Optimal. Leaf size=39 \[ -\frac{49}{3 (3 x+2)}-\frac{121}{5 (5 x+3)}+154 \log (3 x+2)-154 \log (5 x+3) \]
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Rubi [A] time = 0.0177119, antiderivative size = 39, 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} \[ -\frac{49}{3 (3 x+2)}-\frac{121}{5 (5 x+3)}+154 \log (3 x+2)-154 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2}{(2+3 x)^2 (3+5 x)^2} \, dx &=\int \left (\frac{49}{(2+3 x)^2}+\frac{462}{2+3 x}+\frac{121}{(3+5 x)^2}-\frac{770}{3+5 x}\right ) \, dx\\ &=-\frac{49}{3 (2+3 x)}-\frac{121}{5 (3+5 x)}+154 \log (2+3 x)-154 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0303634, size = 61, normalized size = 1.56 \[ -\frac{-2310 \left (15 x^2+19 x+6\right ) \log (5 (3 x+2))+2310 \left (15 x^2+19 x+6\right ) \log (5 x+3)+2314 x+1461}{15 (3 x+2) (5 x+3)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 36, normalized size = 0.9 \begin{align*} -{\frac{49}{6+9\,x}}-{\frac{121}{15+25\,x}}+154\,\ln \left ( 2+3\,x \right ) -154\,\ln \left ( 3+5\,x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09228, size = 49, normalized size = 1.26 \begin{align*} -\frac{2314 \, x + 1461}{15 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}} - 154 \, \log \left (5 \, x + 3\right ) + 154 \, \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 = 1.512, size = 166, normalized size = 4.26 \begin{align*} -\frac{2310 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (5 \, x + 3\right ) - 2310 \,{\left (15 \, x^{2} + 19 \, x + 6\right )} \log \left (3 \, x + 2\right ) + 2314 \, x + 1461}{15 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.131609, size = 31, normalized size = 0.79 \begin{align*} - \frac{2314 x + 1461}{225 x^{2} + 285 x + 90} - 154 \log{\left (x + \frac{3}{5} \right )} + 154 \log{\left (x + \frac{2}{3} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.62428, size = 51, normalized size = 1.31 \begin{align*} -\frac{121}{5 \,{\left (5 \, x + 3\right )}} + \frac{245}{\frac{1}{5 \, x + 3} + 3} + 154 \, \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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