Optimal. Leaf size=48 \[ -\frac{81 x^4}{50}-\frac{261 x^3}{125}+\frac{378 x^2}{625}+\frac{5511 x}{3125}-\frac{11}{15625 (5 x+3)}+\frac{26 \log (5 x+3)}{3125} \]
[Out]
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Rubi [A] time = 0.0591258, antiderivative size = 48, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{81 x^4}{50}-\frac{261 x^3}{125}+\frac{378 x^2}{625}+\frac{5511 x}{3125}-\frac{11}{15625 (5 x+3)}+\frac{26 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
[In] Int[((1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x)^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ - \frac{81 x^{4}}{50} - \frac{261 x^{3}}{125} + \frac{26 \log{\left (5 x + 3 \right )}}{3125} + \int \frac{5511}{3125}\, dx + \frac{756 \int x\, dx}{625} - \frac{11}{15625 \left (5 x + 3\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((1-2*x)*(2+3*x)**4/(3+5*x)**2,x)
[Out]
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Mathematica [A] time = 0.0272926, size = 49, normalized size = 1.02 \[ \frac{-50625 x^5-95625 x^4-20250 x^3+66450 x^2+51795 x+52 (5 x+3) \log (5 x+3)+11233}{6250 (5 x+3)} \]
Antiderivative was successfully verified.
[In] Integrate[((1 - 2*x)*(2 + 3*x)^4)/(3 + 5*x)^2,x]
[Out]
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Maple [A] time = 0.009, size = 37, normalized size = 0.8 \[{\frac{5511\,x}{3125}}+{\frac{378\,{x}^{2}}{625}}-{\frac{261\,{x}^{3}}{125}}-{\frac{81\,{x}^{4}}{50}}-{\frac{11}{46875+78125\,x}}+{\frac{26\,\ln \left ( 3+5\,x \right ) }{3125}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((1-2*x)*(2+3*x)^4/(3+5*x)^2,x)
[Out]
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Maxima [A] time = 1.34341, size = 49, normalized size = 1.02 \[ -\frac{81}{50} \, x^{4} - \frac{261}{125} \, x^{3} + \frac{378}{625} \, x^{2} + \frac{5511}{3125} \, x - \frac{11}{15625 \,{\left (5 \, x + 3\right )}} + \frac{26}{3125} \, \log \left (5 \, x + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^4*(2*x - 1)/(5*x + 3)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.213603, size = 63, normalized size = 1.31 \[ -\frac{253125 \, x^{5} + 478125 \, x^{4} + 101250 \, x^{3} - 332250 \, x^{2} - 260 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 165330 \, x + 22}{31250 \,{\left (5 \, x + 3\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^4*(2*x - 1)/(5*x + 3)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.224754, size = 41, normalized size = 0.85 \[ - \frac{81 x^{4}}{50} - \frac{261 x^{3}}{125} + \frac{378 x^{2}}{625} + \frac{5511 x}{3125} + \frac{26 \log{\left (5 x + 3 \right )}}{3125} - \frac{11}{78125 x + 46875} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((1-2*x)*(2+3*x)**4/(3+5*x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.212437, size = 89, normalized size = 1.85 \[ \frac{3}{31250} \,{\left (5 \, x + 3\right )}^{4}{\left (\frac{150}{5 \, x + 3} + \frac{360}{{\left (5 \, x + 3\right )}^{2}} + \frac{380}{{\left (5 \, x + 3\right )}^{3}} - 27\right )} - \frac{11}{15625 \,{\left (5 \, x + 3\right )}} - \frac{26}{3125} \,{\rm ln}\left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(-(3*x + 2)^4*(2*x - 1)/(5*x + 3)^2,x, algorithm="giac")
[Out]