Optimal. Leaf size=32 \[ -\frac{9}{32 (1-2 x)}+\frac{41}{128} \log (1-2 x)-\frac{25}{128} \log (2 x+3) \]
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Rubi [A] time = 0.0258633, antiderivative size = 32, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043, Rules used = {893} \[ -\frac{9}{32 (1-2 x)}+\frac{41}{128} \log (1-2 x)-\frac{25}{128} \log (2 x+3) \]
Antiderivative was successfully verified.
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Rule 893
Rubi steps
\begin{align*} \int \frac{-4+3 x+x^2}{(-1+2 x)^2 (3+2 x)} \, dx &=\int \left (-\frac{9}{16 (-1+2 x)^2}+\frac{41}{64 (-1+2 x)}-\frac{25}{64 (3+2 x)}\right ) \, dx\\ &=-\frac{9}{32 (1-2 x)}+\frac{41}{128} \log (1-2 x)-\frac{25}{128} \log (3+2 x)\\ \end{align*}
Mathematica [A] time = 0.0154008, size = 32, normalized size = 1. \[ \frac{9}{32 (2 x-1)}+\frac{41}{128} \log (1-2 x)-\frac{25}{128} \log (2 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 27, normalized size = 0.8 \begin{align*} -{\frac{25\,\ln \left ( 3+2\,x \right ) }{128}}+{\frac{9}{64\,x-32}}+{\frac{41\,\ln \left ( 2\,x-1 \right ) }{128}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.92048, size = 35, normalized size = 1.09 \begin{align*} \frac{9}{32 \,{\left (2 \, x - 1\right )}} - \frac{25}{128} \, \log \left (2 \, x + 3\right ) + \frac{41}{128} \, \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 = 1.83746, size = 107, normalized size = 3.34 \begin{align*} -\frac{25 \,{\left (2 \, x - 1\right )} \log \left (2 \, x + 3\right ) - 41 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 36}{128 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.12268, size = 26, normalized size = 0.81 \begin{align*} \frac{41 \log{\left (x - \frac{1}{2} \right )}}{128} - \frac{25 \log{\left (x + \frac{3}{2} \right )}}{128} + \frac{9}{64 x - 32} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06433, size = 58, normalized size = 1.81 \begin{align*} \frac{9}{32 \,{\left (2 \, x - 1\right )}} - \frac{1}{8} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) - \frac{25}{128} \, \log \left ({\left | -\frac{4}{2 \, x - 1} - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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