Optimal. Leaf size=52 \[ -\frac{375 x^3}{8}-\frac{10425 x^2}{32}-\frac{5695 x}{4}-\frac{144837}{64 (1-2 x)}+\frac{65219}{128 (1-2 x)^2}-\frac{64317}{32} \log (1-2 x) \]
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Rubi [A] time = 0.0269712, antiderivative size = 52, 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, Rules used = {88} \[ -\frac{375 x^3}{8}-\frac{10425 x^2}{32}-\frac{5695 x}{4}-\frac{144837}{64 (1-2 x)}+\frac{65219}{128 (1-2 x)^2}-\frac{64317}{32} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2 (3+5 x)^3}{(1-2 x)^3} \, dx &=\int \left (-\frac{5695}{4}-\frac{10425 x}{16}-\frac{1125 x^2}{8}-\frac{65219}{32 (-1+2 x)^3}-\frac{144837}{32 (-1+2 x)^2}-\frac{64317}{16 (-1+2 x)}\right ) \, dx\\ &=\frac{65219}{128 (1-2 x)^2}-\frac{144837}{64 (1-2 x)}-\frac{5695 x}{4}-\frac{10425 x^2}{32}-\frac{375 x^3}{8}-\frac{64317}{32} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0182344, size = 47, normalized size = 0.9 \[ \frac{1}{32} \left (-\frac{2 \left (3000 x^5+17850 x^4+71020 x^3-137055 x^2+1509 x+15270\right )}{(1-2 x)^2}-64317 \log (1-2 x)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 41, normalized size = 0.8 \begin{align*} -{\frac{375\,{x}^{3}}{8}}-{\frac{10425\,{x}^{2}}{32}}-{\frac{5695\,x}{4}}-{\frac{64317\,\ln \left ( 2\,x-1 \right ) }{32}}+{\frac{65219}{128\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{144837}{128\,x-64}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.31, size = 55, normalized size = 1.06 \begin{align*} -\frac{375}{8} \, x^{3} - \frac{10425}{32} \, x^{2} - \frac{5695}{4} \, x + \frac{847 \,{\left (684 \, x - 265\right )}}{128 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{64317}{32} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.5263, size = 185, normalized size = 3.56 \begin{align*} -\frac{24000 \, x^{5} + 142800 \, x^{4} + 568160 \, x^{3} - 687260 \, x^{2} + 257268 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 397108 \, x + 224455}{128 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.161134, size = 42, normalized size = 0.81 \begin{align*} - \frac{375 x^{3}}{8} - \frac{10425 x^{2}}{32} - \frac{5695 x}{4} + \frac{579348 x - 224455}{512 x^{2} - 512 x + 128} - \frac{64317 \log{\left (2 x - 1 \right )}}{32} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.87369, size = 50, normalized size = 0.96 \begin{align*} -\frac{375}{8} \, x^{3} - \frac{10425}{32} \, x^{2} - \frac{5695}{4} \, x + \frac{847 \,{\left (684 \, x - 265\right )}}{128 \,{\left (2 \, x - 1\right )}^{2}} - \frac{64317}{32} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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