Optimal. Leaf size=32 \[ -\frac{121}{25 (5 x+3)}+\frac{49}{3} \log (3 x+2)-\frac{407}{25} \log (5 x+3) \]
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Rubi [A] time = 0.0130116, 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} \[ -\frac{121}{25 (5 x+3)}+\frac{49}{3} \log (3 x+2)-\frac{407}{25} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{(2+3 x) (3+5 x)^2} \, dx &=\int \left (\frac{49}{2+3 x}+\frac{121}{5 (3+5 x)^2}-\frac{407}{5 (3+5 x)}\right ) \, dx\\ &=-\frac{121}{25 (3+5 x)}+\frac{49}{3} \log (2+3 x)-\frac{407}{25} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0185814, size = 32, normalized size = 1. \[ -\frac{121}{125 x+75}+\frac{49}{3} \log (3 x+2)-\frac{407}{25} \log (-3 (5 x+3)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 27, normalized size = 0.8 \begin{align*} -{\frac{121}{75+125\,x}}+{\frac{49\,\ln \left ( 2+3\,x \right ) }{3}}-{\frac{407\,\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 = 1.13099, size = 35, normalized size = 1.09 \begin{align*} -\frac{121}{25 \,{\left (5 \, x + 3\right )}} - \frac{407}{25} \, \log \left (5 \, x + 3\right ) + \frac{49}{3} \, \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 = 1.57761, size = 112, normalized size = 3.5 \begin{align*} -\frac{1221 \,{\left (5 \, x + 3\right )} \log \left (5 \, x + 3\right ) - 1225 \,{\left (5 \, x + 3\right )} \log \left (3 \, x + 2\right ) + 363}{75 \,{\left (5 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.127628, size = 26, normalized size = 0.81 \begin{align*} - \frac{407 \log{\left (x + \frac{3}{5} \right )}}{25} + \frac{49 \log{\left (x + \frac{2}{3} \right )}}{3} - \frac{121}{125 x + 75} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.0157, size = 58, normalized size = 1.81 \begin{align*} -\frac{121}{25 \,{\left (5 \, x + 3\right )}} - \frac{4}{75} \, \log \left (\frac{{\left | 5 \, x + 3 \right |}}{5 \,{\left (5 \, x + 3\right )}^{2}}\right ) + \frac{49}{3} \, \log \left ({\left | -\frac{1}{5 \, x + 3} - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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