Optimal. Leaf size=50 \[ -\frac{135 x^3}{8}-\frac{3861 x^2}{32}-540 x-\frac{57281}{64 (1-2 x)}+\frac{26411}{128 (1-2 x)^2}-\frac{24843}{32} \log (1-2 x) \]
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Rubi [A] time = 0.0244445, antiderivative size = 50, 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} \[ -\frac{135 x^3}{8}-\frac{3861 x^2}{32}-540 x-\frac{57281}{64 (1-2 x)}+\frac{26411}{128 (1-2 x)^2}-\frac{24843}{32} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^4 (3+5 x)}{(1-2 x)^3} \, dx &=\int \left (-540-\frac{3861 x}{16}-\frac{405 x^2}{8}-\frac{26411}{32 (-1+2 x)^3}-\frac{57281}{32 (-1+2 x)^2}-\frac{24843}{16 (-1+2 x)}\right ) \, dx\\ &=\frac{26411}{128 (1-2 x)^2}-\frac{57281}{64 (1-2 x)}-540 x-\frac{3861 x^2}{32}-\frac{135 x^3}{8}-\frac{24843}{32} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0150803, size = 51, normalized size = 1.02 \[ -\frac{2160 x^5+13284 x^4+54216 x^3-103950 x^2-1310 x+24843 (1-2 x)^2 \log (1-2 x)+12365}{32 (1-2 x)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 41, normalized size = 0.8 \begin{align*} -{\frac{135\,{x}^{3}}{8}}-{\frac{3861\,{x}^{2}}{32}}-540\,x-{\frac{24843\,\ln \left ( 2\,x-1 \right ) }{32}}+{\frac{26411}{128\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{57281}{128\,x-64}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.15089, size = 55, normalized size = 1.1 \begin{align*} -\frac{135}{8} \, x^{3} - \frac{3861}{32} \, x^{2} - 540 \, x + \frac{343 \,{\left (668 \, x - 257\right )}}{128 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{24843}{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 = 1.29251, size = 180, normalized size = 3.6 \begin{align*} -\frac{8640 \, x^{5} + 53136 \, x^{4} + 216864 \, x^{3} - 261036 \, x^{2} + 99372 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 160004 \, x + 88151}{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 = 0.122987, size = 41, normalized size = 0.82 \begin{align*} - \frac{135 x^{3}}{8} - \frac{3861 x^{2}}{32} - 540 x + \frac{229124 x - 88151}{512 x^{2} - 512 x + 128} - \frac{24843 \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 = 1.72152, size = 50, normalized size = 1. \begin{align*} -\frac{135}{8} \, x^{3} - \frac{3861}{32} \, x^{2} - 540 \, x + \frac{343 \,{\left (668 \, x - 257\right )}}{128 \,{\left (2 \, x - 1\right )}^{2}} - \frac{24843}{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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