,x) --R --R ---R (242) +--R (7) --R 2 2 2 2 4 --R ((- a c + a b )cos(x) - a c + a b )sin(x) --R + @@ -15811,13 +15955,16 @@ d0848b:= D(m0848b,x) --R Type: Expression(Integer) --E 253 +)clear all + + --S 254 of 526 t0849:= (A+C*sin(x))/(a+b*cos(x)+c*sin(x)) --R --R ---R C sin(x) + A ---R (243) ----------------------- ---R c sin(x) + b cos(x) + a +--R C sin(x) + A +--R (1) ----------------------- +--R c sin(x) + b cos(x) + a --R Type: Expression(Integer) --E 254 @@ -15827,7 +15974,7 @@ r0849:= c*C*x/(b^2+c^2)+2*(A-a*c*C/(b^2+c^2))*_ b*C*log(a+b*cos(x)+c*sin(x))/(b^2+c^2) --R --R ---R (244) +--R (2) --R +--------------+ --R | 2 2 2 --R - C b\|- c - b + a log(c sin(x) + b cos(x) + a) @@ -15850,7 +15997,7 @@ r0849:= c*C*x/(b^2+c^2)+2*(A-a*c*C/(b^2+c^2))*_ a0849:= integrate(t0849,x) --R --R ---R (245) +--R (3) --R [ --R 2 2 --R (- A c + C a c - A b ) @@ -15925,7 +16072,7 @@ a0849:= integrate(t0849,x) m0849a:= a0849.1-r0849 --R --R ---R (246) +--R (4) --R +--------------+ --R 2 2 | 2 2 2 --R (- A c + C a c - A b )\|- c - b + a @@ -15978,7 +16125,7 @@ m0849a:= a0849.1-r0849 d0849a:= D(m0849a,x) --R --R ---R (247) +--R (5) --R 3 2 2 2 3 2 2 3 --R (- A b + 2A a b - A a b)c + (C a b - 2C a b + C a b)c --R + @@ -16504,7 +16651,7 @@ d0849a:= D(m0849a,x) m0849b:= a0849.2-r0849 --R --R ---R (248) +--R (6) --R +--------------+ --R | 2 2 2 --R C b\|- c - b + a log(c sin(x) + b cos(x) + a) @@ -16547,7 +16694,7 @@ m0849b:= a0849.2-r0849 d0849b:= D(m0849b,x) --R --R ---R (249) +--R (7) --R 2 2 3 2 2 --R ((- A b + A a)c + (C a b - C a )c - A b + A a b )sin(x) --R + @@ -16645,15 +16792,17 @@ d0849b:= D(m0849b,x) --R Type: Expression(Integer) --E 260 +)clear all + + --S 261 of 526 t0850:= (A+C*sin(x))/(a+b*cos(x)+c*sin(x))^2 --R --R ---R (250) ---R C sin(x) + A ---R --------------------------------------------------------------------- ---R 2 2 2 2 2 ---R c sin(x) + (2b c cos(x) + 2a c)sin(x) + b cos(x) + 2a b cos(x) + a +--R C sin(x) + A +--R (1) --------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sin(x) + (2b c cos(x) + 2a c)sin(x) + b cos(x) + 2a b cos(x) + a --R Type: Expression(Integer) --E 261 @@ -16663,7 +16812,7 @@ r0850:= 2*(a*A-c*C)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/_ (a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x)) --R --R ---R (251) +--R (2) --R 2 2 --R ((- 2C c + 2A a c)sin(x) + (- 2C b c + 2A a b)cos(x) - 2C a c + 2A a ) --R * @@ -16692,7 +16841,7 @@ r0850:= 2*(a*A-c*C)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/_ a0850:= integrate(t0850,x) --R --R ---R (252) +--R (3) --R [ --R 2 2 --R ((C b - C a)c + (- A a b + A a )c)sin(x) @@ -16789,7 +16938,7 @@ a0850:= integrate(t0850,x) m0850a:= a0850.1-r0850 --R --R ---R (253) +--R (4) --R +--------------+ --R 2 | 2 2 2 --R ((C b - C a)c - A a b + A a )\|- c - b + a @@ -16832,7 +16981,7 @@ m0850a:= a0850.1-r0850 d0850a:= D(m0850a,x) --R --R ---R (254) +--R (5) --R 3 2 2 3 2 2 3 2 --R ((- C b + 2C a b - C a b)c + A a b - 2A a b + A a b)sin(x) --R + @@ -17293,7 +17442,7 @@ d0850a:= D(m0850a,x) m0850b:= a0850.2-r0850 --R --R ---R (255) +--R (6) --R 2 --R ((2C b - 2C a)c - 2A a b + 2A a ) --R * @@ -17326,7 +17475,7 @@ m0850b:= a0850.2-r0850 d0850b:= D(m0850b,x) --R --R ---R (256) +--R (7) --R 2 2 --R ((- C b + C a)c + A a b - A a )sin(x) --R + @@ -17427,11 +17576,14 @@ d0850b:= D(m0850b,x) --R Type: Expression(Integer) --E 267 +)clear all + + --S 268 of 526 t0851:= (A+C*sin(x))/(a+b*cos(x)+c*sin(x))^3 --R --R ---R (257) +--R (1) --R C sin(x) + A --R / --R 3 3 2 2 2 @@ -17453,7 +17605,7 @@ r0851:= (2*a^2*A+A*b^2+c*(A*c-3*a*C))*atan((c+(a-b)*tan(1/2*x))/_ sin(x))/(a^2-b^2-c^2)^2/(a+b*cos(x)+c*sin(x)) --R --R ---R (258) +--R (2) --R 4 3 2 2 2 2 --R (- 2A c + 6C a c + (- 2A b - 4A a )c )sin(x) --R + @@ -17536,7 +17688,7 @@ r0851:= (2*a^2*A+A*b^2+c*(A*c-3*a*C))*atan((c+(a-b)*tan(1/2*x))/_ a0851:= integrate(t0851,x) --R --R ---R (259) +--R (3) --R [ --R 3 2 2 3 --R (2A b - 4A a b + 2A a b)c @@ -17912,7 +18064,7 @@ a0851:= integrate(t0851,x) m0851a:= a0851.1-r0851 --R --R ---R (260) +--R (4) --R 3 2 2 5 --R (2A b - 4A a b + 2A a b)c --R + @@ -18779,7 +18931,7 @@ m0851a:= a0851.1-r0851 m0851b:= a0851.2-r0851 --R --R ---R (261) +--R (5) --R 3 2 2 5 --R (4A b - 8A a b + 4A a b)c --R + @@ -19632,13 +19784,16 @@ m0851b:= a0851.2-r0851 --d0851b:= D(m0851b,x) --E 274 +)clear all + + --S 275 of 526 t0852:= (A+B*cos(x))/(a+b*cos(x)+c*sin(x)) --R --R ---R B cos(x) + A ---R (262) ----------------------- ---R c sin(x) + b cos(x) + a +--R B cos(x) + A +--R (1) ----------------------- +--R c sin(x) + b cos(x) + a --R Type: Expression(Integer) --E 275 @@ -19648,7 +19803,7 @@ r0852:= b*B*x/(b^2+c^2)+2*(A-a*b*B/(b^2+c^2))*atan((c+(a-b)*_ B*c*log(a+b*cos(x)+c*sin(x))/(b^2+c^2) --R --R ---R (263) +--R (2) --R +--------------+ --R | 2 2 2 --R B c\|- c - b + a log(c sin(x) + b cos(x) + a) @@ -19671,7 +19826,7 @@ r0852:= b*B*x/(b^2+c^2)+2*(A-a*b*B/(b^2+c^2))*atan((c+(a-b)*_ a0852:= integrate(t0852,x) --R --R ---R (264) +--R (3) --R [ --R 2 2 --R (- A c - A b + B a b) @@ -19746,7 +19901,7 @@ a0852:= integrate(t0852,x) m0852a:= a0852.1-r0852 --R --R ---R (265) +--R (4) --R +--------------+ --R 2 2 | 2 2 2 --R (- A c - A b + B a b)\|- c - b + a @@ -19799,7 +19954,7 @@ m0852a:= a0852.1-r0852 d0852a:= D(m0852a,x) --R --R ---R (266) +--R (5) --R 3 2 2 2 5 4 --R (- A b + 2A a b - A a b)c - A b + (B + 2A)a b --R + @@ -20304,7 +20459,7 @@ d0852a:= D(m0852a,x) m0852b:= a0852.2-r0852 --R --R ---R (267) +--R (6) --R +--------------+ --R | 2 2 2 --R - B c\|- c - b + a log(c sin(x) + b cos(x) + a) @@ -20347,7 +20502,7 @@ m0852b:= a0852.2-r0852 d0852b:= D(m0852b,x) --R --R ---R (268) +--R (7) --R 2 3 2 2 2 --R ((- A b + A a)c - A b + (B + A)a b - B a b)sin(x) --R + @@ -20452,15 +20607,17 @@ d0852b:= D(m0852b,x) --R Type: Expression(Integer) --E 281 +)clear all + + --S 282 of 526 t0853:= (A+B*cos(x))/(a+b*cos(x)+c*sin(x))^2 --R --R ---R (269) ---R B cos(x) + A ---R --------------------------------------------------------------------- ---R 2 2 2 2 2 ---R c sin(x) + (2b c cos(x) + 2a c)sin(x) + b cos(x) + 2a b cos(x) + a +--R B cos(x) + A +--R (1) --------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sin(x) + (2b c cos(x) + 2a c)sin(x) + b cos(x) + 2a b cos(x) + a --R Type: Expression(Integer) --E 282 @@ -20470,7 +20627,7 @@ r0853:= 2*(a*A-b*B)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/_ (A*b-a*B)*sin(x))/(a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x)) --R --R ---R (270) +--R (2) --R 2 2 --R ((- 2B b + 2A a)c sin(x) + (- 2B b + 2A a b)cos(x) - 2B a b + 2A a ) --R * @@ -20499,7 +20656,7 @@ r0853:= 2*(a*A-b*B)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/_ a0853:= integrate(t0853,x) --R --R ---R (271) +--R (3) --R [ --R 2 2 --R (B b + (- B - A)a b + A a )c sin(x) @@ -20591,7 +20748,7 @@ a0853:= integrate(t0853,x) m0853a:= a0853.1-r0853 --R --R ---R (272) +--R (4) --R +--------------+ --R 2 2 | 2 2 2 --R (B b + (- B - A)a b + A a )\|- c - b + a @@ -20634,7 +20791,7 @@ m0853a:= a0853.1-r0853 d0853a:= D(m0853a,x) --R --R ---R (273) +--R (5) --R 4 3 2 2 3 2 --R (- B b + (2B + A)a b + (- B - 2A)a b + A a b)sin(x) --R + @@ -21058,7 +21215,7 @@ d0853a:= D(m0853a,x) m0853b:= a0853.2-r0853 --R --R ---R (274) +--R (6) --R 2 2 --R (2B b + (- 2B - 2A)a b + 2A a ) --R * @@ -21091,7 +21248,7 @@ m0853b:= a0853.2-r0853 d0853b:= D(m0853b,x) --R --R ---R (275) +--R (7) --R 2 2 2 --R (- B b + (B + A)a b - A a )sin(x) --R + @@ -21189,11 +21346,14 @@ d0853b:= D(m0853b,x) --R Type: Expression(Integer) --E 288 +)clear all + + --S 289 of 526 t0854:= (A+B*cos(x))/(a+b*cos(x)+c*sin(x))^3 --R --R ---R (276) +--R (1) --R B cos(x) + A --R / --R 3 3 2 2 2 @@ -21215,7 +21375,7 @@ r0854:= (2*a^2*A+b*(A*b-3*a*B)+A*c^2)*atan((c+(a-b)*tan(1/2*x))/_ (2*b^2*B-a*(3*A*b-a*B))*sin(x))/(a^2-b^2-c^2)^2/(a+b*cos(x)+c*sin(x)) --R --R ---R (277) +--R (2) --R 4 2 2 2 2 --R (- 2A c + (- 2A b + 6B a b - 4A a )c )sin(x) --R + @@ -21295,7 +21455,7 @@ r0854:= (2*a^2*A+b*(A*b-3*a*B)+A*c^2)*atan((c+(a-b)*tan(1/2*x))/_ a0854:= integrate(t0854,x) --R --R ---R (278) +--R (3) --R [ --R 3 2 2 3 --R (2A b - 4A a b + 2A a b)c @@ -21672,7 +21832,7 @@ a0854:= integrate(t0854,x) m0854a:= a0854.1-r0854 --R --R ---R (279) +--R (4) --R 3 2 2 5 --R (2A b - 4A a b + 2A a b)c --R + @@ -22668,7 +22828,7 @@ m0854a:= a0854.1-r0854 m0854b:= a0854.2-r0854 --R --R ---R (280) +--R (5) --R 3 2 2 5 --R (4A b - 8A a b + 4A a b)c --R + @@ -23653,13 +23813,16 @@ m0854b:= a0854.2-r0854 --d0854b:= D(m0854b,x) --E 295 +)clear all + + --S 296 of 526 t0855:= (A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x)) --R --R ---R C sin(x) + B cos(x) + A ---R (281) ----------------------- ---R c sin(x) + b cos(x) + a +--R C sin(x) + B cos(x) + A +--R (1) ----------------------- +--R c sin(x) + b cos(x) + a --R Type: Expression(Integer) --E 296 @@ -23669,7 +23832,7 @@ r0855:= (b*B+c*C)*x/(b^2+c^2)+2*(A-a*(b*B+c*C)/(b^2+c^2))*_ (B*c-b*C)*log(a+b*cos(x)+c*sin(x))/(b^2+c^2) --R --R ---R (282) +--R (2) --R +--------------+ --R | 2 2 2 --R (B c - C b)\|- c - b + a log(c sin(x) + b cos(x) + a) @@ -23696,7 +23859,7 @@ r0855:= (b*B+c*C)*x/(b^2+c^2)+2*(A-a*(b*B+c*C)/(b^2+c^2))*_ a0855:= integrate(t0855,x) --R --R ---R (283) +--R (3) --R [ --R 2 2 --R (- A c + C a c - A b + B a b) @@ -23771,7 +23934,7 @@ a0855:= integrate(t0855,x) m0855a:= a0855.1-r0855 --R --R ---R (284) +--R (4) --R +--------------+ --R 2 2 | 2 2 2 --R (- A c + C a c - A b + B a b)\|- c - b + a @@ -23827,7 +23990,7 @@ m0855a:= a0855.1-r0855 d0855a:= D(m0855a,x) --R --R ---R (285) +--R (5) --R 3 2 2 2 3 2 2 3 --R (- A b + 2A a b - A a b)c + (C a b - 2C a b + C a b)c --R + @@ -24376,7 +24539,7 @@ d0855a:= D(m0855a,x) m0855b:= a0855.2-r0855 --R --R ---R (286) +--R (6) --R +--------------+ --R | 2 2 2 --R (- B c + C b)\|- c - b + a log(c sin(x) + b cos(x) + a) @@ -24419,7 +24582,7 @@ m0855b:= a0855.2-r0855 d0855b:= D(m0855b,x) --R --R ---R (287) +--R (7) --R 2 2 3 2 2 --R ((- A b + A a)c + (C a b - C a )c - A b + (B + A)a b - B a b) --R * @@ -24542,15 +24705,17 @@ d0855b:= D(m0855b,x) --R Type: Expression(Integer) --E 302 +)clear all + + --S 303 of 526 t0856:= (A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^2 --R --R ---R (288) ---R C sin(x) + B cos(x) + A ---R --------------------------------------------------------------------- ---R 2 2 2 2 2 ---R c sin(x) + (2b c cos(x) + 2a c)sin(x) + b cos(x) + 2a b cos(x) + a +--R C sin(x) + B cos(x) + A +--R (1) --------------------------------------------------------------------- +--R 2 2 2 2 2 +--R c sin(x) + (2b c cos(x) + 2a c)sin(x) + b cos(x) + 2a b cos(x) + a --R Type: Expression(Integer) --E 303 @@ -24560,7 +24725,7 @@ r0856:= 2*(a*A-b*B-c*C)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/_ (a^2-b^2-c^2)/(a+b*cos(x)+c*sin(x)) --R --R ---R (289) +--R (2) --R 2 --R (- 2C c + (- 2B b + 2A a)c)sin(x) --R + @@ -24592,7 +24757,7 @@ r0856:= 2*(a*A-b*B-c*C)*atan((c+(a-b)*tan(1/2*x))/(a^2-b^2-c^2)^(1/2))/_ a0856:= integrate(t0856,x) --R --R ---R (290) +--R (3) --R [ --R 2 2 2 --R ((C b - C a)c + (B b + (- B - A)a b + A a )c)sin(x) @@ -24689,7 +24854,7 @@ a0856:= integrate(t0856,x) m0856a:= a0856.1-r0856 --R --R ---R (291) +--R (4) --R +--------------+ --R 2 2 | 2 2 2 --R ((C b - C a)c + B b + (- B - A)a b + A a )\|- c - b + a @@ -24736,7 +24901,7 @@ m0856a:= a0856.1-r0856 d0856a:= D(m0856a,x) --R --R ---R (292) +--R (5) --R 3 2 2 4 3 --R (- C b + 2C a b - C a b)c - B b + (2B + A)a b --R + @@ -25284,7 +25449,7 @@ d0856a:= D(m0856a,x) m0856b:= a0856.2-r0856 --R --R ---R (293) +--R (6) --R 2 2 --R ((2C b - 2C a)c + 2B b + (- 2B - 2A)a b + 2A a ) --R * @@ -25317,7 +25482,7 @@ m0856b:= a0856.2-r0856 d0856b:= D(m0856b,x) --R --R ---R (294) +--R (7) --R 2 2 2 --R ((- C b + C a)c - B b + (B + A)a b - A a )sin(x) --R + @@ -25424,11 +25589,14 @@ d0856b:= D(m0856b,x) --R Type: Expression(Integer) --E 309 +)clear all + + --S 310 of 526 t0857:= (A+B*cos(x)+C*sin(x))/(a+b*cos(x)+c*sin(x))^3 --R --R ---R (295) +--R (1) --R C sin(x) + B cos(x) + A --R / --R 3 3 2 2 2 @@ -25452,7 +25620,7 @@ r0857:= -(b*(A*b-a*B)+c*(A*c-a*C)+2*a*(a*A-b*B-c*C))*_ (-a^2+b^2+c^2)/(a+b*cos(x)+c*sin(x)) --R --R ---R (296) +--R (2) --R 4 3 2 2 2 2 --R (- 2A c + 6C a c + (- 2A b + 6B a b - 4A a )c )sin(x) --R + @@ -25540,7 +25708,7 @@ r0857:= -(b*(A*b-a*B)+c*(A*c-a*C)+2*a*(a*A-b*B-c*C))*_ a0857:= integrate(t0857,x) --R --R ---R (297) +--R (3) --R [ --R 3 2 2 3 --R (2A b - 4A a b + 2A a b)c @@ -25986,7 +26154,7 @@ a0857:= integrate(t0857,x) m0857a:= a0857.1-r0857 --R --R ---R (298) +--R (4) --R 3 2 2 5 --R (2A b - 4A a b + 2A a b)c --R + @@ -27177,7 +27345,7 @@ m0857a:= a0857.1-r0857 m0857b:= a0857.2-r0857 --R --R ---R (299) +--R (5) --R 3 2 2 5 --R (4A b - 8A a b + 4A a b)c --R + @@ -28360,15 +28528,18 @@ m0857b:= a0857.2-r0857 --d0857b:= D(m0857b,x) --E 316 +)clear all + + --S 317 of 526 t0858:= sin(x)^3/(cos(x)^3+sin(x)^3) --R --R ---R 3 ---R sin(x) ---R (300) ----------------- ---R 3 3 ---R sin(x) + cos(x) +--R 3 +--R sin(x) +--R (1) ----------------- +--R 3 3 +--R sin(x) + cos(x) --R Type: Expression(Integer) --E 317 @@ -28376,9 +28547,9 @@ t0858:= sin(x)^3/(cos(x)^3+sin(x)^3) r0858:= 1/2*x-1/6*log(cos(x)+sin(x))+1/3*log(1-cos(x)*sin(x)) --R --R ---R - log(sin(x) + cos(x)) + 2log(- cos(x)sin(x) + 1) + 3x ---R (301) ------------------------------------------------------ ---R 6 +--R - log(sin(x) + cos(x)) + 2log(- cos(x)sin(x) + 1) + 3x +--R (2) ------------------------------------------------------ +--R 6 --R Type: Expression(Integer) --E 318 @@ -28386,7 +28557,7 @@ r0858:= 1/2*x-1/6*log(cos(x)+sin(x))+1/3*log(1-cos(x)*sin(x)) a0858:= integrate(t0858,x) --R --R ---R (302) +--R (3) --R 2 - 2sin(x) - 2cos(x) --R - 3log(----------) - log(-------------------) --R cos(x) + 1 cos(x) + 1 @@ -28404,7 +28575,7 @@ a0858:= integrate(t0858,x) m0858:= a0858-r0858 --R --R ---R (303) +--R (4) --R 2 - 2sin(x) - 2cos(x) --R log(sin(x) + cos(x)) - 3log(----------) - log(-------------------) --R cos(x) + 1 cos(x) + 1 @@ -28422,19 +28593,22 @@ m0858:= a0858-r0858 d0858:= D(m0858,x) --R --R ---R (304) 0 +--R (5) 0 --R Type: Expression(Integer) --E 321 +)clear all + + --S 322 of 526 t0859:= cos(x)^3/(cos(x)^3+sin(x)^3) --R --R ---R 3 ---R cos(x) ---R (305) ----------------- ---R 3 3 ---R sin(x) + cos(x) +--R 3 +--R cos(x) +--R (1) ----------------- +--R 3 3 +--R sin(x) + cos(x) --R Type: Expression(Integer) --E 322 @@ -28442,9 +28616,9 @@ t0859:= cos(x)^3/(cos(x)^3+sin(x)^3) r0859:= 1/2*x+1/6*log(cos(x)+sin(x))-1/3*log(1-cos(x)*sin(x)) --R --R ---R log(sin(x) + cos(x)) - 2log(- cos(x)sin(x) + 1) + 3x ---R (306) ---------------------------------------------------- ---R 6 +--R log(sin(x) + cos(x)) - 2log(- cos(x)sin(x) + 1) + 3x +--R (2) ---------------------------------------------------- +--R 6 --R Type: Expression(Integer) --E 323 @@ -28452,7 +28626,7 @@ r0859:= 1/2*x+1/6*log(cos(x)+sin(x))-1/3*log(1-cos(x)*sin(x)) a0859:= integrate(t0859,x) --R --R ---R (307) +--R (3) --R 2 - 2sin(x) - 2cos(x) - 4cos(x)sin(x) + 4 --R 3log(----------) + log(-------------------) - 2log(---------------------) --R cos(x) + 1 cos(x) + 1 2 @@ -28468,7 +28642,7 @@ a0859:= integrate(t0859,x) m0859:= a0859-r0859 --R --R ---R (308) +--R (4) --R 2 - 2sin(x) - 2cos(x) --R - log(sin(x) + cos(x)) + 3log(----------) + log(-------------------) --R cos(x) + 1 cos(x) + 1 @@ -28486,18 +28660,21 @@ m0859:= a0859-r0859 d0859:= D(m0859,x) --R --R ---R (309) 0 +--R (5) 0 --R Type: Expression(Integer) --E 326 +)clear all + + --S 327 of 526 t0860:= 1/(a+b*sin(x)+c*sin(x)^2) --R --R ---R 1 ---R (310) ------------------------ ---R 2 ---R c sin(x) + b sin(x) + a +--R 1 +--R (1) ------------------------ +--R 2 +--R c sin(x) + b sin(x) + a --R Type: Expression(Integer) --E 327 @@ -28510,7 +28687,7 @@ r0860:= -2*2^(1/2)*c*atanh(1/2*(2*c+(b-(b^2-4*a*c)^(1/2))*_ (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) --R --R ---R (311) +--R (2) --R +---------------------------------+ --R | +-----------+ --R | | 2 2 2 @@ -28557,7 +28734,7 @@ r0860:= -2*2^(1/2)*c*atanh(1/2*(2*c+(b-(b^2-4*a*c)^(1/2))*_ a0860:= integrate(t0860,x) --R --R ---R (312) +--R (3) --R - --R ROOT --R 3 2 2 2 2 3 4 @@ -29059,7 +29236,7 @@ a0860:= integrate(t0860,x) m0860:= a0860-r0860 --R --R ---R (313) +--R (4) --R - --R +-------------------------------------+ --R +-----------+ | +-----------+ @@ -29649,7 +29826,7 @@ m0860:= a0860-r0860 d0860:= D(m0860,x) --R --R ---R (314) +--R (5) --R 4 3 --R a sin(x) + (- 2b cos(x) - 2b)sin(x) --R + @@ -29807,15 +29984,18 @@ d0860:= D(m0860,x) --R Type: Expression(Integer) --E 331 +)clear all + + --S 332 of 526 t0861:= sin(x)^2/(a+b*sin(x)+c*sin(x)^2) --R --R ---R 2 ---R sin(x) ---R (315) ------------------------ ---R 2 ---R c sin(x) + b sin(x) + a +--R 2 +--R sin(x) +--R (1) ------------------------ +--R 2 +--R c sin(x) + b sin(x) + a --R Type: Expression(Integer) --E 332 @@ -29829,7 +30009,7 @@ r0861:= x/c+2^(1/2)*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) --R --R ---R (316) +--R (2) --R +---------------------------------+ --R +-----------+ | +-----------+ --R | 2 2 | | 2 2 2 @@ -29890,7 +30070,7 @@ r0861:= x/c+2^(1/2)*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ a0861:= integrate(t0861,x) --R --R ---R (317) +--R (3) --R - --R c --R * @@ -30484,7 +30664,7 @@ a0861:= integrate(t0861,x) m0861:= a0861-r0861 --R --R ---R (318) +--R (4) --R - --R +-------------------------------------+ --R +-----------+ | +-----------+ @@ -31158,7 +31338,7 @@ m0861:= a0861-r0861 d0861:= D(m0861,x) --R --R ---R (319) +--R (5) --R 2 4 3 --R - a sin(x) + (- 2a b cos(x) - 2a b)sin(x) --R + @@ -31354,15 +31534,18 @@ d0861:= D(m0861,x) --R Type: Expression(Integer) --E 336 +)clear all + + --S 337 of 526 t0862:= sin(x)^3/(a+b*sin(x)+c*sin(x)^2) --R --R ---R 3 ---R sin(x) ---R (320) ------------------------ ---R 2 ---R c sin(x) + b sin(x) + a +--R 3 +--R sin(x) +--R (1) ------------------------ +--R 2 +--R c sin(x) + b sin(x) + a --R Type: Expression(Integer) --E 337 @@ -31376,7 +31559,7 @@ r0862:= -b*x/c^2-2^(1/2)*(b^2-a*c-b*(b^2-3*a*c)/(b^2-4*a*c)^(1/2))*_ (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2)-cos(x)/c --R --R ---R (321) +--R (2) --R +-----------+ --R 2 | 2 3 --R ((2a c - 2b )\|- 4a c + b + 6a b c - 2b ) @@ -31445,7 +31628,7 @@ r0862:= -b*x/c^2-2^(1/2)*(b^2-a*c-b*(b^2-3*a*c)/(b^2-4*a*c)^(1/2))*_ a0862:= integrate(t0862,x) --R --R ---R (322) +--R (3) --R 2 --R c --R * @@ -32224,7 +32407,7 @@ a0862:= integrate(t0862,x) m0862:= a0862-r0862 --R --R ---R (323) +--R (4) --R +-------------------------------------+ --R +-----------+ | +-----------+ --R 2 | 2 | | 2 2 2 @@ -33082,7 +33265,7 @@ m0862:= a0862-r0862 d0862:= D(m0862,x) --R --R ---R (324) +--R (5) --R 2 4 2 2 2 2 3 --R a b sin(x) + ((- 4a c + 2a b )cos(x) - 4a c + 2a b )sin(x) --R + @@ -33339,14 +33522,17 @@ d0862:= D(m0862,x) --R Type: Expression(Integer) --E 341 +)clear all + + --S 342 of 526 t0863:= (a+b*sin(x))/(b^2+2*a*b*sin(x)+a^2*sin(x)^2) --R --R ---R b sin(x) + a ---R (325) ---------------------------- ---R 2 2 2 ---R a sin(x) + 2a b sin(x) + b +--R b sin(x) + a +--R (1) ---------------------------- +--R 2 2 2 +--R a sin(x) + 2a b sin(x) + b --R Type: Expression(Integer) --E 342 @@ -33354,9 +33540,9 @@ t0863:= (a+b*sin(x))/(b^2+2*a*b*sin(x)+a^2*sin(x)^2) r0863:= -cos(x)/(b+a*sin(x)) --R --R ---R cos(x) ---R (326) - ------------ ---R a sin(x) + b +--R cos(x) +--R (2) - ------------ +--R a sin(x) + b --R Type: Expression(Integer) --E 343 @@ -33364,10 +33550,10 @@ r0863:= -cos(x)/(b+a*sin(x)) a0863:= integrate(t0863,x) --R --R ---R - a sin(x) - b cos(x) - b ---R (327) ------------------------- ---R 2 ---R a b sin(x) + b +--R - a sin(x) - b cos(x) - b +--R (3) ------------------------- +--R 2 +--R a b sin(x) + b --R Type: Union(Expression(Integer),...) --E 344 @@ -33375,9 +33561,9 @@ a0863:= integrate(t0863,x) m0863:= a0863-r0863 --R --R ---R 1 ---R (328) - - ---R b +--R 1 +--R (4) - - +--R b --R Type: Expression(Integer) --E 345 @@ -33385,18 +33571,21 @@ m0863:= a0863-r0863 d0863:= D(m0863,x) --R --R ---R (329) 0 +--R (5) 0 --R Type: Expression(Integer) --E 346 +)clear all + + --S 347 of 526 t0864:= (d+e*sin(x))/(a+b*sin(x)+c*sin(x)^2) --R --R ---R e sin(x) + d ---R (330) ------------------------ ---R 2 ---R c sin(x) + b sin(x) + a +--R e sin(x) + d +--R (1) ------------------------ +--R 2 +--R c sin(x) + b sin(x) + a --R Type: Expression(Integer) --E 347 @@ -33411,7 +33600,7 @@ r0864:= -2^(1/2)*(e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) --R --R ---R (331) +--R (2) --R +---------------------------------+ --R +-----------+ | +-----------+ --R | 2 | | 2 2 2 @@ -33458,11 +33647,11 @@ r0864:= -2^(1/2)*(e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ --R Type: Expression(Integer) --E 348 ---S 349 of 526 +--S 349 of 526 ok to fail. known bug #7240 in buglist a0864:= integrate(t0864,x) --R --R ---R (332) +--R (3) --R - --R ROOT --R 3 2 2 2 2 3 4 @@ -34466,33 +34655,150 @@ a0864:= integrate(t0864,x) --R Type: Union(Expression(Integer),...) --E 349 ---S 350 of 526 +--S 350 of 526 ok to fail due to known bug (see above) m0864:= a0864-r0864 --R --R ---R (333) ---R - ---R +-------------------------------------+ ---R +-----------+ | +-----------+ ---R | 2 | | 2 2 2 ---R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R * ---R ROOT ---R 3 2 2 2 2 3 4 ---R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b ---R + ---R 2 2 ---R - 2a b ---R * ---R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 3 ---R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e ---R + ---R 2 4 ---R - b d +--R (3) +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (2e\|- 4a c + b + 2b e - 4c d)\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + b tan(-) + 2c +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (- e\|2 \|- 4a c + b + (b e - 2c d)\|2 ) +--R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +-+ +--R \|2 tan(-)\|- 4a c + b - b\|2 tan(-) - 2c\|2 +--R 2 2 +--R atanh(-----------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R a0864\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 350 + +--S 351 of 526 +--d0864:= D(m0864,x) +--E 351 + +)clear all + + +--S 352 of 526 +t0865:= 1/(a+b*cos(x)+c*cos(x)^2) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 +--R c cos(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 526 +r0865:= -2*2^(1/2)*c*atanh(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*_ + tan(1/2*x)*2^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/_ + (b^2-4*a*c)^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)+_ + 4*c*atanh((b+(b^2-4*a*c)^(1/2)-2*c)*tan(1/2*x)/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/(b^2-4*a*c)^(1/2)/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 4c\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + (- 2c + b)tan(-) +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R +-------------------------------------+ +--R | +-----------+ +--R +-+ | | 2 2 2 +--R 2c\|2 \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) +--R 2 2 +--R atanh(---------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 353 + +--S 354 of 526 +a0865:= integrate(t0865,x) +--R +--R +--R (3) +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b --R / --R 5 2 2 4 2 3 3 --R 4a c + (- b + 16a )c + (- 12a b + 24a )c @@ -34502,74 +34808,38 @@ m0864:= a0864-r0864 --R + --R 6 2 4 4 2 --R - b + 2a b - a b ---R + ---R 2 2 2 ---R (4a c - 2b + 4a )e + (4b c - 4a b)d e ---R + ---R 2 2 2 ---R (- 4c - 4a c + 2b )d ---R / ---R 3 2 2 2 2 3 4 2 2 ---R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b ---R * ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|b\|- 4a c + b + 2c + 2a c - b ---R * ---R log ---R 2 4 2 3 3 ---R 8a c + (- 6a b + 24a )c ---R + ---R 4 2 2 4 2 ---R (b - 22a b + 24a )c ---R + ---R 4 3 2 5 6 2 4 4 2 ---R (8a b - 18a b + 8a )c - b + 3a b - 2a b ---R * ---R e ---R + ---R 4 3 2 3 ---R 4a b c + (- b + 4a b)c ---R + ---R 3 3 2 5 2 3 4 ---R (- 5a b - 4a b)c + (b + 5a b - 4a b)c ---R + ---R 5 3 3 ---R - a b + a b ---R * ---R d ---R * ---R cos(x) ---R + ---R 2 4 2 3 3 ---R 8a c + (- 6a b + 24a )c ---R + ---R 4 2 2 4 2 4 3 2 5 ---R (b - 22a b + 24a )c + (8a b - 18a b + 8a )c ---R + ---R 6 2 4 4 2 ---R - b + 3a b - 2a b ---R * ---R e ---R + ---R 4 3 2 3 3 3 2 ---R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c ---R + ---R 5 2 3 4 5 3 3 ---R (b + 5a b - 4a b)c - a b + a b ---R * ---R d ---R * ---R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 ---R (- 4c - 8a c - 2b - 4a )d e ---R + ---R 3 2 4 ---R (4b c + 4a b)d e - b d +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c +--R + +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b +--R * +--R ROOT +--R - +--R 2 +--R b --R / --R 5 2 2 4 2 3 3 --R 4a c + (- b + 16a )c + (- 12a b + 24a )c @@ -34579,49 +34849,21 @@ m0864:= a0864-r0864 --R + --R 4 3 2 5 6 2 4 4 2 --R (8a b - 12a b + 4a )c - b + 2a b - a b ---R + ---R 2 4 3 ---R (4a b c - b )e ---R + ---R 2 3 2 3 2 ---R (- 12a b c + (3b - 12a b)c + 3a b )d e ---R + ---R 3 2 2 2 3 4 2 2 2 ---R (8a c + (- 2b + 16a )c + 8a c - b - 2a b )d e ---R + ---R 2 3 2 3 3 ---R (- 4a b c + (b - 4a b)c + a b )d ---R * ---R cos(x) ---R + ---R 2 4 3 ---R (4a b c - b )e ---R + ---R 2 3 2 3 2 ---R (- 12a b c + (3b - 12a b)c + 3a b )d e ---R + ---R 3 2 2 2 3 4 2 2 2 ---R (8a c + (- 2b + 16a )c + 8a c - b - 2a b )d e ---R + ---R 2 3 2 3 3 ---R (- 4a b c + (b - 4a b)c + a b )d ---R * ---R ROOT ---R 3 2 2 2 2 3 ---R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c ---R + ---R 4 2 2 ---R 2b - 2a b ---R * ---R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 ---R (- 4c - 8a c - 2b - 4a )d e ---R + ---R 3 2 4 ---R (4b c + 4a b)d e - b d +--R + +--R 3 3 +--R (4a b c - b )cos(x) + 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b --R / --R 5 2 2 4 --R 4a c + (- b + 16a )c @@ -34634,492 +34876,79 @@ m0864:= a0864-r0864 --R + --R 4 3 2 5 6 2 4 4 2 --R (8a b - 12a b + 4a )c - b + 2a b - a b ---R + ---R 2 2 2 ---R (4a c - 2b + 4a )e + (4b c - 4a b)d e ---R + ---R 2 2 2 ---R (- 4c - 4a c + 2b )d ---R / ---R 3 2 2 2 2 3 4 2 2 ---R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b ---R + ---R 2 3 2 3 2 2 2 4 ---R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c ---R + ---R 4 3 2 ---R 2a b - 2a b ---R * ---R 2 ---R e ---R + ---R 3 3 2 2 3 3 ---R - 8a b c + (2b - 16a b)c + (12a b - 8a b)c ---R + ---R 5 2 3 ---R - 2b + 2a b ---R * ---R d e ---R + ---R 4 2 2 3 2 3 2 ---R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c ---R + ---R 4 2 2 ---R (2b - 2a b )c ---R * ---R 2 ---R d ---R * ---R cos(x) ---R + ---R 2 3 2 3 2 2 2 4 ---R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c ---R + ---R 4 3 2 ---R 2a b - 2a b ---R * ---R 2 ---R e ---R + ---R 3 3 2 2 3 3 5 ---R - 8a b c + (2b - 16a b)c + (12a b - 8a b)c - 2b ---R + ---R 2 3 ---R 2a b ---R * ---R d e ---R + ---R 4 2 2 3 2 3 2 ---R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c ---R + ---R 4 2 2 ---R (2b - 2a b )c ---R * ---R 2 ---R d ---R * ---R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 3 ---R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e ---R + ---R 2 4 ---R - b d ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 4 3 2 5 ---R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c ---R + ---R 6 2 4 4 2 ---R - b + 2a b - a b ---R + ---R 2 4 2 2 3 3 ---R 4a b e + (- 8a c - 4a b - 8a )d e ---R + ---R 2 2 2 2 2 2 3 ---R (12a b c + 12a b)d e + (- 8a c - 8a c - 4a b )d e ---R + ---R 4 ---R 4a b c d ---R * ---R sin(x) ---R + ---R 2 4 3 2 3 ---R 2a b e + (- 4a b c - 2b - 4a b)d e ---R + ---R 2 2 2 2 2 3 3 2 4 ---R (6b c + 6a b )d e + (- 4b c - 4a b c - 2b )d e + 2b c d ---R * ---R cos(x) ---R + ---R 2 4 3 2 3 2 2 2 2 ---R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e ---R + ---R 2 3 3 2 4 ---R (- 4b c - 4a b c - 2b )d e + 2b c d ---R / ---R cos(x) + 1 ---R + ---R +-------------------------------------+ ---R +-----------+ | +-----------+ ---R | 2 | | 2 2 2 ---R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R * ---R ROOT ---R 3 2 2 2 2 3 4 2 2 ---R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) ---R * ---R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 3 2 4 ---R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 4 3 2 5 6 ---R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b ---R + ---R 2 4 4 2 ---R 2a b - a b ---R + ---R 2 2 2 2 2 2 ---R (4a c - 2b + 4a )e + (4b c - 4a b)d e + (- 4c - 4a c + 2b )d ---R / ---R 3 2 2 2 2 3 4 2 2 ---R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b ---R * ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|b\|- 4a c + b + 2c + 2a c - b ---R * ---R log ---R 2 4 2 3 3 ---R 8a c + (- 6a b + 24a )c ---R + ---R 4 2 2 4 2 4 3 2 5 ---R (b - 22a b + 24a )c + (8a b - 18a b + 8a )c ---R + ---R 6 2 4 4 2 ---R - b + 3a b - 2a b ---R * ---R e ---R + ---R 4 3 2 3 3 3 2 ---R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c ---R + ---R 5 2 3 4 5 3 3 ---R (b + 5a b - 4a b)c - a b + a b ---R * ---R d ---R * ---R cos(x) ---R + ---R 2 4 2 3 3 4 2 2 4 2 ---R 8a c + (- 6a b + 24a )c + (b - 22a b + 24a )c ---R + ---R 4 3 2 5 6 2 4 4 2 ---R (8a b - 18a b + 8a )c - b + 3a b - 2a b ---R * ---R e ---R + ---R 4 3 2 3 3 3 2 ---R 4a b c + (- b + 4a b)c + (- 5a b - 4a b)c ---R + ---R 5 2 3 4 5 3 3 ---R (b + 5a b - 4a b)c - a b + a b ---R * ---R d ---R * ---R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 3 ---R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e ---R + ---R 2 4 ---R - b d ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 4 3 2 5 ---R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c ---R + ---R 6 2 4 4 2 ---R - b + 2a b - a b ---R + ---R 2 4 3 ---R (- 4a b c + b )e ---R + ---R 2 3 2 3 2 ---R (12a b c + (- 3b + 12a b)c - 3a b )d e ---R + ---R 3 2 2 2 3 4 2 2 2 ---R (- 8a c + (2b - 16a )c - 8a c + b + 2a b )d e ---R + ---R 2 3 2 3 3 ---R (4a b c + (- b + 4a b)c - a b )d ---R * ---R cos(x) ---R + ---R 2 4 3 ---R (- 4a b c + b )e ---R + ---R 2 3 2 3 2 ---R (12a b c + (- 3b + 12a b)c - 3a b )d e ---R + ---R 3 2 2 2 3 4 2 2 2 ---R (- 8a c + (2b - 16a )c - 8a c + b + 2a b )d e ---R + ---R 2 3 2 3 3 ---R (4a b c + (- b + 4a b)c - a b )d ---R * ---R ROOT ---R 3 2 2 2 2 3 4 ---R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b ---R + ---R 2 2 ---R 2a b ---R * ---R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 ---R (- 4c - 8a c - 2b - 4a )d e ---R + ---R 3 2 4 ---R (4b c + 4a b)d e - b d ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 ---R (2b - 22a b + 16a )c ---R + ---R 4 3 2 5 6 2 4 4 2 ---R (8a b - 12a b + 4a )c - b + 2a b - a b ---R + ---R 2 2 2 ---R (4a c - 2b + 4a )e + (4b c - 4a b)d e --R + ---R 2 2 2 ---R (- 4c - 4a c + 2b )d +--R 2 2 +--R - 4c - 4a c + 2b --R / --R 3 2 2 2 2 3 4 2 2 --R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R + ---R 2 3 2 3 2 2 2 4 4 ---R - 8a c + (2a b - 16a )c + (12a b - 8a )c - 2a b ---R + ---R 3 2 ---R 2a b ---R * ---R 2 ---R e ---R + ---R 3 3 2 2 3 3 ---R 8a b c + (- 2b + 16a b)c + (- 12a b + 8a b)c ---R + ---R 5 2 3 ---R 2b - 2a b ---R * ---R d e ---R + ---R 4 2 2 3 2 3 2 ---R - 8a c + (2b - 16a )c + (12a b - 8a )c ---R + ---R 4 2 2 ---R (- 2b + 2a b )c ---R * ---R 2 ---R d ---R * ---R cos(x) ---R + ---R 2 3 2 3 2 2 2 4 4 ---R - 8a c + (2a b - 16a )c + (12a b - 8a )c - 2a b ---R + ---R 3 2 ---R 2a b ---R * ---R 2 ---R e ---R + ---R 3 3 2 2 3 3 5 ---R 8a b c + (- 2b + 16a b)c + (- 12a b + 8a b)c + 2b ---R + ---R 2 3 ---R - 2a b ---R * ---R d e ---R + ---R 4 2 2 3 2 3 2 ---R - 8a c + (2b - 16a )c + (12a b - 8a )c ---R + ---R 4 2 2 ---R (- 2b + 2a b )c ---R * ---R 2 ---R d ---R * ---R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 3 2 4 ---R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 4 3 2 5 6 ---R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b ---R + ---R 2 4 4 2 ---R 2a b - a b ---R + ---R 2 4 2 2 3 3 2 2 2 ---R 4a b e + (- 8a c - 4a b - 8a )d e + (12a b c + 12a b)d e ---R + ---R 2 2 2 3 4 ---R (- 8a c - 8a c - 4a b )d e + 4a b c d ---R * ---R sin(x) ---R + ---R 2 4 3 2 3 2 2 2 2 ---R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e ---R + ---R 2 3 3 2 4 ---R (- 4b c - 4a b c - 2b )d e + 2b c d ---R * ---R cos(x) ---R + ---R 2 4 3 2 3 2 2 2 2 ---R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e ---R + ---R 2 3 3 2 4 ---R (- 4b c - 4a b c - 2b )d e + 2b c d +--R 4b c sin(x) --R / --R cos(x) + 1 --R + --R - ---R +-------------------------------------+ ---R +-----------+ | +-----------+ ---R | 2 | | 2 2 2 ---R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R * --R ROOT --R 3 2 2 2 2 3 4 2 2 --R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) --R * --R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 3 ---R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e ---R + ---R 2 4 ---R - b d ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 4 3 2 5 ---R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c ---R + ---R 6 2 4 4 2 ---R - b + 2a b - a b ---R + ---R 2 2 2 ---R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b --R + ---R 2 2 2 ---R (- 4c - 4a c + 2b )d +--R 2 2 +--R - 4c - 4a c + 2b --R / --R 3 2 2 2 2 3 4 2 2 --R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R * ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|b\|- 4a c + b + 2c + 2a c - b ---R * --R log ---R 2 4 2 3 3 ---R - 8a c + (6a b - 24a )c ---R + ---R 4 2 2 4 2 ---R (- b + 22a b - 24a )c ---R + ---R 4 3 2 5 6 2 4 4 2 ---R (- 8a b + 18a b - 8a )c + b - 3a b + 2a b ---R * ---R e ---R + ---R 4 3 2 3 3 3 2 ---R - 4a b c + (b - 4a b)c + (5a b + 4a b)c ---R + ---R 5 2 3 4 5 3 3 ---R (- b - 5a b + 4a b)c + a b - a b ---R * ---R d ---R * ---R cos(x) ---R + ---R 2 4 2 3 3 ---R - 8a c + (6a b - 24a )c ---R + ---R 4 2 2 4 2 ---R (- b + 22a b - 24a )c +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c --R + ---R 4 3 2 5 6 2 4 4 2 ---R (- 8a b + 18a b - 8a )c + b - 3a b + 2a b ---R * ---R e ---R + ---R 4 3 2 3 3 3 2 ---R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c --R + ---R 5 2 3 4 5 3 3 ---R (- b - 5a b + 4a b)c + a b - a b +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b --R * ---R d ---R * ---R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 ---R (- 4c - 8a c - 2b - 4a )d e ---R + ---R 3 2 4 ---R (4b c + 4a b)d e - b d ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 ---R (2b - 22a b + 16a )c ---R + ---R 4 3 2 5 6 2 4 4 2 ---R (8a b - 12a b + 4a )c - b + 2a b - a b ---R + ---R 2 4 3 ---R (4a b c - b )e +--R cos(x) --R + ---R 2 3 2 3 2 ---R (- 12a b c + (3b - 12a b)c + 3a b )d e +--R 4 2 2 3 +--R 8a c + (- 2b + 4a b + 16a )c --R + ---R 3 2 2 2 3 4 2 2 2 ---R (8a c + (- 2b + 16a )c + 8a c - b - 2a b )d e +--R 3 2 2 3 2 +--R (- b - 12a b + 8a b + 8a )c --R + ---R 2 3 2 3 3 ---R (- 4a b c + (b - 4a b)c + a b )d +--R 4 3 2 2 3 5 2 3 +--R (2b - 6a b - 2a b + 4a b)c + b - a b --R * ---R cos(x) ---R + ---R 2 4 3 ---R (4a b c - b )e ---R + ---R 2 3 2 3 2 ---R (- 12a b c + (3b - 12a b)c + 3a b )d e ---R + ---R 3 2 2 2 3 4 2 2 2 ---R (8a c + (- 2b + 16a )c + 8a c - b - 2a b )d e +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b --R + ---R 2 3 2 3 3 ---R (- 4a b c + (b - 4a b)c + a b )d +--R 3 3 +--R (- 4a b c + b )cos(x) - 4a b c + b --R * --R ROOT --R 3 2 2 2 2 3 4 @@ -35129,505 +34958,253 @@ m0864:= a0864-r0864 --R 2a b --R * --R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 ---R (- 4c - 8a c - 2b - 4a )d e ---R + ---R 3 2 4 ---R (4b c + 4a b)d e - b d ---R / ---R 5 2 2 4 ---R 4a c + (- b + 16a )c ---R + ---R 2 3 3 ---R (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 ---R (2b - 22a b + 16a )c ---R + ---R 4 3 2 5 6 2 4 4 2 ---R (8a b - 12a b + 4a )c - b + 2a b - a b ---R + ---R 2 2 2 ---R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b --R + ---R 2 2 2 ---R (- 4c - 4a c + 2b )d +--R 2 2 +--R - 4c - 4a c + 2b --R / --R 3 2 2 2 2 3 4 2 2 --R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R + ---R 2 3 2 3 2 2 2 4 ---R - 8a c + (2a b - 16a )c + (12a b - 8a )c ---R + ---R 4 3 2 ---R - 2a b + 2a b ---R * ---R 2 ---R e ---R + ---R 3 3 2 2 3 3 ---R 8a b c + (- 2b + 16a b)c + (- 12a b + 8a b)c ---R + ---R 5 2 3 ---R 2b - 2a b ---R * ---R d e ---R + ---R 4 2 2 3 2 3 2 ---R - 8a c + (2b - 16a )c + (12a b - 8a )c ---R + ---R 4 2 2 ---R (- 2b + 2a b )c ---R * ---R 2 ---R d ---R * ---R cos(x) ---R + ---R 2 3 2 3 2 2 2 4 4 ---R - 8a c + (2a b - 16a )c + (12a b - 8a )c - 2a b ---R + ---R 3 2 ---R 2a b ---R * ---R 2 ---R e ---R + ---R 3 3 2 2 3 3 ---R 8a b c + (- 2b + 16a b)c + (- 12a b + 8a b)c ---R + ---R 5 2 3 ---R 2b - 2a b ---R * ---R d e ---R + ---R 4 2 2 3 2 3 2 ---R - 8a c + (2b - 16a )c + (12a b - 8a )c ---R + ---R 4 2 2 ---R (- 2b + 2a b )c ---R * ---R 2 ---R d ---R * ---R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 3 ---R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e ---R + ---R 2 4 ---R - b d ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 4 3 2 5 ---R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c ---R + ---R 6 2 4 4 2 ---R - b + 2a b - a b ---R + ---R 2 4 2 2 3 3 ---R 4a b e + (- 8a c - 4a b - 8a )d e ---R + ---R 2 2 2 2 2 2 3 ---R (12a b c + 12a b)d e + (- 8a c - 8a c - 4a b )d e ---R + ---R 4 ---R 4a b c d ---R * ---R sin(x) ---R + ---R 2 4 3 2 3 ---R 2a b e + (- 4a b c - 2b - 4a b)d e ---R + ---R 2 2 2 2 2 3 3 2 4 ---R (6b c + 6a b )d e + (- 4b c - 4a b c - 2b )d e + 2b c d ---R * ---R cos(x) ---R + ---R 2 4 3 2 3 2 2 2 2 ---R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e ---R + ---R 2 3 3 2 4 ---R (- 4b c - 4a b c - 2b )d e + 2b c d +--R 4b c sin(x) --R / --R cos(x) + 1 --R + ---R +-------------------------------------+ ---R +-----------+ | +-----------+ ---R | 2 | | 2 2 2 ---R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R * --R ROOT ---R 3 2 2 2 2 3 4 2 2 ---R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) --R * --R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 3 2 4 ---R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 4 3 2 5 6 ---R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b ---R + ---R 2 4 4 2 ---R 2a b - a b +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b --R + ---R 2 2 2 2 2 2 ---R (4a c - 2b + 4a )e + (4b c - 4a b)d e + (- 4c - 4a c + 2b )d +--R 2 2 +--R - 4c - 4a c + 2b --R / --R 3 2 2 2 2 3 4 2 2 --R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R * ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|b\|- 4a c + b + 2c + 2a c - b ---R * --R log ---R 2 4 2 3 3 ---R - 8a c + (6a b - 24a )c ---R + ---R 4 2 2 4 2 ---R (- b + 22a b - 24a )c ---R + ---R 4 3 2 5 6 2 4 4 2 ---R (- 8a b + 18a b - 8a )c + b - 3a b + 2a b ---R * ---R e ---R + ---R 4 3 2 3 3 3 2 ---R - 4a b c + (b - 4a b)c + (5a b + 4a b)c ---R + ---R 5 2 3 4 5 3 3 ---R (- b - 5a b + 4a b)c + a b - a b ---R * ---R d ---R * ---R cos(x) ---R + ---R 2 4 2 3 3 ---R - 8a c + (6a b - 24a )c ---R + ---R 4 2 2 4 2 4 3 2 5 ---R (- b + 22a b - 24a )c + (- 8a b + 18a b - 8a )c +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c --R + ---R 6 2 4 4 2 ---R b - 3a b + 2a b ---R * ---R e ---R + ---R 4 3 2 3 3 3 2 ---R - 4a b c + (b - 4a b)c + (5a b + 4a b)c +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c --R + ---R 5 2 3 4 5 3 3 ---R (- b - 5a b + 4a b)c + a b - a b +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b --R * ---R d ---R * ---R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 3 ---R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e ---R + ---R 2 4 ---R - b d ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 4 3 2 5 ---R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c ---R + ---R 6 2 4 4 2 ---R - b + 2a b - a b ---R + ---R 2 4 3 ---R (- 4a b c + b )e +--R cos(x) --R + ---R 2 3 2 3 2 ---R (12a b c + (- 3b + 12a b)c - 3a b )d e +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c --R + ---R 3 2 2 2 3 4 2 2 2 ---R (- 8a c + (2b - 16a )c - 8a c + b + 2a b )d e +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c --R + ---R 2 3 2 3 3 ---R (4a b c + (- b + 4a b)c - a b )d +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b --R * ---R cos(x) ---R + ---R 2 4 3 ---R (- 4a b c + b )e ---R + ---R 2 3 2 3 2 ---R (12a b c + (- 3b + 12a b)c - 3a b )d e ---R + ---R 3 2 2 2 3 4 2 2 2 ---R (- 8a c + (2b - 16a )c - 8a c + b + 2a b )d e +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b --R + ---R 2 3 2 3 3 ---R (4a b c + (- b + 4a b)c - a b )d +--R 3 3 +--R (4a b c - b )cos(x) + 4a b c - b --R * --R ROOT ---R 3 2 2 2 2 3 4 ---R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b --R + ---R 2 2 ---R - 2a b +--R 2 2 +--R 2a b --R * --R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 ---R (- 4c - 8a c - 2b - 4a )d e ---R + ---R 3 2 4 ---R (4b c + 4a b)d e - b d ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 ---R (2b - 22a b + 16a )c ---R + ---R 4 3 2 5 6 2 4 4 2 ---R (8a b - 12a b + 4a )c - b + 2a b - a b ---R + ---R 2 2 2 ---R (4a c - 2b + 4a )e + (4b c - 4a b)d e +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b --R + ---R 2 2 2 ---R (- 4c - 4a c + 2b )d +--R 2 2 +--R - 4c - 4a c + 2b --R / --R 3 2 2 2 2 3 4 2 2 --R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R + ---R 2 3 2 3 2 2 2 4 ---R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c ---R + ---R 4 3 2 ---R 2a b - 2a b ---R * ---R 2 ---R e ---R + ---R 3 3 2 2 3 3 5 ---R - 8a b c + (2b - 16a b)c + (12a b - 8a b)c - 2b ---R + ---R 2 3 ---R 2a b ---R * ---R d e ---R + ---R 4 2 2 3 2 3 2 ---R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c ---R + ---R 4 2 2 ---R (2b - 2a b )c ---R * ---R 2 ---R d ---R * ---R cos(x) ---R + ---R 2 3 2 3 2 2 2 4 4 ---R 8a c + (- 2a b + 16a )c + (- 12a b + 8a )c + 2a b ---R + ---R 3 2 ---R - 2a b ---R * ---R 2 ---R e ---R + ---R 3 3 2 2 3 3 5 ---R - 8a b c + (2b - 16a b)c + (12a b - 8a b)c - 2b ---R + ---R 2 3 ---R 2a b ---R * ---R d e ---R + ---R 4 2 2 3 2 3 2 ---R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c ---R + ---R 4 2 2 ---R (2b - 2a b )c ---R * ---R 2 ---R d ---R * ---R ROOT ---R 2 4 3 ---R - b e + (4b c + 4a b)d e ---R + ---R 2 2 2 2 2 3 2 4 ---R (- 4c - 8a c - 2b - 4a )d e + (4b c + 4a b)d e - b d ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 4 3 2 5 6 ---R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c - b ---R + ---R 2 4 4 2 ---R 2a b - a b ---R + ---R 2 4 2 2 3 3 2 2 2 ---R 4a b e + (- 8a c - 4a b - 8a )d e + (12a b c + 12a b)d e ---R + ---R 2 2 2 3 4 ---R (- 8a c - 8a c - 4a b )d e + 4a b c d ---R * ---R sin(x) ---R + ---R 2 4 3 2 3 2 2 2 2 ---R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e ---R + ---R 2 3 3 2 4 ---R (- 4b c - 4a b c - 2b )d e + 2b c d ---R * ---R cos(x) ---R + ---R 2 4 3 2 3 2 2 2 2 ---R 2a b e + (- 4a b c - 2b - 4a b)d e + (6b c + 6a b )d e ---R + ---R 2 3 3 2 4 ---R (- 4b c - 4a b c - 2b )d e + 2b c d +--R 4b c sin(x) --R / --R cos(x) + 1 --R + ---R +---------------------------------+ ---R +-----------+ | +-----------+ ---R | 2 | | 2 2 2 ---R (4e\|- 4a c + b + 4b e - 8c d)\|b\|- 4a c + b + 2c + 2a c - b ---R * ---R +-----------+ ---R x | 2 x ---R tan(-)\|- 4a c + b + b tan(-) + 2c ---R 2 2 ---R atanh(----------------------------------------) ---R +-------------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R + ---R +-----------+ ---R +-+ | 2 +-+ ---R (- 2e\|2 \|- 4a c + b + (2b e - 4c d)\|2 ) ---R * ---R +-------------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R * ---R +-----------+ ---R +-+ x | 2 +-+ x +-+ ---R \|2 tan(-)\|- 4a c + b - b\|2 tan(-) - 2c\|2 ---R 2 2 ---R atanh(-----------------------------------------------) ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R 2\|b\|- 4a c + b + 2c + 2a c - b +--R - +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R * +--R log +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R cos(x) +--R + +--R 4 2 2 3 +--R - 8a c + (2b - 4a b - 16a )c +--R + +--R 3 2 2 3 2 +--R (b + 12a b - 8a b - 8a )c +--R + +--R 4 3 2 2 3 5 2 3 +--R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (- 4a b c + b )cos(x) - 4a b c + b +--R * +--R ROOT +--R 3 2 2 2 2 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R + +--R 4 2 2 +--R 2b - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 +--R (8a b - 12a b + 4a )c - b + 2a b +--R + +--R 4 2 +--R - a b +--R + +--R 2 2 +--R - 4c - 4a c + 2b +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4b c sin(x) +--R / +--R cos(x) + 1 --R / ---R +-------------------------------------+ ---R +-----------+ | +-----------+ ---R | 2 | | 2 2 2 ---R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R * ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|b\|- 4a c + b + 2c + 2a c - b ---R Type: Expression(Integer) ---E 350 - ---S 351 of 526 ---d0864:= D(m0864,x) ---E 351 - ---S 352 of 526 -t0865:= 1/(a+b*cos(x)+c*cos(x)^2) ---R ---R ---R 1 ---R (334) ------------------------ ---R 2 ---R c cos(x) + b cos(x) + a ---R Type: Expression(Integer) ---E 352 +--R 2 +--R Type: Union(Expression(Integer),...) +--E 354 ---S 353 of 526 -r0865:= -2*2^(1/2)*c*atanh(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*_ - tan(1/2*x)*2^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/_ - (b^2-4*a*c)^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)+_ - 4*c*atanh((b+(b^2-4*a*c)^(1/2)-2*c)*tan(1/2*x)/_ - (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/(b^2-4*a*c)^(1/2)/_ - (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--S 355 of 526 +m0865:= a0865-r0865 --R --R ---R (335) ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R 4c\|b\|- 4a c + b + 2c + 2a c - b +--R (4) +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b --R * ---R +-----------+ ---R x | 2 x ---R tan(-)\|- 4a c + b + (- 2c + b)tan(-) ---R 2 2 ---R atanh(----------------------------------------) ---R +-------------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R + ---R +-------------------------------------+ ---R | +-----------+ ---R +-+ | | 2 2 2 ---R 2c\|2 \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b --R * ---R +-----------+ ---R +-+ x | 2 +-+ x ---R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) ---R 2 2 ---R atanh(---------------------------------------------) ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R 2\|b\|- 4a c + b + 2c + 2a c - b ---R / ---R +-------------------------------------+ ---R +-----------+ | +-----------+ ---R | 2 | | 2 2 2 ---R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R * ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|b\|- 4a c + b + 2c + 2a c - b ---R Type: Expression(Integer) ---E 353 - ---S 354 of 526 -a0865:= integrate(t0865,x) ---R ---R ---R (336) --R ROOT --R 3 2 2 2 2 3 4 2 2 --R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) @@ -35725,6 +35302,10 @@ a0865:= integrate(t0865,x) --R cos(x) + 1 --R + --R - +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * --R ROOT --R 3 2 2 2 2 3 4 2 2 --R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) @@ -35749,6 +35330,16 @@ a0865:= integrate(t0865,x) --R 3 2 2 2 2 3 4 2 2 --R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * --R log --R 4 2 2 3 --R 8a c + (- 2b + 4a b + 16a )c @@ -35824,6 +35415,10 @@ a0865:= integrate(t0865,x) --R / --R cos(x) + 1 --R + +--R +-----------+ +--R | 2 +--R \|- 4a c + b +--R * --R ROOT --R 3 2 2 2 2 3 4 2 2 --R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) @@ -35848,6 +35443,16 @@ a0865:= integrate(t0865,x) --R 3 2 2 2 2 3 4 2 2 --R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R * +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * --R log --R 4 2 2 3 --R - 8a c + (2b - 4a b - 16a )c @@ -35921,6 +35526,16 @@ a0865:= integrate(t0865,x) --R cos(x) + 1 --R + --R - +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R * --R ROOT --R 3 2 2 2 2 3 4 --R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b @@ -36022,130 +35637,259 @@ a0865:= integrate(t0865,x) --R 4b c sin(x) --R / --R cos(x) + 1 +--R + +--R - +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 8c\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + (- 2c + b)tan(-) +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R + +--R - +--R +-------------------------------------+ +--R | +-----------+ +--R +-+ | | 2 2 2 +--R 4c\|2 \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) +--R 2 2 +--R atanh(---------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b --R / ---R 2 ---R Type: Union(Expression(Integer),...) ---E 354 +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 355 ---S 355 of 526 -m0865:= a0865-r0865 +--S 356 of 526 +d0865:= D(m0865,x) --R --R ---R (337) ---R +-------------------------------------+ ---R +-----------+ | +-----------+ ---R | 2 | | 2 2 2 ---R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R (5) +--R 4 +--R (c - b + a)sin(x) +--R + +--R 2 2 +--R ((6c - 4b + 2a)cos(x) + (10c - 6b + 2a)cos(x) + 4c - 2b)sin(x) +--R + +--R 4 3 2 +--R (c - 3b + a)cos(x) + (2c - 10b + 2a)cos(x) - 12b cos(x) +--R + +--R (- 2c - 6b - 2a)cos(x) - c - b - a --R * ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|b\|- 4a c + b + 2c + 2a c - b +--R x 4 +--R tan(-) +--R 2 +--R + +--R 4 +--R (- 6c + 2b + 2a)sin(x) +--R + +--R 2 2 +--R ((- 4c + 4a)cos(x) + (- 4c + 4a)cos(x))sin(x) +--R + +--R 4 3 +--R (- 6c - 2b + 2a)cos(x) + (- 20c - 8b + 4a)cos(x) +--R + +--R 2 +--R (- 24c - 12b)cos(x) + (- 12c - 8b - 4a)cos(x) - 2c - 2b - 2a --R * ---R ROOT ---R 3 2 2 2 2 3 4 2 2 ---R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) ---R * ---R ROOT ---R - ---R 2 ---R b ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 4 3 2 5 ---R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c ---R + ---R 6 2 4 4 2 ---R - b + 2a b - a b ---R + ---R 2 2 ---R - 4c - 4a c + 2b ---R / ---R 3 2 2 2 2 3 4 2 2 ---R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R x 2 +--R tan(-) +--R 2 +--R + +--R 4 +--R (c + 3b + a)sin(x) +--R + +--R 2 2 +--R ((6c + 4b + 2a)cos(x) + (10c + 6b + 2a)cos(x) + 4c + 2b)sin(x) +--R + +--R 4 3 +--R (c + b + a)cos(x) + (2c + 2b + 2a)cos(x) + (- 2c - 2b - 2a)cos(x) - c +--R + +--R - b - a +--R / +--R 2 2 2 4 +--R (c + (- 2b + 2a)c + b - 2a b + a )sin(x) +--R + +--R 2 2 2 +--R (- 2c + 2b c - 2a b + 2a )cos(x) +--R + +--R 2 2 2 2 +--R (- 4c + 4b c - 4a b + 4a )cos(x) - 2c + 2b c - 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 4 2 2 2 3 +--R (c + 2a c - b + a )cos(x) + (4c + 8a c - 4b + 4a )cos(x) +--R + +--R 2 2 2 2 2 2 2 +--R (6c + 12a c - 6b + 6a )cos(x) + (4c + 8a c - 4b + 4a )cos(x) +--R + +--R 2 2 2 +--R c + 2a c - b + a --R * ---R log ---R 4 2 2 3 ---R 8a c + (- 2b + 4a b + 16a )c ---R + ---R 3 2 2 3 2 ---R (- b - 12a b + 8a b + 8a )c ---R + ---R 4 3 2 2 3 5 2 3 ---R (2b - 6a b - 2a b + 4a b)c + b - a b ---R * ---R cos(x) ---R + ---R 4 2 2 3 ---R 8a c + (- 2b + 4a b + 16a )c ---R + ---R 3 2 2 3 2 ---R (- b - 12a b + 8a b + 8a )c ---R + ---R 4 3 2 2 3 5 2 3 ---R (2b - 6a b - 2a b + 4a b)c + b - a b ---R * ---R ROOT ---R - ---R 2 ---R b ---R / ---R 5 2 2 4 2 3 3 ---R 4a c + (- b + 16a )c + (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 ---R (2b - 22a b + 16a )c ---R + ---R 4 3 2 5 6 2 4 4 2 ---R (8a b - 12a b + 4a )c - b + 2a b - a b ---R + ---R 3 3 ---R (4a b c - b )cos(x) + 4a b c - b ---R * ---R ROOT ---R 3 2 2 2 2 3 4 ---R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b ---R + ---R 2 2 ---R - 2a b ---R * ---R ROOT ---R - ---R 2 ---R b ---R / ---R 5 2 2 4 ---R 4a c + (- b + 16a )c ---R + ---R 2 3 3 ---R (- 12a b + 24a )c ---R + ---R 4 2 2 4 2 ---R (2b - 22a b + 16a )c ---R + ---R 4 3 2 5 6 2 4 4 2 ---R (8a b - 12a b + 4a )c - b + 2a b - a b ---R + ---R 2 2 ---R - 4c - 4a c + 2b ---R / ---R 3 2 2 2 2 3 4 2 2 ---R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b ---R + ---R 4b c sin(x) ---R / ---R cos(x) + 1 +--R x 4 +--R tan(-) +--R 2 +--R + +--R 2 2 4 +--R (- 2c + 2b c - 2a b + 2a )sin(x) +--R + +--R 2 2 2 2 2 2 +--R (4c - 8a c + 4a )cos(x) + (8c - 16a c + 8a )cos(x) + 4c +--R + +--R 2 +--R - 8a c + 4a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 4 +--R (- 2c - 2b c + 2a b + 2a )cos(x) +--R + +--R 2 2 3 +--R (- 8c - 8b c + 8a b + 8a )cos(x) +--R + +--R 2 2 2 +--R (- 12c - 12b c + 12a b + 12a )cos(x) +--R + +--R 2 2 2 2 +--R (- 8c - 8b c + 8a b + 8a )cos(x) - 2c - 2b c + 2a b + 2a +--R * +--R x 2 +--R tan(-) +--R 2 +--R + +--R 2 2 2 4 +--R (c + 2a c - b + a )sin(x) +--R + +--R 2 2 2 +--R (- 2c - 2b c + 2a b + 2a )cos(x) +--R + +--R 2 2 2 2 +--R (- 4c - 4b c + 4a b + 4a )cos(x) - 2c - 2b c + 2a b + 2a +--R * +--R 2 +--R sin(x) +--R + +--R 2 2 2 4 +--R (c + (2b + 2a)c + b + 2a b + a )cos(x) +--R + +--R 2 2 2 3 +--R (4c + (8b + 8a)c + 4b + 8a b + 4a )cos(x) +--R + +--R 2 2 2 2 +--R (6c + (12b + 12a)c + 6b + 12a b + 6a )cos(x) +--R + +--R 2 2 2 2 2 +--R (4c + (8b + 8a)c + 4b + 8a b + 4a )cos(x) + c + (2b + 2a)c + b + 2a b +--R + +--R 2 +--R a +--R Type: Expression(Integer) +--E 356 + +)clear all + + +--S 357 of 526 +t0866:= cos(x)/(a+b*cos(x)+c*cos(x)^2) +--R +--R +--R cos(x) +--R (1) ------------------------ +--R 2 +--R c cos(x) + b cos(x) + a +--R Type: Expression(Integer) +--E 357 + +--S 358 of 526 +r0866:= -2^(1/2)*(1-b/(b^2-4*a*c)^(1/2))*_ + atanh(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*tan(1/2*x)*_ + 2^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/_ + (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)-_ + 2*(1+b/(b^2-4*a*c)^(1/2))*atanh((b+(b^2-4*a*c)^(1/2)-2*c)*_ + tan(1/2*x)/(4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/_ + (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) +--R +--R +--R (2) +--R +---------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R (- 2\|- 4a c + b - 2b)\|b\|- 4a c + b + 2c + 2a c - b +--R * +--R +-----------+ +--R x | 2 x +--R tan(-)\|- 4a c + b + (- 2c + b)tan(-) +--R 2 2 +--R atanh(----------------------------------------) +--R +-------------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|- 2b\|- 4a c + b + 4c + 4a c - 2b --R + +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 2 2 +--R (\|2 \|- 4a c + b - b\|2 )\|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +-----------+ +--R +-+ x | 2 +-+ x +--R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) +--R 2 2 +--R atanh(---------------------------------------------) +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R 2\|b\|- 4a c + b + 2c + 2a c - b +--R / +--R +-------------------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 2 2 +--R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R * +--R +---------------------------------+ +--R | +-----------+ +--R | | 2 2 2 +--R \|b\|- 4a c + b + 2c + 2a c - b +--R Type: Expression(Integer) +--E 358 + +--S 359 of 526 +a0866:= integrate(t0866,x) +--R +--R +--R (3) --R - ---R +-----------+ ---R | 2 ---R \|- 4a c + b ---R * --R ROOT ---R 3 2 2 2 2 3 4 2 2 ---R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b --R * --R ROOT --R - @@ -36161,42 +35905,32 @@ m0865:= a0865-r0865 --R 6 2 4 4 2 --R - b + 2a b - a b --R + ---R 2 2 ---R - 4c - 4a c + 2b +--R 2 2 +--R 4a c - 2b + 4a --R / --R 3 2 2 2 2 3 4 2 2 --R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R * ---R +-------------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R * ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|b\|- 4a c + b + 2c + 2a c - b ---R * --R log ---R 4 2 2 3 ---R 8a c + (- 2b + 4a b + 16a )c +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c --R + ---R 3 2 2 3 2 ---R (- b - 12a b + 8a b + 8a )c +--R 3 2 2 3 4 5 4 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b --R + ---R 4 3 2 2 3 5 2 3 ---R (2b - 6a b - 2a b + 4a b)c + b - a b +--R 2 3 3 2 +--R - a b - 2a b --R * --R cos(x) --R + ---R 4 2 2 3 ---R 8a c + (- 2b + 4a b + 16a )c +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c --R + ---R 3 2 2 3 2 ---R (- b - 12a b + 8a b + 8a )c +--R 3 2 2 3 4 5 4 2 3 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b - a b --R + ---R 4 3 2 2 3 5 2 3 ---R (2b - 6a b - 2a b + 4a b)c + b - a b +--R 3 2 +--R - 2a b --R * --R ROOT --R - @@ -36216,11 +35950,11 @@ m0865:= a0865-r0865 --R (- 4a b c + b )cos(x) - 4a b c + b --R * --R ROOT ---R 3 2 2 2 2 3 4 ---R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b +--R 3 2 2 2 2 3 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c --R + ---R 2 2 ---R 2a b +--R 4 2 2 +--R 2b - 2a b --R * --R ROOT --R - @@ -36242,20 +35976,16 @@ m0865:= a0865-r0865 --R 4 2 --R - a b --R + ---R 2 2 ---R - 4c - 4a c + 2b +--R 2 2 +--R 4a c - 2b + 4a --R / --R 3 2 2 2 2 3 4 2 2 --R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R + ---R 4b c sin(x) +--R 4a b sin(x) --R / --R cos(x) + 1 --R + ---R +-----------+ ---R | 2 ---R \|- 4a c + b ---R * --R ROOT --R 3 2 2 2 2 3 4 2 2 --R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) @@ -36274,42 +36004,32 @@ m0865:= a0865-r0865 --R 6 2 4 4 2 --R - b + 2a b - a b --R + ---R 2 2 ---R - 4c - 4a c + 2b +--R 2 2 +--R 4a c - 2b + 4a --R / --R 3 2 2 2 2 3 4 2 2 --R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R * ---R +-------------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R * ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|b\|- 4a c + b + 2c + 2a c - b ---R * --R log ---R 4 2 2 3 ---R - 8a c + (2b - 4a b - 16a )c +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c --R + ---R 3 2 2 3 2 ---R (b + 12a b - 8a b - 8a )c +--R 3 2 2 3 4 5 4 2 3 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b - a b --R + ---R 4 3 2 2 3 5 2 3 ---R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R 3 2 +--R - 2a b --R * --R cos(x) --R + ---R 4 2 2 3 ---R - 8a c + (2b - 4a b - 16a )c +--R 2 3 3 2 2 3 2 +--R (4a b + 8a )c + (- b - 2a b + 8a b + 16a )c --R + ---R 3 2 2 3 2 ---R (b + 12a b - 8a b - 8a )c +--R 3 2 2 3 4 5 4 2 3 +--R (- 6a b - 12a b + 4a b + 8a )c + b + 2a b - a b --R + ---R 4 3 2 2 3 5 2 3 ---R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R 3 2 +--R - 2a b --R * --R ROOT --R - @@ -36352,33 +36072,20 @@ m0865:= a0865-r0865 --R 4 3 2 5 6 2 4 4 2 --R (8a b - 12a b + 4a )c - b + 2a b - a b --R + ---R 2 2 ---R - 4c - 4a c + 2b +--R 2 2 +--R 4a c - 2b + 4a --R / --R 3 2 2 2 2 3 4 2 2 --R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R + ---R 4b c sin(x) +--R 4a b sin(x) --R / --R cos(x) + 1 --R + --R - ---R +-------------------------------------+ ---R +-----------+ | +-----------+ ---R | 2 | | 2 2 2 ---R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R * ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|b\|- 4a c + b + 2c + 2a c - b ---R * --R ROOT ---R 3 2 2 2 2 3 4 ---R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b ---R + ---R 2 2 ---R - 2a b +--R 3 2 2 2 2 3 4 2 2 +--R (- 8a c + (2b - 16a )c + (12a b - 8a )c - 2b + 2a b ) --R * --R ROOT --R - @@ -36394,32 +36101,32 @@ m0865:= a0865-r0865 --R 6 2 4 4 2 --R - b + 2a b - a b --R + ---R 2 2 ---R - 4c - 4a c + 2b +--R 2 2 +--R 4a c - 2b + 4a --R / --R 3 2 2 2 2 3 4 2 2 --R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R * --R log ---R 4 2 2 3 ---R - 8a c + (2b - 4a b - 16a )c +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c --R + ---R 3 2 2 3 2 ---R (b + 12a b - 8a b - 8a )c +--R 3 2 2 3 4 5 4 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b --R + ---R 4 3 2 2 3 5 2 3 ---R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R 2 3 3 2 +--R a b + 2a b --R * --R cos(x) --R + ---R 4 2 2 3 ---R - 8a c + (2b - 4a b - 16a )c +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c --R + ---R 3 2 2 3 2 ---R (b + 12a b - 8a b - 8a )c +--R 3 2 2 3 4 5 4 2 3 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b + a b --R + ---R 4 3 2 2 3 5 2 3 ---R (- 2b + 6a b + 2a b - 4a b)c - b + a b +--R 3 2 +--R 2a b --R * --R ROOT --R - @@ -36439,11 +36146,11 @@ m0865:= a0865-r0865 --R (- 4a b c + b )cos(x) - 4a b c + b --R * --R ROOT ---R 3 2 2 2 2 3 ---R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c +--R 3 2 2 2 2 3 4 +--R - 8a c + (2b - 16a )c + (12a b - 8a )c - 2b --R + ---R 4 2 2 ---R 2b - 2a b +--R 2 2 +--R 2a b --R * --R ROOT --R - @@ -36465,269 +36172,118 @@ m0865:= a0865-r0865 --R 4 2 --R - a b --R + ---R 2 2 ---R - 4c - 4a c + 2b +--R 2 2 +--R 4a c - 2b + 4a --R / --R 3 2 2 2 2 3 4 2 2 --R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R + ---R 4b c sin(x) +--R 4a b sin(x) --R / --R cos(x) + 1 --R + ---R - ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R 8c\|b\|- 4a c + b + 2c + 2a c - b ---R * ---R +-----------+ ---R x | 2 x ---R tan(-)\|- 4a c + b + (- 2c + b)tan(-) ---R 2 2 ---R atanh(----------------------------------------) ---R +-------------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R + ---R - ---R +-------------------------------------+ ---R | +-----------+ ---R +-+ | | 2 2 2 ---R 4c\|2 \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R * ---R +-----------+ ---R +-+ x | 2 +-+ x ---R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) ---R 2 2 ---R atanh(---------------------------------------------) ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R 2\|b\|- 4a c + b + 2c + 2a c - b ---R / ---R +-------------------------------------+ ---R +-----------+ | +-----------+ ---R | 2 | | 2 2 2 ---R 2\|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R * ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|b\|- 4a c + b + 2c + 2a c - b ---R Type: Expression(Integer) ---E 355 - ---S 356 of 526 -d0865:= D(m0865,x) ---R ---R ---R (338) ---R 4 ---R (c - b + a)sin(x) ---R + ---R 2 2 ---R ((6c - 4b + 2a)cos(x) + (10c - 6b + 2a)cos(x) + 4c - 2b)sin(x) ---R + ---R 4 3 2 ---R (c - 3b + a)cos(x) + (2c - 10b + 2a)cos(x) - 12b cos(x) ---R + ---R (- 2c - 6b - 2a)cos(x) - c - b - a ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 4 ---R (- 6c + 2b + 2a)sin(x) ---R + ---R 2 2 ---R ((- 4c + 4a)cos(x) + (- 4c + 4a)cos(x))sin(x) ---R + ---R 4 3 ---R (- 6c - 2b + 2a)cos(x) + (- 20c - 8b + 4a)cos(x) ---R + ---R 2 ---R (- 24c - 12b)cos(x) + (- 12c - 8b - 4a)cos(x) - 2c - 2b - 2a ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 4 ---R (c + 3b + a)sin(x) ---R + ---R 2 2 ---R ((6c + 4b + 2a)cos(x) + (10c + 6b + 2a)cos(x) + 4c + 2b)sin(x) ---R + ---R 4 3 ---R (c + b + a)cos(x) + (2c + 2b + 2a)cos(x) + (- 2c - 2b - 2a)cos(x) - c ---R + ---R - b - a ---R / ---R 2 2 2 4 ---R (c + (- 2b + 2a)c + b - 2a b + a )sin(x) ---R + ---R 2 2 2 ---R (- 2c + 2b c - 2a b + 2a )cos(x) ---R + ---R 2 2 2 2 ---R (- 4c + 4b c - 4a b + 4a )cos(x) - 2c + 2b c - 2a b + 2a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 2 4 2 2 2 3 ---R (c + 2a c - b + a )cos(x) + (4c + 8a c - 4b + 4a )cos(x) ---R + ---R 2 2 2 2 2 2 2 ---R (6c + 12a c - 6b + 6a )cos(x) + (4c + 8a c - 4b + 4a )cos(x) ---R + ---R 2 2 2 ---R c + 2a c - b + a ---R * ---R x 4 ---R tan(-) ---R 2 ---R + ---R 2 2 4 ---R (- 2c + 2b c - 2a b + 2a )sin(x) ---R + ---R 2 2 2 2 2 2 ---R (4c - 8a c + 4a )cos(x) + (8c - 16a c + 8a )cos(x) + 4c ---R + ---R 2 ---R - 8a c + 4a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 4 ---R (- 2c - 2b c + 2a b + 2a )cos(x) ---R + ---R 2 2 3 ---R (- 8c - 8b c + 8a b + 8a )cos(x) ---R + ---R 2 2 2 ---R (- 12c - 12b c + 12a b + 12a )cos(x) ---R + ---R 2 2 2 2 ---R (- 8c - 8b c + 8a b + 8a )cos(x) - 2c - 2b c + 2a b + 2a ---R * ---R x 2 ---R tan(-) ---R 2 ---R + ---R 2 2 2 4 ---R (c + 2a c - b + a )sin(x) ---R + ---R 2 2 2 ---R (- 2c - 2b c + 2a b + 2a )cos(x) ---R + ---R 2 2 2 2 ---R (- 4c - 4b c + 4a b + 4a )cos(x) - 2c - 2b c + 2a b + 2a ---R * ---R 2 ---R sin(x) ---R + ---R 2 2 2 4 ---R (c + (2b + 2a)c + b + 2a b + a )cos(x) ---R + ---R 2 2 2 3 ---R (4c + (8b + 8a)c + 4b + 8a b + 4a )cos(x) ---R + ---R 2 2 2 2 ---R (6c + (12b + 12a)c + 6b + 12a b + 6a )cos(x) ---R + ---R 2 2 2 2 2 ---R (4c + (8b + 8a)c + 4b + 8a b + 4a )cos(x) + c + (2b + 2a)c + b + 2a b ---R + ---R 2 ---R a ---R Type: Expression(Integer) ---E 356 - ---S 357 of 526 -t0866:= cos(x)/(a+b*cos(x)+c*cos(x)^2) ---R ---R ---R cos(x) ---R (339) ------------------------ ---R 2 ---R c cos(x) + b cos(x) + a ---R Type: Expression(Integer) ---E 357 - ---S 358 of 526 -r0866:= -2^(1/2)*(1-b/(b^2-4*a*c)^(1/2))*_ - atanh(1/2*(b-2*c-(b^2-4*a*c)^(1/2))*tan(1/2*x)*_ - 2^(1/2)/(-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2))/_ - (-b^2+2*c*(a+c)+(b^2-4*a*c)^(1/2)*b)^(1/2)-_ - 2*(1+b/(b^2-4*a*c)^(1/2))*atanh((b+(b^2-4*a*c)^(1/2)-2*c)*_ - tan(1/2*x)/(4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2))/_ - (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) ---R ---R ---R (340) ---R +---------------------------------+ ---R +-----------+ | +-----------+ ---R | 2 | | 2 2 2 ---R (- 2\|- 4a c + b - 2b)\|b\|- 4a c + b + 2c + 2a c - b ---R * ---R +-----------+ ---R x | 2 x ---R tan(-)\|- 4a c + b + (- 2c + b)tan(-) ---R 2 2 ---R atanh(----------------------------------------) ---R +-------------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R + ---R +-------------------------------------+ ---R +-----------+ | +-----------+ ---R +-+ | 2 +-+ | | 2 2 2 ---R (\|2 \|- 4a c + b - b\|2 )\|- 2b\|- 4a c + b + 4c + 4a c - 2b +--R ROOT +--R 3 2 2 2 2 3 4 2 2 +--R (8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b - 2a b ) +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 4 3 2 5 +--R (2b - 22a b + 16a )c + (8a b - 12a b + 4a )c +--R + +--R 6 2 4 4 2 +--R - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b --R * ---R +-----------+ ---R +-+ x | 2 +-+ x ---R \|2 tan(-)\|- 4a c + b + (2c - b)\|2 tan(-) ---R 2 2 ---R atanh(---------------------------------------------) ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R 2\|b\|- 4a c + b + 2c + 2a c - b +--R log +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b + a b +--R + +--R 3 2 +--R 2a b +--R * +--R cos(x) +--R + +--R 2 3 3 2 2 3 2 +--R (- 4a b - 8a )c + (b + 2a b - 8a b - 16a )c +--R + +--R 3 2 2 3 4 5 4 2 3 3 2 +--R (6a b + 12a b - 4a b - 8a )c - b - 2a b + a b + 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 2 3 3 +--R 4a c + (- b + 16a )c + (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 3 3 +--R (4a b c - b )cos(x) + 4a b c - b +--R * +--R ROOT +--R 3 2 2 2 2 3 4 +--R 8a c + (- 2b + 16a )c + (- 12a b + 8a )c + 2b +--R + +--R 2 2 +--R - 2a b +--R * +--R ROOT +--R - +--R 2 +--R b +--R / +--R 5 2 2 4 +--R 4a c + (- b + 16a )c +--R + +--R 2 3 3 +--R (- 12a b + 24a )c +--R + +--R 4 2 2 4 2 +--R (2b - 22a b + 16a )c +--R + +--R 4 3 2 5 6 2 4 4 2 +--R (8a b - 12a b + 4a )c - b + 2a b - a b +--R + +--R 2 2 +--R 4a c - 2b + 4a +--R / +--R 3 2 2 2 2 3 4 2 2 +--R 4a c + (- b + 8a )c + (- 6a b + 4a )c + b - a b +--R + +--R 4a b sin(x) +--R / +--R cos(x) + 1 --R / ---R +-------------------------------------+ ---R +-----------+ | +-----------+ ---R | 2 | | 2 2 2 ---R \|- 4a c + b \|- 2b\|- 4a c + b + 4c + 4a c - 2b ---R * ---R +---------------------------------+ ---R | +-----------+ ---R | | 2 2 2 ---R \|b\|- 4a c + b + 2c + 2a c - b ---R Type: Expression(Integer) ---E 358 - ---S 359 of 526 -a0866:= integrate(t0866,x) ---R ---R ---R >> Error detected within library code: ---R Table construction failed in MLIFT ---R ---R Continuing to read the file... ---R +--R 2 +--R Type: Union(Expression(Integer),...) --E 359 --S 360 of 526 m0866:= a0866-r0866 --R --R ---R (341) +--R (4) --R - --R +-------------------------------------+ --R +-----------+ | +-----------+ @@ -37218,7 +36774,7 @@ m0866:= a0866-r0866 d0866:= D(m0866,x) --R --R ---R (342) +--R (5) --R 4 --R (- c + b - a)sin(x) --R + @@ -37339,15 +36895,18 @@ d0866:= D(m0866,x) --R Type: Expression(Integer) --E 361 +)clear all + + --S 362 of 526 t0867:= cos(x)^2/(a+b*cos(x)+c*cos(x)^2) --R --R ---R 2 ---R cos(x) ---R (343) ------------------------ ---R 2 ---R c cos(x) + b cos(x) + a +--R 2 +--R cos(x) +--R (1) ------------------------ +--R 2 +--R c cos(x) + b cos(x) + a --R Type: Expression(Integer) --E 362 @@ -37361,7 +36920,7 @@ r0867:= x/c+2^(1/2)*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) --R --R ---R (344) +--R (2) --R +---------------------------------+ --R +-----------+ | +-----------+ --R | 2 2 | | 2 2 2 @@ -37422,7 +36981,7 @@ r0867:= x/c+2^(1/2)*(b-(b^2-2*a*c)/(b^2-4*a*c)^(1/2))*_ a0867:= integrate(t0867,x) --R --R ---R (345) +--R (3) --R c --R * --R ROOT @@ -37923,7 +37482,7 @@ a0867:= integrate(t0867,x) m0867:= a0867-r0867 --R --R ---R (346) +--R (4) --R +-------------------------------------+ --R +-----------+ | +-----------+ --R | 2 | | 2 2 2 @@ -38504,7 +38063,7 @@ m0867:= a0867-r0867 d0867:= D(m0867,x) --R --R ---R (347) +--R (5) --R 2 2 4 --R ((b - a)c - b + 2a b - a )sin(x) --R + @@ -38663,15 +38222,18 @@ d0867:= D(m0867,x) --R Type: Expression(Integer) --E 366 +)clear all + + --S 367 of 526 t0868:= cos(x)^3/(a+b*cos(x)+c*cos(x)^2) --R --R ---R 3 ---R cos(x) ---R (348) ------------------------ ---R 2 ---R c cos(x) + b cos(x) + a +--R 3 +--R cos(x) +--R (1) ------------------------ +--R 2 +--R c cos(x) + b cos(x) + a --R Type: Expression(Integer) --E 367 @@ -38685,7 +38247,7 @@ r0868:= -b*x/c^2-2^(1/2)*(b^2-a*c-b*(b^2-3*a*c)/(b^2-4*a*c)^(1/2))*_ (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2)+sin(x)/c --R --R ---R (349) +--R (2) --R +-----------+ --R 2 | 2 3 --R ((2a c - 2b )\|- 4a c + b + 6a b c - 2b ) @@ -38750,7 +38312,7 @@ r0868:= -b*x/c^2-2^(1/2)*(b^2-a*c-b*(b^2-3*a*c)/(b^2-4*a*c)^(1/2))*_ a0868:= integrate(t0868,x) --R --R ---R (350) +--R (3) --R 2 --R c --R * @@ -39388,7 +38950,7 @@ a0868:= integrate(t0868,x) m0868:= a0868-r0868 --R --R ---R (351) +--R (4) --R +-------------------------------------+ --R +-----------+ | +-----------+ --R 2 | 2 | | 2 2 2 @@ -40105,7 +39667,7 @@ m0868:= a0868-r0868 d0868:= D(m0868,x) --R --R ---R (352) +--R (5) --R 2 2 2 3 2 2 4 --R (a c + (- b + a )c + b - 2a b + a b)sin(x) --R + @@ -40289,14 +39851,17 @@ d0868:= D(m0868,x) --R Type: Expression(Integer) --E 371 +)clear all + + --S 372 of 526 t0869:= (d+e*cos(x))/(a+b*cos(x)+c*cos(x)^2) --R --R ---R e cos(x) + d ---R (353) ------------------------ ---R 2 ---R c cos(x) + b cos(x) + a +--R e cos(x) + d +--R (1) ------------------------ +--R 2 +--R c cos(x) + b cos(x) + a --R Type: Expression(Integer) --E 372 @@ -40310,7 +39875,7 @@ r0869:= -2^(1/2)*(e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ (4*c^2-(b+(b^2-4*a*c)^(1/2))^2)^(1/2) --R --R ---R (354) +--R (2) --R +---------------------------------+ --R +-----------+ | +-----------+ --R | 2 | | 2 2 2 @@ -40361,7 +39926,7 @@ r0869:= -2^(1/2)*(e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ a0869:= integrate(t0869,x) --R --R ---R (355) +--R (3) --R - --R ROOT --R 3 2 2 2 2 3 4 @@ -41051,7 +40616,7 @@ a0869:= integrate(t0869,x) m0869:= a0869-r0869 --R --R ---R (356) +--R (4) --R - --R +-------------------------------------+ --R +-----------+ | +-----------+ @@ -41823,7 +41388,7 @@ m0869:= a0869-r0869 d0869:= D(m0869,x) --R --R ---R (357) +--R (5) --R 4 --R ((- c + b - a)e + (c - b + a)d)sin(x) --R + @@ -41983,14 +41548,17 @@ d0869:= D(m0869,x) --R Type: Expression(Integer) --E 376 +)clear all + + --S 377 of 526 t0870:= cos(x)/(2-3*sin(x)+sin(x)^2) --R --R ---R cos(x) ---R (358) --------------------- ---R 2 ---R sin(x) - 3sin(x) + 2 +--R cos(x) +--R (1) --------------------- +--R 2 +--R sin(x) - 3sin(x) + 2 --R Type: Expression(Integer) --E 377 @@ -41998,7 +41566,7 @@ t0870:= cos(x)/(2-3*sin(x)+sin(x)^2) r0870:= -2*atanh(-3+2*sin(x)) --R --R ---R (359) - 2atanh(2sin(x) - 3) +--R (2) - 2atanh(2sin(x) - 3) --R Type: Expression(Integer) --E 378 @@ -42006,9 +41574,9 @@ r0870:= -2*atanh(-3+2*sin(x)) a0870:= integrate(t0870,x) --R --R ---R sin(x) - cos(x) - 1 - sin(x) + 2 ---R (360) - 2log(-------------------) + log(------------) ---R cos(x) + 1 cos(x) + 1 +--R sin(x) - cos(x) - 1 - sin(x) + 2 +--R (3) - 2log(-------------------) + log(------------) +--R cos(x) + 1 cos(x) + 1 --R Type: Union(Expression(Integer),...) --E 379 @@ -42016,10 +41584,9 @@ a0870:= integrate(t0870,x) m0870:= a0870-r0870 --R --R ---R (361) ---R sin(x) - cos(x) - 1 - sin(x) + 2 ---R - 2log(-------------------) + log(------------) + 2atanh(2sin(x) - 3) ---R cos(x) + 1 cos(x) + 1 +--R sin(x) - cos(x) - 1 - sin(x) + 2 +--R (4) - 2log(-------------------) + log(------------) + 2atanh(2sin(x) - 3) +--R cos(x) + 1 cos(x) + 1 --R Type: Expression(Integer) --E 380 @@ -42027,7 +41594,7 @@ m0870:= a0870-r0870 d0870:= D(m0870,x) --R --R ---R (362) +--R (5) --R 3 2 2 3 --R - sin(x) - cos(x)sin(x) + (- cos(x) + 1)sin(x) - cos(x) + cos(x) --R ----------------------------------------------------------------------------- @@ -42036,15 +41603,18 @@ d0870:= D(m0870,x) --R Type: Expression(Integer) --E 381 +)clear all + + --S 382 of 526 t0871:= csc(x)*(cos(x)+sin(x))^(1/2)/cos(x)^(3/2) --R --R ---R +---------------+ ---R csc(x)\|sin(x) + cos(x) ---R (363) ------------------------ ---R +------+ ---R cos(x)\|cos(x) +--R +---------------+ +--R csc(x)\|sin(x) + cos(x) +--R (1) ------------------------ +--R +------+ +--R cos(x)\|cos(x) --R Type: Expression(Integer) --E 382 @@ -42053,7 +41623,7 @@ r0871:= -log(sin(x))+2*log(-cos(x)^(1/2)+(cos(x)+sin(x))^(1/2))+_ 2*(cos(x)+sin(x))^(1/2)/cos(x)^(1/2) --R --R ---R (364) +--R (2) --R +------+ +---------------+ +------+ +---------------+ --R 2\|cos(x) log(\|sin(x) + cos(x) - \|cos(x) ) + 2\|sin(x) + cos(x) --R + @@ -42080,7 +41650,7 @@ a0871:= integrate(t0871,x) m0871:= a0871-r0871 --R --R ---R (365) +--R (3) --R +------+ +---------------+ +------+ +---------------+ --R - 2\|cos(x) log(\|sin(x) + cos(x) - \|cos(x) ) - 2\|sin(x) + cos(x) --R + @@ -42096,7 +41666,7 @@ m0871:= a0871-r0871 d0871:= D(m0871,x) --R --R ---R (366) +--R (4) --R 2 2 +------+ +---------------+ 3 2 --R (sin(x) + cos(x) )\|cos(x) \|sin(x) + cos(x) - sin(x) - cos(x)sin(x) --R + @@ -42108,14 +41678,17 @@ d0871:= D(m0871,x) --R Type: Expression(Integer) --E 386 +)clear all + + --S 387 of 526 t0872:= (cos(x)+sin(x))/(1+sin(2*x))^(1/2) --R --R ---R sin(x) + cos(x) ---R (367) --------------- ---R +-----------+ ---R \|sin(2x) + 1 +--R sin(x) + cos(x) +--R (1) --------------- +--R +-----------+ +--R \|sin(2x) + 1 --R Type: Expression(Integer) --E 387 @@ -42123,10 +41696,10 @@ t0872:= (cos(x)+sin(x))/(1+sin(2*x))^(1/2) r0872:= x*(cos(x)+sin(x))/(1+sin(2*x))^(1/2) --R --R ---R x sin(x) + x cos(x) ---R (368) ------------------- ---R +-----------+ ---R \|sin(2x) + 1 +--R x sin(x) + x cos(x) +--R (2) ------------------- +--R +-----------+ +--R \|sin(2x) + 1 --R Type: Expression(Integer) --E 388 @@ -42134,7 +41707,7 @@ r0872:= x*(cos(x)+sin(x))/(1+sin(2*x))^(1/2) a0872:= integrate(t0872,x) --R --R ---R (369) - x +--R (3) - x --R Type: Union(Expression(Integer),...) --E 389 @@ -42142,11 +41715,11 @@ a0872:= integrate(t0872,x) m0872:= a0872-r0872 --R --R ---R +-----------+ ---R - x\|sin(2x) + 1 - x sin(x) - x cos(x) ---R (370) --------------------------------------- ---R +-----------+ ---R \|sin(2x) + 1 +--R +-----------+ +--R - x\|sin(2x) + 1 - x sin(x) - x cos(x) +--R (4) --------------------------------------- +--R +-----------+ +--R \|sin(2x) + 1 --R Type: Expression(Integer) --E 390 @@ -42154,7 +41727,7 @@ m0872:= a0872-r0872 d0872:= D(m0872,x) --R --R ---R (371) +--R (5) --R +-----------+ --R (- sin(2x) - 1)\|sin(2x) + 1 + ((x - 1)sin(x) + (- x - 1)cos(x))sin(2x) --R + @@ -42165,12 +41738,15 @@ d0872:= D(m0872,x) --R Type: Expression(Integer) --E 391 +)clear all + + --S 392 of 526 t0873:= csc(x)^(1/2)*(x*cos(x)-4*sec(x)*tan(x)) --R --R ---R +------+ ---R (372) (- 4sec(x)tan(x) + x cos(x))\|csc(x) +--R +------+ +--R (1) (- 4sec(x)tan(x) + x cos(x))\|csc(x) --R Type: Expression(Integer) --E 392 @@ -42178,10 +41754,10 @@ t0873:= csc(x)^(1/2)*(x*cos(x)-4*sec(x)*tan(x)) r0873:= 2*x/csc(x)^(1/2)-4*sec(x)/csc(x)^(3/2) --R --R ---R - 4sec(x) + 2x csc(x) ---R (373) --------------------- ---R +------+ ---R csc(x)\|csc(x) +--R - 4sec(x) + 2x csc(x) +--R (2) --------------------- +--R +------+ +--R csc(x)\|csc(x) --R Type: Expression(Integer) --E 393 @@ -42200,11 +41776,11 @@ a0873:= integrate(t0873,x) m0873:= a0873-r0873 --R --R ---R +------+ ---R a0873 csc(x)\|csc(x) + 4sec(x) - 2x csc(x) ---R (374) ------------------------------------------- ---R +------+ ---R csc(x)\|csc(x) +--R +------+ +--R a0873 csc(x)\|csc(x) + 4sec(x) - 2x csc(x) +--R (3) ------------------------------------------- +--R +------+ +--R csc(x)\|csc(x) --R Type: Expression(Integer) --E 395 @@ -42212,18 +41788,21 @@ m0873:= a0873-r0873 d0873:= D(m0873,x) --R --R ---R 4sec(x)tan(x) + 6cot(x)sec(x) + (- x cot(x) - 2)csc(x) ---R (375) ------------------------------------------------------ ---R +------+ ---R csc(x)\|csc(x) +--R 4sec(x)tan(x) + 6cot(x)sec(x) + (- x cot(x) - 2)csc(x) +--R (4) ------------------------------------------------------ +--R +------+ +--R csc(x)\|csc(x) --R Type: Expression(Integer) --E 396 +)clear all + + --S 397 of 526 t0874:= cos(x)*(-1+csc(x)^2)^(1/2)*(1-sin(x)^2)^3 --R --R ---R (376) +--R (1) --R +-----------+ --R 6 4 2 | 2 --R (- cos(x)sin(x) + 3cos(x)sin(x) - 3cos(x)sin(x) + cos(x))\|csc(x) - 1 @@ -42235,7 +41814,7 @@ r0874:= -1/105*(105*atanh(cos(x))-105*cos(x)-35*cos(x)^3-_ 21*cos(x)^5-15*cos(x)^7)*(cot(x)^2)^(1/2)*tan(x) --R --R ---R (377) +--R (2) --R - 105tan(x)atanh(cos(x)) --R + --R 7 5 3 @@ -42253,11 +41832,11 @@ r0874:= -1/105*(105*atanh(cos(x))-105*cos(x)-35*cos(x)^3-_ a0874:= integrate(t0874,x) --R --R ---R sin(x) 7 5 3 ---R - 105log(----------) - 15cos(x) - 21cos(x) - 35cos(x) - 105cos(x) ---R cos(x) + 1 ---R (378) -------------------------------------------------------------------- ---R 105 +--R sin(x) 7 5 3 +--R - 105log(----------) - 15cos(x) - 21cos(x) - 35cos(x) - 105cos(x) +--R cos(x) + 1 +--R (3) -------------------------------------------------------------------- +--R 105 --R Type: Union(Expression(Integer),...) --E 399 @@ -42265,7 +41844,7 @@ a0874:= integrate(t0874,x) m0874:= a0874-r0874 --R --R ---R (379) +--R (4) --R 105tan(x)atanh(cos(x)) --R + --R 7 5 3 @@ -42287,7 +41866,7 @@ m0874:= a0874-r0874 d0874:= D(m0874,x) --R --R ---R (380) +--R (5) --R +-------+ --R 8 2 3 | 2 --R ((105cos(x) - 105cos(x))sin(x) - 105cos(x) + 105cos(x))\|cot(x) @@ -42333,12 +41912,15 @@ d0874:= D(m0874,x) --R Type: Expression(Integer) --E 401 +)clear all + + --S 402 of 526 t0875:= cos(x)*csc(x)^(7/3) --R --R ---R 2 3+------+ ---R (381) cos(x)csc(x) \|csc(x) +--R 2 3+------+ +--R (1) cos(x)csc(x) \|csc(x) --R Type: Expression(Integer) --E 402 @@ -42346,10 +41928,10 @@ t0875:= cos(x)*csc(x)^(7/3) r0875:= -3/4*csc(x)^(4/3) --R --R ---R 3+------+ ---R 3csc(x)\|csc(x) ---R (382) - ---------------- ---R 4 +--R 3+------+ +--R 3csc(x)\|csc(x) +--R (2) - ---------------- +--R 4 --R Type: Expression(Integer) --E 403 @@ -42357,14 +41939,14 @@ r0875:= -3/4*csc(x)^(4/3) a0875:= integrate(t0875,x) --R --R ---R +-------------+ ---R 2 | 1 ---R (6cos(x) - 3)sin(x) |- ----------- ---R 6| 2 ---R \| cos(x) - 1 ---R (383) ------------------------------------ ---R 4 2 ---R 16cos(x) - 32cos(x) + 16 +--R +-------------+ +--R 2 | 1 +--R (6cos(x) - 3)sin(x) |- ----------- +--R 6| 2 +--R \| cos(x) - 1 +--R (3) ------------------------------------ +--R 4 2 +--R 16cos(x) - 32cos(x) + 16 --R Type: Union(Expression(Integer),...) --E 404 @@ -42372,7 +41954,7 @@ a0875:= integrate(t0875,x) m0875:= a0875-r0875 --R --R ---R (384) +--R (4) --R 4 2 3+------+ --R (12cos(x) - 24cos(x) + 12)csc(x)\|csc(x) --R + @@ -42391,7 +41973,7 @@ m0875:= a0875-r0875 d0875:= D(m0875,x) --R --R ---R (385) +--R (5) --R 3 2 5 3 3+------+2 --R ((- 14cos(x) + cos(x))sin(x) - 6cos(x) + 9cos(x) - 3cos(x))\|csc(x) --R + @@ -42415,12 +41997,15 @@ d0875:= D(m0875,x) --R Type: Expression(Integer) --E 406 +)clear all + + --S 407 of 526 t0876:= cos(x)*(1+csc(x))^(1/2) --R --R ---R +----------+ ---R (386) cos(x)\|csc(x) + 1 +--R +----------+ +--R (1) cos(x)\|csc(x) + 1 --R Type: Expression(Integer) --E 407 @@ -42428,8 +42013,8 @@ t0876:= cos(x)*(1+csc(x))^(1/2) r0876:= atanh((1+csc(x))^(1/2))+(1+csc(x))^(1/2)*sin(x) --R --R ---R +----------+ +----------+ ---R (387) atanh(\|csc(x) + 1 ) + sin(x)\|csc(x) + 1 +--R +----------+ +----------+ +--R (2) atanh(\|csc(x) + 1 ) + sin(x)\|csc(x) + 1 --R Type: Expression(Integer) --E 408 @@ -42437,7 +42022,7 @@ r0876:= atanh((1+csc(x))^(1/2))+(1+csc(x))^(1/2)*sin(x) a0876:= integrate(t0876,x) --R --R ---R (388) +--R (3) --R log --R +-------------+2 --R |- 4cos(x) + 4 @@ -42478,7 +42063,7 @@ a0876:= integrate(t0876,x) m0876:= a0876-r0876 --R --R ---R (389) +--R (4) --R log --R +-------------+2 --R |- 4cos(x) + 4 @@ -42522,7 +42107,7 @@ m0876:= a0876-r0876 d0876:= D(m0876,x) --R --R ---R (390) +--R (5) --R 4 3 2 3 --R (cos(x) + 1)sin(x) + (2cos(x) + 3cos(x) + 3cos(x) + 2)sin(x) --R + @@ -42696,16 +42281,19 @@ d0876:= D(m0876,x) --R Type: Expression(Integer) --E 411 +)clear all + + --S 412 of 526 t0877:= cos(x)^3/(sin(x)^3)^(1/2) --R --R ---R 3 ---R cos(x) ---R (391) ---------- ---R +-------+ ---R | 3 ---R \|sin(x) +--R 3 +--R cos(x) +--R (1) ---------- +--R +-------+ +--R | 3 +--R \|sin(x) --R Type: Expression(Integer) --E 412 @@ -42713,12 +42301,12 @@ t0877:= cos(x)^3/(sin(x)^3)^(1/2) r0877:= 2/3*(-4+cos(x)^2)*sin(x)/(sin(x)^3)^(1/2) --R --R ---R 2 ---R (2cos(x) - 8)sin(x) ---R (392) -------------------- ---R +-------+ ---R | 3 ---R 3\|sin(x) +--R 2 +--R (2cos(x) - 8)sin(x) +--R (2) -------------------- +--R +-------+ +--R | 3 +--R 3\|sin(x) --R Type: Expression(Integer) --E 413 @@ -42726,11 +42314,11 @@ r0877:= 2/3*(-4+cos(x)^2)*sin(x)/(sin(x)^3)^(1/2) a0877:= integrate(t0877,x) --R --R ---R 2 +------+ ---R (- 2cos(x) + 8)sin(x)\|sin(x) ---R (393) ------------------------------- ---R 2 ---R 3cos(x) - 3 +--R 2 +------+ +--R (- 2cos(x) + 8)sin(x)\|sin(x) +--R (3) ------------------------------- +--R 2 +--R 3cos(x) - 3 --R Type: Union(Expression(Integer),...) --E 414 @@ -42738,7 +42326,7 @@ a0877:= integrate(t0877,x) m0877:= a0877-r0877 --R --R ---R (394) +--R (4) --R +-------+ --R 2 +------+ | 3 --R (- 2cos(x) + 8)sin(x)\|sin(x) \|sin(x) @@ -42756,7 +42344,7 @@ m0877:= a0877-r0877 d0877:= D(m0877,x) --R --R ---R (395) +--R (5) --R +-------+ --R 3 5 3 | 3 --R (12cos(x)sin(x) + (- 3cos(x) + 15cos(x) - 12cos(x))sin(x))\|sin(x) @@ -42776,12 +42364,15 @@ d0877:= D(m0877,x) --R Type: Expression(Integer) --E 416 +)clear all + + --S 417 of 526 t0878:= cos(x)^3*csc(x)^(1/2) --R --R ---R 3 +------+ ---R (396) cos(x) \|csc(x) +--R 3 +------+ +--R (1) cos(x) \|csc(x) --R Type: Expression(Integer) --E 417 @@ -42789,13 +42380,13 @@ t0878:= cos(x)^3*csc(x)^(1/2) r0878:= -2/5*(-5+sin(x)^2)/(1/sin(x))^(1/2) --R --R ---R 2 ---R - 2sin(x) + 10 ---R (397) --------------- ---R +------+ ---R | 1 ---R 5 |------ ---R \|sin(x) +--R 2 +--R - 2sin(x) + 10 +--R (2) --------------- +--R +------+ +--R | 1 +--R 5 |------ +--R \|sin(x) --R Type: Expression(Integer) --E 418 @@ -42803,13 +42394,13 @@ r0878:= -2/5*(-5+sin(x)^2)/(1/sin(x))^(1/2) a0878:= integrate(t0878,x) --R --R ---R +-------------+ ---R 2 | 1 ---R (2cos(x) + 8)sin(x) |- ----------- ---R 4| 2 ---R \| cos(x) - 1 ---R (398) ------------------------------------ ---R 5 +--R +-------------+ +--R 2 | 1 +--R (2cos(x) + 8)sin(x) |- ----------- +--R 4| 2 +--R \| cos(x) - 1 +--R (3) ------------------------------------ +--R 5 --R Type: Union(Expression(Integer),...) --E 419 @@ -42817,16 +42408,16 @@ a0878:= integrate(t0878,x) m0878:= a0878-r0878 --R --R ---R +-------------+ +------+ ---R 2 | 1 | 1 2 ---R (2cos(x) + 8)sin(x) |- ----------- |------ + 2sin(x) - 10 ---R 4| 2 \|sin(x) ---R \| cos(x) - 1 ---R (399) ------------------------------------------------------------- ---R +------+ ---R | 1 ---R 5 |------ ---R \|sin(x) +--R +-------------+ +------+ +--R 2 | 1 | 1 2 +--R (2cos(x) + 8)sin(x) |- ----------- |------ + 2sin(x) - 10 +--R 4| 2 \|sin(x) +--R \| cos(x) - 1 +--R (4) ------------------------------------------------------------- +--R +------+ +--R | 1 +--R 5 |------ +--R \|sin(x) --R Type: Expression(Integer) --E 420 @@ -42834,7 +42425,7 @@ m0878:= a0878-r0878 d0878:= D(m0878,x) --R --R ---R (400) +--R (5) --R 3 3 5 3 --R ((3cos(x) - 8cos(x))sin(x) + (- 2cos(x) - 6cos(x) + 8cos(x))sin(x)) --R * @@ -42862,12 +42453,15 @@ d0878:= D(m0878,x) --R Type: Expression(Integer) --E 421 +)clear all + + --S 422 of 526 t0879:= cos(x)^3*csc(x)^(9/2) --R --R ---R 3 4 +------+ ---R (401) cos(x) csc(x) \|csc(x) +--R 3 4 +------+ +--R (1) cos(x) csc(x) \|csc(x) --R Type: Expression(Integer) --E 422 @@ -42875,10 +42469,10 @@ t0879:= cos(x)^3*csc(x)^(9/2) r0879:= 2/3*csc(x)^(3/2)-2/7*csc(x)^(7/2) --R --R ---R 3 +------+ ---R (- 6csc(x) + 14csc(x))\|csc(x) ---R (402) -------------------------------- ---R 21 +--R 3 +------+ +--R (- 6csc(x) + 14csc(x))\|csc(x) +--R (2) -------------------------------- +--R 21 --R Type: Expression(Integer) --E 423 @@ -42886,14 +42480,14 @@ r0879:= 2/3*csc(x)^(3/2)-2/7*csc(x)^(7/2) a0879:= integrate(t0879,x) --R --R ---R +-------------+ ---R 4 2 | 1 ---R (- 14cos(x) + 15cos(x) - 4)sin(x) |- ----------- ---R 4| 2 ---R \| cos(x) - 1 ---R (403) --------------------------------------------------- ---R 6 4 2 ---R 42cos(x) - 126cos(x) + 126cos(x) - 42 +--R +-------------+ +--R 4 2 | 1 +--R (- 14cos(x) + 15cos(x) - 4)sin(x) |- ----------- +--R 4| 2 +--R \| cos(x) - 1 +--R (3) --------------------------------------------------- +--R 6 4 2 +--R 42cos(x) - 126cos(x) + 126cos(x) - 42 --R Type: Union(Expression(Integer),...) --E 424 @@ -42901,7 +42495,7 @@ a0879:= integrate(t0879,x) m0879:= a0879-r0879 --R --R ---R (404) +--R (4) --R 6 4 2 3 --R (12cos(x) - 36cos(x) + 36cos(x) - 12)csc(x) --R + @@ -42926,7 +42520,7 @@ m0879:= a0879-r0879 d0879:= D(m0879,x) --R --R ---R (405) +--R (5) --R 5 3 2 7 5 --R (70cos(x) - 23cos(x) - 8cos(x))sin(x) + 28cos(x) - 58cos(x) --R + @@ -42969,12 +42563,15 @@ d0879:= D(m0879,x) --R Type: Expression(Integer) --E 426 +)clear all + + --S 427 of 526 t0880:= sec(x)^2*(a+b*tan(x))^n --R --R ---R 2 n ---R (406) sec(x) (b tan(x) + a) +--R 2 n +--R (1) sec(x) (b tan(x) + a) --R Type: Expression(Integer) --E 427 @@ -42982,10 +42579,10 @@ t0880:= sec(x)^2*(a+b*tan(x))^n r0880:= (a+b*tan(x))^(1+n)/b/(1+n) --R --R ---R n + 1 ---R (b tan(x) + a) ---R (407) ------------------- ---R b n + b +--R n + 1 +--R (b tan(x) + a) +--R (2) ------------------- +--R b n + b --R Type: Expression(Integer) --E 428 @@ -42993,12 +42590,12 @@ r0880:= (a+b*tan(x))^(1+n)/b/(1+n) a0880:= integrate(t0880,x) --R --R ---R b sin(x) + a cos(x) ---R n log(-------------------) ---R cos(x) ---R (b sin(x) + a cos(x))%e ---R (408) ------------------------------------------------- ---R (b n + b)cos(x) +--R b sin(x) + a cos(x) +--R n log(-------------------) +--R cos(x) +--R (b sin(x) + a cos(x))%e +--R (3) ------------------------------------------------- +--R (b n + b)cos(x) --R Type: Union(Expression(Integer),...) --E 429 @@ -43006,7 +42603,7 @@ a0880:= integrate(t0880,x) m0880:= a0880-r0880 --R --R ---R (409) +--R (4) --R b sin(x) + a cos(x) --R n log(-------------------) --R cos(x) n + 1 @@ -43020,7 +42617,7 @@ m0880:= a0880-r0880 d0880:= D(m0880,x) --R --R ---R (410) +--R (5) --R b sin(x) + a cos(x) --R n log(-------------------) --R 2 2 cos(x) @@ -43034,15 +42631,18 @@ d0880:= D(m0880,x) --R Type: Expression(Integer) --E 431 +)clear all + + --S 432 of 526 t0881:= sec(x)^2/(tan(x)^2+tan(x)^3) --R --R ---R 2 ---R sec(x) ---R (411) ----------------- ---R 3 2 ---R tan(x) + tan(x) +--R 2 +--R sec(x) +--R (1) ----------------- +--R 3 2 +--R tan(x) + tan(x) --R Type: Expression(Integer) --E 432 @@ -43050,7 +42650,7 @@ t0881:= sec(x)^2/(tan(x)^2+tan(x)^3) r0881:= -cot(x)+log(1+cot(x)) --R --R ---R (412) log(cot(x) + 1) - cot(x) +--R (2) log(cot(x) + 1) - cot(x) --R Type: Expression(Integer) --E 433 @@ -43058,11 +42658,11 @@ r0881:= -cot(x)+log(1+cot(x)) a0881:= integrate(t0881,x) --R --R ---R sin(x) - 2sin(x) - 2cos(x) ---R - sin(x)log(----------) + sin(x)log(-------------------) - cos(x) ---R cos(x) + 1 cos(x) + 1 ---R (413) ----------------------------------------------------------------- ---R sin(x) +--R sin(x) - 2sin(x) - 2cos(x) +--R - sin(x)log(----------) + sin(x)log(-------------------) - cos(x) +--R cos(x) + 1 cos(x) + 1 +--R (3) ----------------------------------------------------------------- +--R sin(x) --R Type: Union(Expression(Integer),...) --E 434 @@ -43070,7 +42670,7 @@ a0881:= integrate(t0881,x) m0881:= a0881-r0881 --R --R ---R (414) +--R (4) --R sin(x) --R - sin(x)log(----------) - sin(x)log(cot(x) + 1) --R cos(x) + 1 @@ -43087,7 +42687,7 @@ m0881:= a0881-r0881 d0881:= D(m0881,x) --R --R ---R (415) +--R (5) --R 3 3 3 2 --R (- cot(x) - cot(x))sin(x) + (- cos(x)cot(x) + cos(x))sin(x) --R + @@ -43099,15 +42699,18 @@ d0881:= D(m0881,x) --R Type: Expression(Integer) --E 436 +)clear all + + --S 437 of 526 t0882:= sec(x)^2/(-tan(x)^2+tan(x)^3) --R --R ---R 2 ---R sec(x) ---R (416) ----------------- ---R 3 2 ---R tan(x) - tan(x) +--R 2 +--R sec(x) +--R (1) ----------------- +--R 3 2 +--R tan(x) - tan(x) --R Type: Expression(Integer) --E 437 @@ -43115,7 +42718,7 @@ t0882:= sec(x)^2/(-tan(x)^2+tan(x)^3) r0882:= cot(x)+log(1-cot(x)) --R --R ---R (417) log(- cot(x) + 1) + cot(x) +--R (2) log(- cot(x) + 1) + cot(x) --R Type: Expression(Integer) --E 438 @@ -43123,11 +42726,11 @@ r0882:= cot(x)+log(1-cot(x)) a0882:= integrate(t0882,x) --R --R ---R 2sin(x) - 2cos(x) sin(x) ---R sin(x)log(-----------------) - sin(x)log(----------) + cos(x) ---R cos(x) + 1 cos(x) + 1 ---R (418) ------------------------------------------------------------- ---R sin(x) +--R 2sin(x) - 2cos(x) sin(x) +--R sin(x)log(-----------------) - sin(x)log(----------) + cos(x) +--R cos(x) + 1 cos(x) + 1 +--R (3) ------------------------------------------------------------- +--R sin(x) --R Type: Union(Expression(Integer),...) --E 439 @@ -43135,7 +42738,7 @@ a0882:= integrate(t0882,x) m0882:= a0882-r0882 --R --R ---R (419) +--R (4) --R 2sin(x) - 2cos(x) sin(x) --R sin(x)log(-----------------) - sin(x)log(----------) --R cos(x) + 1 cos(x) + 1 @@ -43150,7 +42753,7 @@ m0882:= a0882-r0882 d0882:= D(m0882,x) --R --R ---R (420) +--R (5) --R 3 3 3 2 --R (cot(x) + cot(x))sin(x) + (- cos(x)cot(x) - cos(x))sin(x) --R + @@ -43162,15 +42765,18 @@ d0882:= D(m0882,x) --R Type: Expression(Integer) --E 441 +)clear all + + --S 442 of 526 t0883:= sec(x)^2/(3-4*tan(x)^3) --R --R ---R 2 ---R sec(x) ---R (421) - ------------ ---R 3 ---R 4tan(x) - 3 +--R 2 +--R sec(x) +--R (1) - ------------ +--R 3 +--R 4tan(x) - 3 --R Type: Expression(Integer) --E 442 @@ -43180,7 +42786,7 @@ r0883:= 1/18*atan(1/6*(6^(1/3)+4*tan(x))*2^(2/3)*3^(1/6))*2^(1/3)*3^(5/6)-_ 2*6^(1/3)*tan(x)+4*tan(x)^2)*6^(1/3) --R --R ---R (422) +--R (2) --R 3+-+ 2 3+-+ 3+-+2 3+-+ 3+-+ --R \|6 log(4tan(x) + 2\|6 tan(x) + \|6 ) - 2\|6 log(- 2tan(x) + \|6 ) --R + @@ -43197,7 +42803,7 @@ r0883:= 1/18*atan(1/6*(6^(1/3)+4*tan(x))*2^(2/3)*3^(1/6))*2^(1/3)*3^(5/6)-_ a0883:= integrate(t0883,x) --R --R ---R (423) +--R (3) --R - --R 3+---+ +-+ --R \|- 1 \|3 @@ -43248,7 +42854,7 @@ a0883:= integrate(t0883,x) m0883:= a0883-r0883 --R --R ---R (424) +--R (4) --R +-+3+-+3+--+ 2 3+-+ 3+-+2 --R - \|3 \|6 \|36 log(4tan(x) + 2\|6 tan(x) + \|6 ) --R + @@ -43310,15 +42916,18 @@ m0883:= a0883-r0883 --d0883:= D(m0883,x) --E 446 +)clear all + + --S 447 of 526 t0884:= sec(x)^2/(1+sec(x)^2-3*tan(x)) --R --R ---R 2 ---R sec(x) ---R (425) - --------------------- ---R 2 ---R 3tan(x) - sec(x) - 1 +--R 2 +--R sec(x) +--R (1) - --------------------- +--R 2 +--R 3tan(x) - sec(x) - 1 --R Type: Expression(Integer) --E 447 @@ -43326,7 +42935,7 @@ t0884:= sec(x)^2/(1+sec(x)^2-3*tan(x)) r0884:= -2*atanh(-3+2*tan(x)) --R --R ---R (426) - 2atanh(2tan(x) - 3) +--R (2) - 2atanh(2tan(x) - 3) --R Type: Expression(Integer) --E 448 @@ -43334,9 +42943,9 @@ r0884:= -2*atanh(-3+2*tan(x)) a0884:= integrate(t0884,x) --R --R ---R 2sin(x) - 2cos(x) sin(x) - 2cos(x) ---R (427) - log(-----------------) + log(----------------) ---R cos(x) + 1 cos(x) + 1 +--R 2sin(x) - 2cos(x) sin(x) - 2cos(x) +--R (3) - log(-----------------) + log(----------------) +--R cos(x) + 1 cos(x) + 1 --R Type: Union(Expression(Integer),...) --E 449 @@ -43344,10 +42953,9 @@ a0884:= integrate(t0884,x) m0884:= a0884-r0884 --R --R ---R (428) ---R 2sin(x) - 2cos(x) sin(x) - 2cos(x) ---R - log(-----------------) + log(----------------) + 2atanh(2tan(x) - 3) ---R cos(x) + 1 cos(x) + 1 +--R 2sin(x) - 2cos(x) sin(x) - 2cos(x) +--R (4) - log(-----------------) + log(----------------) + 2atanh(2tan(x) - 3) +--R cos(x) + 1 cos(x) + 1 --R Type: Expression(Integer) --E 450 @@ -43355,7 +42963,7 @@ m0884:= a0884-r0884 d0884:= D(m0884,x) --R --R ---R (429) +--R (5) --R 2 2 2 2 --R (3cos(x)sin(x) - cos(x) )tan(x) + (- 3sin(x) - 3cos(x) )tan(x) --R + @@ -43373,14 +42981,17 @@ d0884:= D(m0884,x) --R Type: Expression(Integer) --E 451 +)clear all + + --S 452 of 526 t0885:= sec(x)^2*(a+b*tan(x))^2/(c+d*tan(x)) --R --R ---R 2 2 2 2 2 2 ---R b sec(x) tan(x) + 2a b sec(x) tan(x) + a sec(x) ---R (430) ------------------------------------------------- ---R d tan(x) + c +--R 2 2 2 2 2 2 +--R b sec(x) tan(x) + 2a b sec(x) tan(x) + a sec(x) +--R (1) ------------------------------------------------- +--R d tan(x) + c --R Type: Expression(Integer) --E 452 @@ -43389,7 +43000,7 @@ r0885:= (b*c-a*d)^2*log(c+d*tan(x))/d^3-b*(b*c-a*d)*_ tan(x)/d^2+1/2*(a+b*tan(x))^2/d --R --R ---R (431) +--R (2) --R 2 2 2 2 2 2 2 --R (2a d - 4a b c d + 2b c )log(d tan(x) + c) + b d tan(x) --R + @@ -43405,7 +43016,7 @@ r0885:= (b*c-a*d)^2*log(c+d*tan(x))/d^3-b*(b*c-a*d)*_ a0885:= integrate(t0885,x) --R --R ---R (432) +--R (3) --R 2 2 2 2 2 2cos(x) --R (- 2a d + 4a b c d - 2b c )cos(x) log(- ----------) --R cos(x) + 1 @@ -43426,7 +43037,7 @@ a0885:= integrate(t0885,x) m0885:= a0885-r0885 --R --R ---R (433) +--R (4) --R 2 2 2 2 2 --R (- 2a d + 4a b c d - 2b c )cos(x) log(d tan(x) + c) --R + @@ -43453,7 +43064,7 @@ m0885:= a0885-r0885 d0885:= D(m0885,x) --R --R ---R (434) +--R (5) --R 2 2 3 2 4 4 --R (- b d cos(x) sin(x) - b c d cos(x) )tan(x) --R + @@ -43482,11 +43093,14 @@ d0885:= D(m0885,x) --R Type: Expression(Integer) --E 456 +)clear all + + --S 457 of 526 t0886:= sec(x)^2*(a+b*tan(x))^3/(c+d*tan(x)) --R --R ---R (435) +--R (1) --R 3 2 3 2 2 2 2 2 3 2 --R b sec(x) tan(x) + 3a b sec(x) tan(x) + 3a b sec(x) tan(x) + a sec(x) --R ----------------------------------------------------------------------- @@ -43499,7 +43113,7 @@ r0886:= -(b*c-a*d)^3*log(c+d*tan(x))/d^4+b*(b*c-a*d)^2*_ tan(x)/d^3-1/2*(b*c-a*d)*(a+b*tan(x))^2/d^2+1/3*(a+b*tan(x))^3/d --R --R ---R (436) +--R (2) --R 3 3 2 2 2 2 3 3 3 3 3 --R (6a d - 18a b c d + 18a b c d - 6b c )log(d tan(x) + c) + 2b d tan(x) --R + @@ -43518,7 +43132,7 @@ r0886:= -(b*c-a*d)^3*log(c+d*tan(x))/d^4+b*(b*c-a*d)^2*_ a0886:= integrate(t0886,x) --R --R ---R (437) +--R (3) --R 3 3 2 2 2 2 3 3 3 2cos(x) --R (- 6a d + 18a b c d - 18a b c d + 6b c )cos(x) log(- ----------) --R cos(x) + 1 @@ -43545,7 +43159,7 @@ a0886:= integrate(t0886,x) m0886:= a0886-r0886 --R --R ---R (438) +--R (4) --R 3 3 2 2 2 2 3 3 3 --R (- 6a d + 18a b c d - 18a b c d + 6b c )cos(x) log(d tan(x) + c) --R + @@ -43581,7 +43195,7 @@ m0886:= a0886-r0886 d0886:= D(m0886,x) --R --R ---R (439) +--R (5) --R 3 3 4 3 2 5 5 --R (- 3b d cos(x) sin(x) - 3b c d cos(x) )tan(x) --R + @@ -43635,12 +43249,15 @@ d0886:= D(m0886,x) --R Type: Expression(Integer) --E 461 +)clear all + + --S 462 of 526 t0887:= sec(x)^4*(-1+sec(x)^2)^2*tan(x) --R --R ---R 8 6 4 ---R (440) (sec(x) - 2sec(x) + sec(x) )tan(x) +--R 8 6 4 +--R (1) (sec(x) - 2sec(x) + sec(x) )tan(x) --R Type: Expression(Integer) --E 462 @@ -43648,10 +43265,10 @@ t0887:= sec(x)^4*(-1+sec(x)^2)^2*tan(x) r0887:= 1/24*tan(x)^6*(4+3*tan(x)^2) --R --R ---R 8 6 ---R 3tan(x) + 4tan(x) ---R (441) ------------------- ---R 24 +--R 8 6 +--R 3tan(x) + 4tan(x) +--R (2) ------------------- +--R 24 --R Type: Expression(Integer) --E 463 @@ -43659,11 +43276,11 @@ r0887:= 1/24*tan(x)^6*(4+3*tan(x)^2) a0887:= integrate(t0887,x) --R --R ---R 8 4 2 ---R - cos(x) + 6cos(x) - 8cos(x) + 3 ---R (442) ----------------------------------- ---R 8 ---R 24cos(x) +--R 8 4 2 +--R - cos(x) + 6cos(x) - 8cos(x) + 3 +--R (3) ----------------------------------- +--R 8 +--R 24cos(x) --R Type: Union(Expression(Integer),...) --E 464 @@ -43671,7 +43288,7 @@ a0887:= integrate(t0887,x) m0887:= a0887-r0887 --R --R ---R (443) +--R (4) --R 8 8 8 6 8 4 2 --R - 3cos(x) tan(x) - 4cos(x) tan(x) - cos(x) + 6cos(x) - 8cos(x) + 3 --R ----------------------------------------------------------------------- @@ -43684,7 +43301,7 @@ m0887:= a0887-r0887 d0887:= D(m0887,x) --R --R ---R (444) +--R (5) --R 9 9 9 7 9 5 --R - cos(x) tan(x) - 2cos(x) tan(x) - cos(x) tan(x) --R + @@ -43696,12 +43313,15 @@ d0887:= D(m0887,x) --R Type: Expression(Integer) --E 466 +)clear all + + --S 467 of 526 t0888:= tan(x)^n*sec(x)^4 --R --R ---R 4 n ---R (445) sec(x) tan(x) +--R 4 n +--R (1) sec(x) tan(x) --R Type: Expression(Integer) --E 467 @@ -43709,11 +43329,11 @@ t0888:= tan(x)^n*sec(x)^4 r0888:= tan(x)^(1+n)/(1+n)+tan(x)^(3+n)/(3+n) --R --R ---R n + 3 n + 1 ---R (n + 1)tan(x) + (n + 3)tan(x) ---R (446) --------------------------------------- ---R 2 ---R n + 4n + 3 +--R n + 3 n + 1 +--R (n + 1)tan(x) + (n + 3)tan(x) +--R (2) --------------------------------------- +--R 2 +--R n + 4n + 3 --R Type: Expression(Integer) --E 468 @@ -43721,13 +43341,13 @@ r0888:= tan(x)^(1+n)/(1+n)+tan(x)^(3+n)/(3+n) a0888:= integrate(t0888,x) --R --R ---R sin(x) ---R n log(------) ---R 2 cos(x) ---R (2cos(x) + n + 1)sin(x)%e ---R (447) --------------------------------------- ---R 2 3 ---R (n + 4n + 3)cos(x) +--R sin(x) +--R n log(------) +--R 2 cos(x) +--R (2cos(x) + n + 1)sin(x)%e +--R (3) --------------------------------------- +--R 2 3 +--R (n + 4n + 3)cos(x) --R Type: Union(Expression(Integer),...) --E 469 @@ -43735,7 +43355,7 @@ a0888:= integrate(t0888,x) m0888:= a0888-r0888 --R --R ---R (448) +--R (4) --R sin(x) --R n log(------) --R 2 cos(x) 3 n + 3 @@ -43753,7 +43373,7 @@ m0888:= a0888-r0888 d0888:= D(m0888,x) --R --R ---R (449) +--R (5) --R sin(x) --R n log(------) --R 2 2 4 2 cos(x) @@ -43770,16 +43390,19 @@ d0888:= D(m0888,x) --R Type: Expression(Integer) --E 471 +)clear all + + --S 472 of 526 t0889:= sec(x)^2/(4-sec(x)^2)^(1/2) --R --R ---R 2 ---R sec(x) ---R (450) ---------------- ---R +-------------+ ---R | 2 ---R \|- sec(x) + 4 +--R 2 +--R sec(x) +--R (1) ---------------- +--R +-------------+ +--R | 2 +--R \|- sec(x) + 4 --R Type: Expression(Integer) --E 472 @@ -43787,10 +43410,10 @@ t0889:= sec(x)^2/(4-sec(x)^2)^(1/2) r0889:= asin(1/3*tan(x)*3^(1/2)) --R --R ---R +-+ ---R \|3 tan(x) ---R (451) asin(----------) ---R 3 +--R +-+ +--R \|3 tan(x) +--R (2) asin(----------) +--R 3 --R Type: Expression(Integer) --E 473 @@ -43798,19 +43421,19 @@ r0889:= asin(1/3*tan(x)*3^(1/2)) a0889:= integrate(t0889,x) --R --R ---R +---------------------+ ---R | 2 ---R | 16cos(x) - 4 ---R (cos(x) + 1)sin(x) |--------------------- - 4cos(x)sin(x) ---R | 2 ---R \|cos(x) + 2cos(x) + 1 ---R (452) atan(-----------------------------------------------------------) ---R +---------------------+ ---R | 2 ---R 2 | 16cos(x) - 4 2 ---R (2cos(x) + 2cos(x)) |--------------------- - 8cos(x) + 2 ---R | 2 ---R \|cos(x) + 2cos(x) + 1 +--R +---------------------+ +--R | 2 +--R | 16cos(x) - 4 +--R (cos(x) + 1)sin(x) |--------------------- - 4cos(x)sin(x) +--R | 2 +--R \|cos(x) + 2cos(x) + 1 +--R (3) atan(-----------------------------------------------------------) +--R +---------------------+ +--R | 2 +--R 2 | 16cos(x) - 4 2 +--R (2cos(x) + 2cos(x)) |--------------------- - 8cos(x) + 2 +--R | 2 +--R \|cos(x) + 2cos(x) + 1 --R Type: Union(Expression(Integer),...) --E 474 @@ -43818,7 +43441,7 @@ a0889:= integrate(t0889,x) m0889:= a0889-r0889 --R --R ---R (453) +--R (4) --R +---------------------+ --R | 2 --R | 16cos(x) - 4 @@ -43844,7 +43467,7 @@ m0889:= a0889-r0889 d0889:= D(m0889,x) --R --R ---R (454) +--R (5) --R 2 3 2 2 --R ((- cos(x) - 1)sin(x) - 4cos(x) - 4cos(x) + cos(x) + 1)tan(x) --R + @@ -43875,16 +43498,19 @@ d0889:= D(m0889,x) --R Type: Expression(Integer) --E 476 +)clear all + + --S 477 of 526 t0890:= sec(x)^2/(1-4*tan(x)^2)^(1/2) --R --R ---R 2 ---R sec(x) ---R (455) ----------------- ---R +--------------+ ---R | 2 ---R \|- 4tan(x) + 1 +--R 2 +--R sec(x) +--R (1) ----------------- +--R +--------------+ +--R | 2 +--R \|- 4tan(x) + 1 --R Type: Expression(Integer) --E 477 @@ -43892,9 +43518,9 @@ t0890:= sec(x)^2/(1-4*tan(x)^2)^(1/2) r0890:= 1/2*asin(2*tan(x)) --R --R ---R asin(2tan(x)) ---R (456) ------------- ---R 2 +--R asin(2tan(x)) +--R (2) ------------- +--R 2 --R Type: Expression(Integer) --E 478 @@ -43902,7 +43528,7 @@ r0890:= 1/2*asin(2*tan(x)) a0890:= integrate(t0890,x) --R --R ---R (457) +--R (3) --R +---------------------+ --R | 2 --R | 20cos(x) - 16 +-+ @@ -43925,7 +43551,7 @@ a0890:= integrate(t0890,x) m0890:= a0890-r0890 --R --R ---R (458) +--R (4) --R +---------------------+ --R | 2 --R | 20cos(x) - 16 +-+ @@ -43950,7 +43576,7 @@ m0890:= a0890-r0890 d0890:= D(m0890,x) --R --R ---R (459) +--R (5) --R 2 3 2 2 --R ((- 4cos(x) - 4)sin(x) - 5cos(x) - 5cos(x) + 4cos(x) + 4)tan(x) --R + @@ -43980,16 +43606,19 @@ d0890:= D(m0890,x) --R Type: Expression(Integer) --E 481 +)clear all + + --S 482 of 526 t0891:= sec(x)^2/(-4+tan(x)^2)^(1/2) --R --R ---R 2 ---R sec(x) ---R (460) -------------- ---R +-----------+ ---R | 2 ---R \|tan(x) - 4 +--R 2 +--R sec(x) +--R (1) -------------- +--R +-----------+ +--R | 2 +--R \|tan(x) - 4 --R Type: Expression(Integer) --E 482 @@ -43997,9 +43626,9 @@ t0891:= sec(x)^2/(-4+tan(x)^2)^(1/2) r0891:= atanh(cot(x)*(-4+tan(x)^2)^(1/2)) --R --R ---R +-----------+ ---R | 2 ---R (461) atanh(cot(x)\|tan(x) - 4 ) +--R +-----------+ +--R | 2 +--R (2) atanh(cot(x)\|tan(x) - 4 ) --R Type: Expression(Integer) --E 483 @@ -44007,7 +43636,7 @@ r0891:= atanh(cot(x)*(-4+tan(x)^2)^(1/2)) a0891:= integrate(t0891,x) --R --R ---R (462) +--R (3) --R +---------------------+ --R | 2 --R | - 5cos(x) + 1 +-+ 2 @@ -44030,7 +43659,7 @@ a0891:= integrate(t0891,x) m0891:= a0891-r0891 --R --R ---R (463) +--R (4) --R +---------------------+ --R | 2 --R | - 5cos(x) + 1 +-+ 2 @@ -44057,7 +43686,7 @@ m0891:= a0891-r0891 d0891:= D(m0891,x) --R --R ---R (464) +--R (5) --R 2 2 2 --R (- 5cos(x) - 5cos(x))cot(x) sin(x) --R + @@ -44237,13 +43866,16 @@ d0891:= D(m0891,x) --R Type: Expression(Integer) --E 486 +)clear all + + --S 487 of 526 t0892:= sec(x)^2*(1-cot(x)^2)^(1/2) --R --R ---R +-------------+ ---R 2 | 2 ---R (465) sec(x) \|- cot(x) + 1 +--R +-------------+ +--R 2 | 2 +--R (1) sec(x) \|- cot(x) + 1 --R Type: Expression(Integer) --E 487 @@ -44251,9 +43883,9 @@ t0892:= sec(x)^2*(1-cot(x)^2)^(1/2) r0892:= asin(cot(x))+(1-cot(x)^2)^(1/2)*tan(x) --R --R ---R +-------------+ ---R | 2 ---R (466) tan(x)\|- cot(x) + 1 + asin(cot(x)) +--R +-------------+ +--R | 2 +--R (2) tan(x)\|- cot(x) + 1 + asin(cot(x)) --R Type: Expression(Integer) --E 488 @@ -44261,7 +43893,7 @@ r0892:= asin(cot(x))+(1-cot(x)^2)^(1/2)*tan(x) a0892:= integrate(t0892,x) --R --R ---R (467) +--R (3) --R +---------------------+ --R | 2 --R +-+ 2 +-+ | - 8cos(x) + 4 @@ -44311,7 +43943,7 @@ a0892:= integrate(t0892,x) m0892:= a0892-r0892 --R --R ---R (468) +--R (4) --R +---------------------+ --R | 2 --R +-+ 2 +-+ | - 8cos(x) + 4 @@ -44375,7 +44007,7 @@ m0892:= a0892-r0892 d0892:= D(m0892,x) --R --R ---R (469) +--R (5) --R +-+ 5 +-+ 4 +-+ 3 +-+ 2 --R - 32\|2 cos(x) - 32\|2 cos(x) + 40\|2 cos(x) + 40\|2 cos(x) --R + @@ -44558,13 +44190,16 @@ d0892:= D(m0892,x) --R Type: Expression(Integer) --E 491 +)clear all + + --S 492 of 526 t0893:= sec(x)^2*(1-tan(x)^2)^(1/2) --R --R ---R +-------------+ ---R 2 | 2 ---R (470) sec(x) \|- tan(x) + 1 +--R +-------------+ +--R 2 | 2 +--R (1) sec(x) \|- tan(x) + 1 --R Type: Expression(Integer) --E 492 @@ -44572,11 +44207,11 @@ t0893:= sec(x)^2*(1-tan(x)^2)^(1/2) r0893:= 1/2*asin(tan(x))+1/2*tan(x)*(1-tan(x)^2)^(1/2) --R --R ---R +-------------+ ---R | 2 ---R tan(x)\|- tan(x) + 1 + asin(tan(x)) ---R (471) ------------------------------------- ---R 2 +--R +-------------+ +--R | 2 +--R tan(x)\|- tan(x) + 1 + asin(tan(x)) +--R (2) ------------------------------------- +--R 2 --R Type: Expression(Integer) --E 493 @@ -44584,7 +44219,7 @@ r0893:= 1/2*asin(tan(x))+1/2*tan(x)*(1-tan(x)^2)^(1/2) a0893:= integrate(t0893,x) --R --R ---R (472) +--R (3) --R +-+ 6 +-+ 5 +-+ 4 +-+ 3 --R (16\|2 cos(x) + 16\|2 cos(x) - 4\|2 cos(x) - 4\|2 cos(x) ) --R * @@ -44644,7 +44279,7 @@ a0893:= integrate(t0893,x) m0893:= a0893-r0893 --R --R ---R (473) +--R (4) --R +-+ 6 +-+ 5 +-+ 4 +-+ 3 --R (16\|2 cos(x) + 16\|2 cos(x) - 4\|2 cos(x) - 4\|2 cos(x) ) --R * @@ -44723,7 +44358,7 @@ m0893:= a0893-r0893 d0893:= D(m0893,x) --R --R ---R (474) +--R (5) --R +-+ 10 +-+ 9 +-+ 8 --R 1024\|2 cos(x) + 1024\|2 cos(x) - 1792\|2 cos(x) --R + @@ -44926,14 +44561,17 @@ d0893:= D(m0893,x) --R Type: Expression(Integer) --E 496 +)clear all + + --S 497 of 526 t0894:= csc(x)^2/(a+b*cot(x)) --R --R ---R 2 ---R csc(x) ---R (475) ------------ ---R b cot(x) + a +--R 2 +--R csc(x) +--R (1) ------------ +--R b cot(x) + a --R Type: Expression(Integer) --E 497 @@ -44941,9 +44579,9 @@ t0894:= csc(x)^2/(a+b*cot(x)) r0894:= -log(a+b*cot(x))/b --R --R ---R log(b cot(x) + a) ---R (476) - ----------------- ---R b +--R log(b cot(x) + a) +--R (2) - ----------------- +--R b --R Type: Expression(Integer) --E 498 @@ -44951,11 +44589,11 @@ r0894:= -log(a+b*cot(x))/b a0894:= integrate(t0894,x) --R --R ---R sin(x) - 2a sin(x) - 2b cos(x) ---R log(----------) - log(-----------------------) ---R cos(x) + 1 cos(x) + 1 ---R (477) ---------------------------------------------- ---R b +--R sin(x) - 2a sin(x) - 2b cos(x) +--R log(----------) - log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R (3) ---------------------------------------------- +--R b --R Type: Union(Expression(Integer),...) --E 499 @@ -44963,11 +44601,11 @@ a0894:= integrate(t0894,x) m0894:= a0894-r0894 --R --R ---R sin(x) - 2a sin(x) - 2b cos(x) ---R log(----------) + log(b cot(x) + a) - log(-----------------------) ---R cos(x) + 1 cos(x) + 1 ---R (478) ------------------------------------------------------------------ ---R b +--R sin(x) - 2a sin(x) - 2b cos(x) +--R log(----------) + log(b cot(x) + a) - log(-----------------------) +--R cos(x) + 1 cos(x) + 1 +--R (4) ------------------------------------------------------------------ +--R b --R Type: Expression(Integer) --E 500 @@ -44975,7 +44613,7 @@ m0894:= a0894-r0894 d0894:= D(m0894,x) --R --R ---R (479) +--R (5) --R 2 2 2 --R (- a cot(x) + b cot(x))sin(x) + (- b cos(x)cot(x) - b cos(x))sin(x) --R + @@ -44987,12 +44625,15 @@ d0894:= D(m0894,x) --R Type: Expression(Integer) --E 501 +)clear all + + --S 502 of 526 t0895:= csc(x)^2*(a+b*cot(x))^n --R --R ---R 2 n ---R (480) csc(x) (b cot(x) + a) +--R 2 n +--R (1) csc(x) (b cot(x) + a) --R Type: Expression(Integer) --E 502 @@ -45000,10 +44641,10 @@ t0895:= csc(x)^2*(a+b*cot(x))^n r0895:= -(a+b*cot(x))^(1+n)/b/(1+n) --R --R ---R n + 1 ---R (b cot(x) + a) ---R (481) - ------------------- ---R b n + b +--R n + 1 +--R (b cot(x) + a) +--R (2) - ------------------- +--R b n + b --R Type: Expression(Integer) --E 503 @@ -45011,12 +44652,12 @@ r0895:= -(a+b*cot(x))^(1+n)/b/(1+n) a0895:= integrate(t0895,x) --R --R ---R a sin(x) + b cos(x) ---R n log(-------------------) ---R sin(x) ---R (- a sin(x) - b cos(x))%e ---R (482) --------------------------------------------------- ---R (b n + b)sin(x) +--R a sin(x) + b cos(x) +--R n log(-------------------) +--R sin(x) +--R (- a sin(x) - b cos(x))%e +--R (3) --------------------------------------------------- +--R (b n + b)sin(x) --R Type: Union(Expression(Integer),...) --E 504 @@ -45024,7 +44665,7 @@ a0895:= integrate(t0895,x) m0895:= a0895-r0895 --R --R ---R (483) +--R (4) --R a sin(x) + b cos(x) --R n log(-------------------) --R sin(x) @@ -45041,7 +44682,7 @@ m0895:= a0895-r0895 d0895:= D(m0895,x) --R --R ---R (484) +--R (5) --R a sin(x) + b cos(x) --R n log(-------------------) --R 2 2 sin(x) @@ -45055,12 +44696,15 @@ d0895:= D(m0895,x) --R Type: Expression(Integer) --E 506 +)clear all + + --S 507 of 526 t0896:= 2+cot(x)^2 --R --R ---R 2 ---R (485) cot(x) + 2 +--R 2 +--R (1) cot(x) + 2 --R Type: Expression(Integer) --E 507 @@ -45068,7 +44712,7 @@ t0896:= 2+cot(x)^2 r0896:= x-cot(x) --R --R ---R (486) - cot(x) + x +--R (2) - cot(x) + x --R Type: Expression(Integer) --E 508 @@ -45076,9 +44720,9 @@ r0896:= x-cot(x) a0896:= integrate(t0896,x) --R --R ---R x sin(2x) - cos(2x) - 1 ---R (487) ----------------------- ---R sin(2x) +--R x sin(2x) - cos(2x) - 1 +--R (3) ----------------------- +--R sin(2x) --R Type: Union(Expression(Integer),...) --E 509 @@ -45086,9 +44730,9 @@ a0896:= integrate(t0896,x) m0896:= a0896-r0896 --R --R ---R cot(x)sin(2x) - cos(2x) - 1 ---R (488) --------------------------- ---R sin(2x) +--R cot(x)sin(2x) - cos(2x) - 1 +--R (4) --------------------------- +--R sin(2x) --R Type: Expression(Integer) --E 510 @@ -45096,22 +44740,25 @@ m0896:= a0896-r0896 d0896:= D(m0896,x) --R --R ---R 2 2 2 ---R (- cot(x) + 1)sin(2x) + 2cos(2x) + 2cos(2x) ---R (489) ---------------------------------------------- ---R 2 ---R sin(2x) +--R 2 2 2 +--R (- cot(x) + 1)sin(2x) + 2cos(2x) + 2cos(2x) +--R (5) ---------------------------------------------- +--R 2 +--R sin(2x) --R Type: Expression(Integer) --E 511 +)clear all + + --S 512 of 526 t0897:= csc(x)^2*(a+b*cot(x))/(c+d*cot(x)) --R --R ---R 2 ---R (b cot(x) + a)csc(x) ---R (490) --------------------- ---R d cot(x) + c +--R 2 +--R (b cot(x) + a)csc(x) +--R (1) --------------------- +--R d cot(x) + c --R Type: Expression(Integer) --E 512 @@ -45119,10 +44766,10 @@ t0897:= csc(x)^2*(a+b*cot(x))/(c+d*cot(x)) r0897:= -b*cot(x)/d+(b*c-a*d)*log(c+d*cot(x))/d^2 --R --R ---R (- a d + b c)log(d cot(x) + c) - b d cot(x) ---R (491) ------------------------------------------- ---R 2 ---R d +--R (- a d + b c)log(d cot(x) + c) - b d cot(x) +--R (2) ------------------------------------------- +--R 2 +--R d --R Type: Expression(Integer) --E 513 @@ -45130,7 +44777,7 @@ r0897:= -b*cot(x)/d+(b*c-a*d)*log(c+d*cot(x))/d^2 a0897:= integrate(t0897,x) --R --R ---R (492) +--R (3) --R sin(x) --R (a d - b c)sin(x)log(----------) --R cos(x) + 1 @@ -45148,7 +44795,7 @@ a0897:= integrate(t0897,x) m0897:= a0897-r0897 --R --R ---R (493) +--R (4) --R sin(x) --R (a d - b c)sin(x)log(----------) + (a d - b c)sin(x)log(d cot(x) + c) --R cos(x) + 1 @@ -45168,7 +44815,7 @@ m0897:= a0897-r0897 d0897:= D(m0897,x) --R --R ---R (494) +--R (5) --R 3 2 3 --R (- b c cot(x) - a c cot(x) + (a d - b c)cot(x))sin(x) --R + @@ -45183,14 +44830,17 @@ d0897:= D(m0897,x) --R Type: Expression(Integer) --E 516 +)clear all + + --S 517 of 526 t0898:= csc(x)^2*(a+b*cot(x))^2/(c+d*cot(x)) --R --R ---R 2 2 2 2 ---R (b cot(x) + 2a b cot(x) + a )csc(x) ---R (495) ------------------------------------- ---R d cot(x) + c +--R 2 2 2 2 +--R (b cot(x) + 2a b cot(x) + a )csc(x) +--R (1) ------------------------------------- +--R d cot(x) + c --R Type: Expression(Integer) --E 517 @@ -45199,7 +44849,7 @@ r0898:= b*(b*c-a*d)*cot(x)/d^2-1/2*(a+b*cot(x))^2/d-_ (b*c-a*d)^2*log(c+d*cot(x))/d^3 --R --R ---R (496) +--R (2) --R 2 2 2 2 2 2 2 --R (- 2a d + 4a b c d - 2b c )log(d cot(x) + c) - b d cot(x) --R + @@ -45215,7 +44865,7 @@ r0898:= b*(b*c-a*d)*cot(x)/d^2-1/2*(a+b*cot(x))^2/d-_ a0898:= integrate(t0898,x) --R --R ---R (497) +--R (3) --R 2 2 2 2 2 2 2 2 2 --R ((4a d - 8a b c d + 4b c )cos(x) - 4a d + 8a b c d - 4b c ) --R * @@ -45242,7 +44892,7 @@ a0898:= integrate(t0898,x) m0898:= a0898-r0898 --R --R ---R (498) +--R (4) --R 2 2 2 2 2 2 2 2 2 --R ((4a d - 8a b c d + 4b c )cos(x) - 4a d + 8a b c d - 4b c ) --R * @@ -45280,7 +44930,7 @@ m0898:= a0898-r0898 d0898:= D(m0898,x) --R --R ---R (499) +--R (5) --R 2 2 2 2 2 2 2 --R ((2a b c d - b c d)cos(x) + 2a b c d - b c d)cot(x) --R + @@ -45387,14 +45037,17 @@ d0898:= D(m0898,x) --R Type: Expression(Integer) --E 521 +)clear all + + --S 522 of 526 t0899:= csc(x)^2*(a+b*cot(x))^3/(c+d*cot(x)) --R --R ---R 3 3 2 2 2 3 2 ---R (b cot(x) + 3a b cot(x) + 3a b cot(x) + a )csc(x) ---R (500) ---------------------------------------------------- ---R d cot(x) + c +--R 3 3 2 2 2 3 2 +--R (b cot(x) + 3a b cot(x) + 3a b cot(x) + a )csc(x) +--R (1) ---------------------------------------------------- +--R d cot(x) + c --R Type: Expression(Integer) --E 522 @@ -45403,7 +45056,7 @@ r0899:= -b*(b*c-a*d)^2*cot(x)/d^3+1/2*(b*c-a*d)*(a+b*cot(x))^2/d^2-_ 1/3*(a+b*cot(x))^3/d+(b*c-a*d)^3*log(c+d*cot(x))/d^4 --R --R ---R (501) +--R (2) --R 3 3 2 2 2 2 3 3 --R (- 6a d + 18a b c d - 18a b c d + 6b c )log(d cot(x) + c) --R + @@ -45422,7 +45075,7 @@ r0899:= -b*(b*c-a*d)^2*cot(x)/d^3+1/2*(b*c-a*d)*(a+b*cot(x))^2/d^2-_ a0899:= integrate(t0899,x) --R --R ---R (502) +--R (3) --R 3 3 2 2 2 2 3 3 2 3 3 --R (12a d - 36a b c d + 36a b c d - 12b c )cos(x) - 12a d --R + @@ -45461,7 +45114,7 @@ a0899:= integrate(t0899,x) m0899:= a0899-r0899 --R --R ---R (503) +--R (4) --R 3 3 2 2 2 2 3 3 2 3 3 --R (12a d - 36a b c d + 36a b c d - 12b c )cos(x) - 12a d --R + @@ -45527,7 +45180,7 @@ m0899:= a0899-r0899 d0899:= D(m0899,x) --R --R ---R (504) +--R (5) --R 2 2 3 2 2 2 3 3 4 --R ((9a b c d - 3b c d)cos(x)cot(x) + (9a b c d - 3b c )cos(x))sin(x) --R +