Optimal. Leaf size=34 \[ -\frac{9 x^2}{25}+\frac{33 x}{125}-\frac{11}{625 (5 x+3)}+\frac{64}{625} \log (5 x+3) \]
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Rubi [A] time = 0.0148097, antiderivative size = 34, 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} \[ -\frac{9 x^2}{25}+\frac{33 x}{125}-\frac{11}{625 (5 x+3)}+\frac{64}{625} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (2+3 x)^2}{(3+5 x)^2} \, dx &=\int \left (\frac{33}{125}-\frac{18 x}{25}+\frac{11}{125 (3+5 x)^2}+\frac{64}{125 (3+5 x)}\right ) \, dx\\ &=\frac{33 x}{125}-\frac{9 x^2}{25}-\frac{11}{625 (3+5 x)}+\frac{64}{625} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0136871, size = 41, normalized size = 1.21 \[ \frac{-1125 x^3+150 x^2+1545 x+64 (5 x+3) \log (-3 (5 x+3))+619}{625 (5 x+3)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 27, normalized size = 0.8 \begin{align*}{\frac{33\,x}{125}}-{\frac{9\,{x}^{2}}{25}}-{\frac{11}{1875+3125\,x}}+{\frac{64\,\ln \left ( 3+5\,x \right ) }{625}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.994804, size = 35, normalized size = 1.03 \begin{align*} -\frac{9}{25} \, x^{2} + \frac{33}{125} \, x - \frac{11}{625 \,{\left (5 \, x + 3\right )}} + \frac{64}{625} \, \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 = 1.46311, size = 108, normalized size = 3.18 \begin{align*} -\frac{1125 \, x^{3} - 150 \, x^{2} - 64 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 495 \, x + 11}{625 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.096639, size = 27, normalized size = 0.79 \begin{align*} - \frac{9 x^{2}}{25} + \frac{33 x}{125} + \frac{64 \log{\left (5 x + 3 \right )}}{625} - \frac{11}{3125 x + 1875} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.24429, size = 65, normalized size = 1.91 \begin{align*} \frac{3}{625} \,{\left (5 \, x + 3\right )}^{2}{\left (\frac{29}{5 \, x + 3} - 3\right )} - \frac{11}{625 \,{\left (5 \, x + 3\right )}} - \frac{64}{625} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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