Optimal. Leaf size=33 \[ -\frac{17}{2 (1-2 x)}+\frac{77}{16 (1-2 x)^2}-\frac{15}{8} \log (1-2 x) \]
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Rubi [A] time = 0.022907, antiderivative size = 33, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ -\frac{17}{2 (1-2 x)}+\frac{77}{16 (1-2 x)^2}-\frac{15}{8} \log (1-2 x) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(2+3 x) (3+5 x)}{(1-2 x)^3} \, dx &=\int \left (-\frac{77}{4 (-1+2 x)^3}-\frac{17}{(-1+2 x)^2}-\frac{15}{4 (-1+2 x)}\right ) \, dx\\ &=\frac{77}{16 (1-2 x)^2}-\frac{17}{2 (1-2 x)}-\frac{15}{8} \log (1-2 x)\\ \end{align*}
Mathematica [A] time = 0.0064193, size = 33, normalized size = 1. \[ -\frac{17}{2 (1-2 x)}+\frac{77}{16 (1-2 x)^2}-\frac{15}{8} \log (1-2 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 28, normalized size = 0.9 \begin{align*} -{\frac{15\,\ln \left ( 2\,x-1 \right ) }{8}}+{\frac{77}{16\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{17}{4\,x-2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.13722, size = 38, normalized size = 1.15 \begin{align*} \frac{272 \, x - 59}{16 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} - \frac{15}{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 = 1.27778, size = 100, normalized size = 3.03 \begin{align*} -\frac{30 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) - 272 \, x + 59}{16 \,{\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 = 0.109109, size = 24, normalized size = 0.73 \begin{align*} \frac{272 x - 59}{64 x^{2} - 64 x + 16} - \frac{15 \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 = 3.27684, size = 32, normalized size = 0.97 \begin{align*} \frac{272 \, x - 59}{16 \,{\left (2 \, x - 1\right )}^{2}} - \frac{15}{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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