Optimal. Leaf size=37 \[ \frac{125 x}{12}+\frac{1331}{56 (1-2 x)}+\frac{1089}{49} \log (1-2 x)-\frac{1}{441} \log (3 x+2) \]
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Rubi [A] time = 0.0166677, antiderivative size = 37, 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} \[ \frac{125 x}{12}+\frac{1331}{56 (1-2 x)}+\frac{1089}{49} \log (1-2 x)-\frac{1}{441} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^3}{(1-2 x)^2 (2+3 x)} \, dx &=\int \left (\frac{125}{12}+\frac{1331}{28 (-1+2 x)^2}+\frac{2178}{49 (-1+2 x)}-\frac{1}{147 (2+3 x)}\right ) \, dx\\ &=\frac{1331}{56 (1-2 x)}+\frac{125 x}{12}+\frac{1089}{49} \log (1-2 x)-\frac{1}{441} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.022045, size = 37, normalized size = 1. \[ \frac{12250 (3 x+2)+\frac{83853}{1-2 x}+78408 \log (3-6 x)-8 \log (3 x+2)}{3528} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 30, normalized size = 0.8 \begin{align*}{\frac{125\,x}{12}}-{\frac{1331}{112\,x-56}}+{\frac{1089\,\ln \left ( 2\,x-1 \right ) }{49}}-{\frac{\ln \left ( 2+3\,x \right ) }{441}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.12592, size = 39, normalized size = 1.05 \begin{align*} \frac{125}{12} \, x - \frac{1331}{56 \,{\left (2 \, x - 1\right )}} - \frac{1}{441} \, \log \left (3 \, x + 2\right ) + \frac{1089}{49} \, \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 = 1.26168, size = 143, normalized size = 3.86 \begin{align*} \frac{73500 \, x^{2} - 8 \,{\left (2 \, x - 1\right )} \log \left (3 \, x + 2\right ) + 78408 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 36750 \, x - 83853}{3528 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.130678, size = 29, normalized size = 0.78 \begin{align*} \frac{125 x}{12} + \frac{1089 \log{\left (x - \frac{1}{2} \right )}}{49} - \frac{\log{\left (x + \frac{2}{3} \right )}}{441} - \frac{1331}{112 x - 56} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.67098, size = 63, normalized size = 1.7 \begin{align*} \frac{125}{12} \, x - \frac{1331}{56 \,{\left (2 \, x - 1\right )}} - \frac{200}{9} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) - \frac{1}{441} \, \log \left ({\left | -\frac{7}{2 \, x - 1} - 3 \right |}\right ) - \frac{125}{24} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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