Optimal. Leaf size=33 \[ -\frac{27 x^2}{20}-\frac{513 x}{100}-\frac{343}{88} \log (1-2 x)+\frac{\log (5 x+3)}{1375} \]
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Rubi [A] time = 0.0136325, 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} \[ -\frac{27 x^2}{20}-\frac{513 x}{100}-\frac{343}{88} \log (1-2 x)+\frac{\log (5 x+3)}{1375} \]
Antiderivative was successfully verified.
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Rule 72
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3}{(1-2 x) (3+5 x)} \, dx &=\int \left (-\frac{513}{100}-\frac{27 x}{10}-\frac{343}{44 (-1+2 x)}+\frac{1}{275 (3+5 x)}\right ) \, dx\\ &=-\frac{513 x}{100}-\frac{27 x^2}{20}-\frac{343}{88} \log (1-2 x)+\frac{\log (3+5 x)}{1375}\\ \end{align*}
Mathematica [A] time = 0.0136481, size = 35, normalized size = 1.06 \[ \frac{-330 \left (45 x^2+171 x+94\right )-42875 \log (3-6 x)+8 \log (-3 (5 x+3))}{11000} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 26, normalized size = 0.8 \begin{align*} -{\frac{27\,{x}^{2}}{20}}-{\frac{513\,x}{100}}-{\frac{343\,\ln \left ( 2\,x-1 \right ) }{88}}+{\frac{\ln \left ( 3+5\,x \right ) }{1375}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03344, size = 34, normalized size = 1.03 \begin{align*} -\frac{27}{20} \, x^{2} - \frac{513}{100} \, x + \frac{1}{1375} \, \log \left (5 \, x + 3\right ) - \frac{343}{88} \, \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 = 1.30842, size = 92, normalized size = 2.79 \begin{align*} -\frac{27}{20} \, x^{2} - \frac{513}{100} \, x + \frac{1}{1375} \, \log \left (5 \, x + 3\right ) - \frac{343}{88} \, \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 = 0.119686, size = 29, normalized size = 0.88 \begin{align*} - \frac{27 x^{2}}{20} - \frac{513 x}{100} - \frac{343 \log{\left (x - \frac{1}{2} \right )}}{88} + \frac{\log{\left (x + \frac{3}{5} \right )}}{1375} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.02467, size = 36, normalized size = 1.09 \begin{align*} -\frac{27}{20} \, x^{2} - \frac{513}{100} \, x + \frac{1}{1375} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{343}{88} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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