Optimal. Leaf size=45 \[ -\frac{27 x^2}{125}+\frac{81 x}{625}-\frac{97}{3125 (5 x+3)}-\frac{11}{6250 (5 x+3)^2}+\frac{279 \log (5 x+3)}{3125} \]
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Rubi [A] time = 0.0203152, antiderivative size = 45, 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, Rules used = {77} \[ -\frac{27 x^2}{125}+\frac{81 x}{625}-\frac{97}{3125 (5 x+3)}-\frac{11}{6250 (5 x+3)^2}+\frac{279 \log (5 x+3)}{3125} \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (2+3 x)^3}{(3+5 x)^3} \, dx &=\int \left (\frac{81}{625}-\frac{54 x}{125}+\frac{11}{625 (3+5 x)^3}+\frac{97}{625 (3+5 x)^2}+\frac{279}{625 (3+5 x)}\right ) \, dx\\ &=\frac{81 x}{625}-\frac{27 x^2}{125}-\frac{11}{6250 (3+5 x)^2}-\frac{97}{3125 (3+5 x)}+\frac{279 \log (3+5 x)}{3125}\\ \end{align*}
Mathematica [A] time = 0.0144965, size = 48, normalized size = 1.07 \[ \frac{-33750 x^4-20250 x^3+40650 x^2+40520 x+558 (5 x+3)^2 \log (-3 (5 x+3))+9667}{6250 (5 x+3)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 36, normalized size = 0.8 \begin{align*}{\frac{81\,x}{625}}-{\frac{27\,{x}^{2}}{125}}-{\frac{11}{6250\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{97}{9375+15625\,x}}+{\frac{279\,\ln \left ( 3+5\,x \right ) }{3125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0455, size = 49, normalized size = 1.09 \begin{align*} -\frac{27}{125} \, x^{2} + \frac{81}{625} \, x - \frac{970 \, x + 593}{6250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac{279}{3125} \, \log \left (5 \, x + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.51482, size = 161, normalized size = 3.58 \begin{align*} -\frac{33750 \, x^{4} + 20250 \, x^{3} - 12150 \, x^{2} - 558 \,{\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 6320 \, x + 593}{6250 \,{\left (25 \, x^{2} + 30 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.117339, size = 36, normalized size = 0.8 \begin{align*} - \frac{27 x^{2}}{125} + \frac{81 x}{625} - \frac{970 x + 593}{156250 x^{2} + 187500 x + 56250} + \frac{279 \log{\left (5 x + 3 \right )}}{3125} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.05293, size = 43, normalized size = 0.96 \begin{align*} -\frac{27}{125} \, x^{2} + \frac{81}{625} \, x - \frac{970 \, x + 593}{6250 \,{\left (5 \, x + 3\right )}^{2}} + \frac{279}{3125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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