Optimal. Leaf size=33 \[ -\frac{4 x^2}{15}+\frac{332 x}{225}-\frac{343}{27} \log (3 x+2)+\frac{1331}{125} \log (5 x+3) \]
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Rubi [A] time = 0.0138556, antiderivative size = 33, 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} \[ -\frac{4 x^2}{15}+\frac{332 x}{225}-\frac{343}{27} \log (3 x+2)+\frac{1331}{125} \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3}{(2+3 x) (3+5 x)} \, dx &=\int \left (\frac{332}{225}-\frac{8 x}{15}-\frac{343}{9 (2+3 x)}+\frac{1331}{25 (3+5 x)}\right ) \, dx\\ &=\frac{332 x}{225}-\frac{4 x^2}{15}-\frac{343}{27} \log (2+3 x)+\frac{1331}{125} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0123518, size = 35, normalized size = 1.06 \[ \frac{60 \left (-15 x^2+83 x+62\right )-42875 \log (3 x+2)+35937 \log (-3 (5 x+3))}{3375} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 26, normalized size = 0.8 \begin{align*}{\frac{332\,x}{225}}-{\frac{4\,{x}^{2}}{15}}-{\frac{343\,\ln \left ( 2+3\,x \right ) }{27}}+{\frac{1331\,\ln \left ( 3+5\,x \right ) }{125}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.7171, size = 34, normalized size = 1.03 \begin{align*} -\frac{4}{15} \, x^{2} + \frac{332}{225} \, x + \frac{1331}{125} \, \log \left (5 \, x + 3\right ) - \frac{343}{27} \, \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 = 1.649, size = 93, normalized size = 2.82 \begin{align*} -\frac{4}{15} \, x^{2} + \frac{332}{225} \, x + \frac{1331}{125} \, \log \left (5 \, x + 3\right ) - \frac{343}{27} \, \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 = 0.112839, size = 31, normalized size = 0.94 \begin{align*} - \frac{4 x^{2}}{15} + \frac{332 x}{225} + \frac{1331 \log{\left (x + \frac{3}{5} \right )}}{125} - \frac{343 \log{\left (x + \frac{2}{3} \right )}}{27} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.00452, size = 36, normalized size = 1.09 \begin{align*} -\frac{4}{15} \, x^{2} + \frac{332}{225} \, x + \frac{1331}{125} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{343}{27} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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