Optimal. Leaf size=26 \[ \frac{4 x}{15}-\frac{49}{9} \log (3 x+2)+\frac{121}{25} \log (5 x+3) \]
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Rubi [A] time = 0.0121358, 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} \[ \frac{4 x}{15}-\frac{49}{9} \log (3 x+2)+\frac{121}{25} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{(2+3 x) (3+5 x)} \, dx &=\int \left (\frac{4}{15}-\frac{49}{3 (2+3 x)}+\frac{121}{5 (3+5 x)}\right ) \, dx\\ &=\frac{4 x}{15}-\frac{49}{9} \log (2+3 x)+\frac{121}{25} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0090238, size = 27, normalized size = 1.04 \[ \frac{1}{225} (60 x-1225 \log (3 x+2)+1089 \log (-3 (5 x+3))+40) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 21, normalized size = 0.8 \begin{align*}{\frac{4\,x}{15}}-{\frac{49\,\ln \left ( 2+3\,x \right ) }{9}}+{\frac{121\,\ln \left ( 3+5\,x \right ) }{25}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.01823, size = 27, normalized size = 1.04 \begin{align*} \frac{4}{15} \, x + \frac{121}{25} \, \log \left (5 \, x + 3\right ) - \frac{49}{9} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45382, size = 68, normalized size = 2.62 \begin{align*} \frac{4}{15} \, x + \frac{121}{25} \, \log \left (5 \, x + 3\right ) - \frac{49}{9} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.111508, size = 24, normalized size = 0.92 \begin{align*} \frac{4 x}{15} + \frac{121 \log{\left (x + \frac{3}{5} \right )}}{25} - \frac{49 \log{\left (x + \frac{2}{3} \right )}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.39439, size = 30, normalized size = 1.15 \begin{align*} \frac{4}{15} \, x + \frac{121}{25} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{49}{9} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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