Optimal. Leaf size=52 \[ -\frac{225 x^3}{8}-\frac{6345 x^2}{32}-\frac{14031 x}{16}-\frac{91091}{64 (1-2 x)}+\frac{41503}{128 (1-2 x)^2}-\frac{39977}{32} \log (1-2 x) \]
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Rubi [A] time = 0.0245302, 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} \[ -\frac{225 x^3}{8}-\frac{6345 x^2}{32}-\frac{14031 x}{16}-\frac{91091}{64 (1-2 x)}+\frac{41503}{128 (1-2 x)^2}-\frac{39977}{32} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3 (3+5 x)^2}{(1-2 x)^3} \, dx &=\int \left (-\frac{14031}{16}-\frac{6345 x}{16}-\frac{675 x^2}{8}-\frac{41503}{32 (-1+2 x)^3}-\frac{91091}{32 (-1+2 x)^2}-\frac{39977}{16 (-1+2 x)}\right ) \, dx\\ &=\frac{41503}{128 (1-2 x)^2}-\frac{91091}{64 (1-2 x)}-\frac{14031 x}{16}-\frac{6345 x^2}{32}-\frac{225 x^3}{8}-\frac{39977}{32} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.018941, size = 47, normalized size = 0.9 \[ \frac{1}{32} \left (-\frac{2 \left (1800 x^5+10890 x^4+43884 x^3-84411 x^2-55 x+9720\right )}{(1-2 x)^2}-39977 \log (1-2 x)\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 41, normalized size = 0.8 \begin{align*} -{\frac{225\,{x}^{3}}{8}}-{\frac{6345\,{x}^{2}}{32}}-{\frac{14031\,x}{16}}-{\frac{39977\,\ln \left ( 2\,x-1 \right ) }{32}}+{\frac{41503}{128\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{91091}{128\,x-64}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.05119, size = 55, normalized size = 1.06 \begin{align*} -\frac{225}{8} \, x^{3} - \frac{6345}{32} \, x^{2} - \frac{14031}{16} \, x + \frac{539 \,{\left (676 \, x - 261\right )}}{128 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{39977}{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 = 1.5715, size = 184, normalized size = 3.54 \begin{align*} -\frac{14400 \, x^{5} + 87120 \, x^{4} + 351072 \, x^{3} - 423612 \, x^{2} + 159908 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 252116 \, x + 140679}{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 = 0.12925, size = 42, normalized size = 0.81 \begin{align*} - \frac{225 x^{3}}{8} - \frac{6345 x^{2}}{32} - \frac{14031 x}{16} + \frac{364364 x - 140679}{512 x^{2} - 512 x + 128} - \frac{39977 \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 = 3.88145, size = 50, normalized size = 0.96 \begin{align*} -\frac{225}{8} \, x^{3} - \frac{6345}{32} \, x^{2} - \frac{14031}{16} \, x + \frac{539 \,{\left (676 \, x - 261\right )}}{128 \,{\left (2 \, x - 1\right )}^{2}} - \frac{39977}{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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