Optimal. Leaf size=45 \[ -\frac{135 x^2}{16}-\frac{1107 x}{16}-\frac{3283}{16 (1-2 x)}+\frac{3773}{64 (1-2 x)^2}-\frac{1071}{8} \log (1-2 x) \]
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Rubi [A] time = 0.0287393, 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} \[ -\frac{135 x^2}{16}-\frac{1107 x}{16}-\frac{3283}{16 (1-2 x)}+\frac{3773}{64 (1-2 x)^2}-\frac{1071}{8} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3 (3+5 x)}{(1-2 x)^3} \, dx &=\int \left (-\frac{1107}{16}-\frac{135 x}{8}-\frac{3773}{16 (-1+2 x)^3}-\frac{3283}{8 (-1+2 x)^2}-\frac{1071}{4 (-1+2 x)}\right ) \, dx\\ &=\frac{3773}{64 (1-2 x)^2}-\frac{3283}{16 (1-2 x)}-\frac{1107 x}{16}-\frac{135 x^2}{16}-\frac{1071}{8} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0136518, size = 46, normalized size = 1.02 \[ -\frac{1080 x^4+7776 x^3-13284 x^2-6220 x+4284 (1-2 x)^2 \log (1-2 x)+3505}{32 (1-2 x)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*} -{\frac{135\,{x}^{2}}{16}}-{\frac{1107\,x}{16}}-{\frac{1071\,\ln \left ( 2\,x-1 \right ) }{8}}+{\frac{3773}{64\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{3283}{32\,x-16}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08979, size = 49, normalized size = 1.09 \begin{align*} -\frac{135}{16} \, x^{2} - \frac{1107}{16} \, x + \frac{49 \,{\left (536 \, x - 191\right )}}{64 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{1071}{8} \, \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 = 1.2883, size = 155, normalized size = 3.44 \begin{align*} -\frac{2160 \, x^{4} + 15552 \, x^{3} - 17172 \, x^{2} + 8568 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 21836 \, x + 9359}{64 \,{\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 = 0.118028, size = 36, normalized size = 0.8 \begin{align*} - \frac{135 x^{2}}{16} - \frac{1107 x}{16} + \frac{26264 x - 9359}{256 x^{2} - 256 x + 64} - \frac{1071 \log{\left (2 x - 1 \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 4.41497, size = 43, normalized size = 0.96 \begin{align*} -\frac{135}{16} \, x^{2} - \frac{1107}{16} \, x + \frac{49 \,{\left (536 \, x - 191\right )}}{64 \,{\left (2 \, x - 1\right )}^{2}} - \frac{1071}{8} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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