Optimal. Leaf size=26 \[ -\frac{25 x}{6}-\frac{121}{28} \log (1-2 x)+\frac{1}{63} \log (3 x+2) \]
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Rubi [A] time = 0.0127887, antiderivative size = 26, 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 = {72} \[ -\frac{25 x}{6}-\frac{121}{28} \log (1-2 x)+\frac{1}{63} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin{align*} \int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)} \, dx &=\int \left (-\frac{25}{6}-\frac{121}{14 (-1+2 x)}+\frac{1}{21 (2+3 x)}\right ) \, dx\\ &=-\frac{25 x}{6}-\frac{121}{28} \log (1-2 x)+\frac{1}{63} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0122791, size = 32, normalized size = 1.23 \[ -\frac{5}{6} (5 x+3)-\frac{121}{28} \log (5-10 x)+\frac{1}{63} \log (5 (3 x+2)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 21, normalized size = 0.8 \begin{align*} -{\frac{25\,x}{6}}-{\frac{121\,\ln \left ( 2\,x-1 \right ) }{28}}+{\frac{\ln \left ( 2+3\,x \right ) }{63}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.36591, size = 27, normalized size = 1.04 \begin{align*} -\frac{25}{6} \, x + \frac{1}{63} \, \log \left (3 \, x + 2\right ) - \frac{121}{28} \, \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 = 1.29075, size = 69, normalized size = 2.65 \begin{align*} -\frac{25}{6} \, x + \frac{1}{63} \, \log \left (3 \, x + 2\right ) - \frac{121}{28} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.116808, size = 22, normalized size = 0.85 \begin{align*} - \frac{25 x}{6} - \frac{121 \log{\left (x - \frac{1}{2} \right )}}{28} + \frac{\log{\left (x + \frac{2}{3} \right )}}{63} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.50511, size = 30, normalized size = 1.15 \begin{align*} -\frac{25}{6} \, x + \frac{1}{63} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{121}{28} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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