Optimal. Leaf size=80 \[ \frac{6561 x^4}{2000}+\frac{12393 x^3}{625}+\frac{6093711 x^2}{100000}+\frac{7680987 x}{50000}+\frac{5764801}{85184 (1-2 x)}-\frac{268}{103984375 (5 x+3)}-\frac{1}{18906250 (5 x+3)^2}+\frac{130943337 \log (1-2 x)}{937024}+\frac{6312 \log (5 x+3)}{228765625} \]
[Out]
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Rubi [A] time = 0.0972569, 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 \[ \frac{6561 x^4}{2000}+\frac{12393 x^3}{625}+\frac{6093711 x^2}{100000}+\frac{7680987 x}{50000}+\frac{5764801}{85184 (1-2 x)}-\frac{268}{103984375 (5 x+3)}-\frac{1}{18906250 (5 x+3)^2}+\frac{130943337 \log (1-2 x)}{937024}+\frac{6312 \log (5 x+3)}{228765625} \]
Antiderivative was successfully verified.
[In] Int[(2 + 3*x)^8/((1 - 2*x)^2*(3 + 5*x)^3),x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{6561 x^{4}}{2000} + \frac{12393 x^{3}}{625} + \frac{130943337 \log{\left (- 2 x + 1 \right )}}{937024} + \frac{6312 \log{\left (5 x + 3 \right )}}{228765625} + \int \frac{7680987}{50000}\, dx + \frac{6093711 \int x\, dx}{50000} - \frac{268}{103984375 \left (5 x + 3\right )} - \frac{1}{18906250 \left (5 x + 3\right )^{2}} + \frac{5764801}{85184 \left (- 2 x + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((2+3*x)**8/(1-2*x)**2/(3+5*x)**3,x)
[Out]
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Mathematica [A] time = 0.185819, size = 74, normalized size = 0.92 \[ \frac{3 \left (\frac{11}{3} \left (21831727500 x^4+131960664000 x^3+405536467050 x^2+1022339369700 x+\frac{450375078125}{1-2 x}-\frac{17152}{5 x+3}-\frac{352}{(5 x+3)^2}+536108166000\right )+3409982734375 \log (3-6 x)+673280 \log (-3 (5 x+3))\right )}{73205000000} \]
Antiderivative was successfully verified.
[In] Integrate[(2 + 3*x)^8/((1 - 2*x)^2*(3 + 5*x)^3),x]
[Out]
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Maple [A] time = 0.016, size = 63, normalized size = 0.8 \[{\frac{6561\,{x}^{4}}{2000}}+{\frac{12393\,{x}^{3}}{625}}+{\frac{6093711\,{x}^{2}}{100000}}+{\frac{7680987\,x}{50000}}-{\frac{1}{18906250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{268}{311953125+519921875\,x}}+{\frac{6312\,\ln \left ( 3+5\,x \right ) }{228765625}}-{\frac{5764801}{-85184+170368\,x}}+{\frac{130943337\,\ln \left ( -1+2\,x \right ) }{937024}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((2+3*x)^8/(1-2*x)^2/(3+5*x)^3,x)
[Out]
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Maxima [A] time = 1.3487, size = 86, normalized size = 1.08 \[ \frac{6561}{2000} \, x^{4} + \frac{12393}{625} \, x^{3} + \frac{6093711}{100000} \, x^{2} + \frac{7680987}{50000} \, x - \frac{11259377124645 \, x^{2} + 13511252361606 \, x + 4053375651317}{6655000000 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} + \frac{6312}{228765625} \, \log \left (5 \, x + 3\right ) + \frac{130943337}{937024} \, \log \left (2 \, x - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^8/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.223982, size = 135, normalized size = 1.69 \[ \frac{12007450125000 \, x^{7} + 80983580287500 \, x^{6} + 270968124487500 \, x^{5} + 698838044478750 \, x^{4} + 327005737947900 \, x^{3} - 298950055409445 \, x^{2} + 2019840 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (5 \, x + 3\right ) + 10229948203125 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )} \log \left (2 \, x - 1\right ) - 249835373577966 \, x - 44587132164487}{73205000000 \,{\left (50 \, x^{3} + 35 \, x^{2} - 12 \, x - 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^8/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.490636, size = 70, normalized size = 0.88 \[ \frac{6561 x^{4}}{2000} + \frac{12393 x^{3}}{625} + \frac{6093711 x^{2}}{100000} + \frac{7680987 x}{50000} - \frac{11259377124645 x^{2} + 13511252361606 x + 4053375651317}{332750000000 x^{3} + 232925000000 x^{2} - 79860000000 x - 59895000000} + \frac{130943337 \log{\left (x - \frac{1}{2} \right )}}{937024} + \frac{6312 \log{\left (x + \frac{3}{5} \right )}}{228765625} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((2+3*x)**8/(1-2*x)**2/(3+5*x)**3,x)
[Out]
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GIAC/XCAS [A] time = 0.208206, size = 151, normalized size = 1.89 \[ \frac{{\left (2 \, x - 1\right )}^{4}{\left (\frac{1230096557250}{2 \, x - 1} + \frac{11539159570125}{{\left (2 \, x - 1\right )}^{2}} + \frac{69299175042900}{{\left (2 \, x - 1\right )}^{3}} + \frac{182728002843460}{{\left (2 \, x - 1\right )}^{4}} + \frac{163740919200408}{{\left (2 \, x - 1\right )}^{5}} + 60037250625\right )}}{11712800000 \,{\left (\frac{11}{2 \, x - 1} + 5\right )}^{2}} - \frac{5764801}{85184 \,{\left (2 \, x - 1\right )}} - \frac{139743873}{1000000} \,{\rm ln}\left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{6312}{228765625} \,{\rm ln}\left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((3*x + 2)^8/((5*x + 3)^3*(2*x - 1)^2),x, algorithm="giac")
[Out]