Optimal. Leaf size=32 \[ \frac{121}{28 (1-2 x)}+\frac{407}{196} \log (1-2 x)+\frac{1}{147} \log (3 x+2) \]
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Rubi [A] time = 0.0141535, antiderivative size = 32, 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} \[ \frac{121}{28 (1-2 x)}+\frac{407}{196} \log (1-2 x)+\frac{1}{147} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^2}{(1-2 x)^2 (2+3 x)} \, dx &=\int \left (\frac{121}{14 (-1+2 x)^2}+\frac{407}{98 (-1+2 x)}+\frac{1}{49 (2+3 x)}\right ) \, dx\\ &=\frac{121}{28 (1-2 x)}+\frac{407}{196} \log (1-2 x)+\frac{1}{147} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0141993, size = 40, normalized size = 1.25 \[ -\frac{363}{28 (2 (3 x+2)-7)}+\frac{1}{147} \log (3 x+2)+\frac{407}{196} \log (7-2 (3 x+2)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 27, normalized size = 0.8 \begin{align*} -{\frac{121}{56\,x-28}}+{\frac{407\,\ln \left ( 2\,x-1 \right ) }{196}}+{\frac{\ln \left ( 2+3\,x \right ) }{147}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12048, size = 35, normalized size = 1.09 \begin{align*} -\frac{121}{28 \,{\left (2 \, x - 1\right )}} + \frac{1}{147} \, \log \left (3 \, x + 2\right ) + \frac{407}{196} \, \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 = 1.22879, size = 109, normalized size = 3.41 \begin{align*} \frac{4 \,{\left (2 \, x - 1\right )} \log \left (3 \, x + 2\right ) + 1221 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 2541}{588 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.13524, size = 24, normalized size = 0.75 \begin{align*} \frac{407 \log{\left (x - \frac{1}{2} \right )}}{196} + \frac{\log{\left (x + \frac{2}{3} \right )}}{147} - \frac{121}{56 x - 28} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.28602, size = 58, normalized size = 1.81 \begin{align*} -\frac{121}{28 \,{\left (2 \, x - 1\right )}} - \frac{25}{12} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{1}{147} \, \log \left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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