Optimal. Leaf size=80 \[ -\frac{6561 x^4}{800}-\frac{123201 x^3}{2000}-\frac{4863159 x^2}{20000}-\frac{81001863 x}{100000}-\frac{79883671}{85184 (1-2 x)}-\frac{1}{20796875 (5 x+3)}+\frac{5764801}{30976 (1-2 x)^2}-\frac{1845559863 \log (1-2 x)}{1874048}+\frac{54 \log (5 x+3)}{45753125} \]
[Out]
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Rubi [A] time = 0.0973772, antiderivative size = 80, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045 \[ -\frac{6561 x^4}{800}-\frac{123201 x^3}{2000}-\frac{4863159 x^2}{20000}-\frac{81001863 x}{100000}-\frac{79883671}{85184 (1-2 x)}-\frac{1}{20796875 (5 x+3)}+\frac{5764801}{30976 (1-2 x)^2}-\frac{1845559863 \log (1-2 x)}{1874048}+\frac{54 \log (5 x+3)}{45753125} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^8/((1 - 2*x)^3*(3 + 5*x)^2),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{6561 x^{4}}{800} - \frac{123201 x^{3}}{2000} - \frac{1845559863 \log{\left (- 2 x + 1 \right )}}{1874048} + \frac{54 \log{\left (5 x + 3 \right )}}{45753125} + \int \left (- \frac{81001863}{100000}\right )\, dx - \frac{4863159 \int x\, dx}{10000} - \frac{1}{20796875 \left (5 x + 3\right )} - \frac{79883671}{85184 \left (- 2 x + 1\right )} + \frac{5764801}{30976 \left (- 2 x + 1\right )^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**8/(1-2*x)**3/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0947457, size = 98, normalized size = 1.22 \[ -\frac{81}{800} (3 x+2)^4-\frac{2943 (3 x+2)^3}{2000}-\frac{315171 (3 x+2)^2}{20000}-\frac{18607401 (3 x+2)}{100000}+\frac{79883671}{85184 (2 x-1)}-\frac{1}{20796875 (5 x+3)}+\frac{5764801}{30976 (1-2 x)^2}-\frac{1845559863 \log (3-6 x)}{1874048}+\frac{54 \log (-3 (5 x+3))}{45753125} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^8/((1 - 2*x)^3*(3 + 5*x)^2),x]
[Out]
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Maple [A] time = 0.017, size = 63, normalized size = 0.8 \[ -{\frac{6561\,{x}^{4}}{800}}-{\frac{123201\,{x}^{3}}{2000}}-{\frac{4863159\,{x}^{2}}{20000}}-{\frac{81001863\,x}{100000}}-{\frac{1}{62390625+103984375\,x}}+{\frac{54\,\ln \left ( 3+5\,x \right ) }{45753125}}+{\frac{5764801}{30976\, \left ( -1+2\,x \right ) ^{2}}}+{\frac{79883671}{-85184+170368\,x}}-{\frac{1845559863\,\ln \left ( -1+2\,x \right ) }{1874048}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^8/(1-2*x)^3/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.35692, size = 86, normalized size = 1.08 \[ -\frac{6561}{800} \, x^{4} - \frac{123201}{2000} \, x^{3} - \frac{4863159}{20000} \, x^{2} - \frac{81001863}{100000} \, x + \frac{49927294373976 \, x^{2} + 9946855297899 \, x - 12005712797131}{5324000000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac{54}{45753125} \, \log \left (5 \, x + 3\right ) - \frac{1845559863}{1874048} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^8/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21127, size = 135, normalized size = 1.69 \[ -\frac{9605960100000 \, x^{7} + 68309049600000 \, x^{6} + 252583384185000 \, x^{5} + 811024095717000 \, x^{4} - 468362848619160 \, x^{3} - 838544848893576 \, x^{2} - 69120 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 57673745718750 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) + 32898384865071 \, x + 132062840768441}{58564000000 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^8/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.543379, size = 70, normalized size = 0.88 \[ - \frac{6561 x^{4}}{800} - \frac{123201 x^{3}}{2000} - \frac{4863159 x^{2}}{20000} - \frac{81001863 x}{100000} + \frac{49927294373976 x^{2} + 9946855297899 x - 12005712797131}{106480000000 x^{3} - 42592000000 x^{2} - 37268000000 x + 15972000000} - \frac{1845559863 \log{\left (x - \frac{1}{2} \right )}}{1874048} + \frac{54 \log{\left (x + \frac{3}{5} \right )}}{45753125} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**8/(1-2*x)**3/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.214802, size = 151, normalized size = 1.89 \[ -\frac{{\left (5 \, x + 3\right )}^{4}{\left (\frac{11185606872}{5 \, x + 3} + \frac{158583727962}{{\left (5 \, x + 3\right )}^{2}} + \frac{3495217526460}{{\left (5 \, x + 3\right )}^{3}} - \frac{86510680819405}{{\left (5 \, x + 3\right )}^{4}} + \frac{317205578854725}{{\left (5 \, x + 3\right )}^{5}} + 768476808\right )}}{14641000000 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}} - \frac{1}{20796875 \,{\left (5 \, x + 3\right )}} + \frac{393919443}{400000} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) - \frac{1845559863}{1874048} \,{\rm ln}\left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^8/((5*x + 3)^2*(2*x - 1)^3),x, algorithm="giac")
[Out]