Optimal. Leaf size=37 \[ -\frac{125 x}{18}+\frac{1}{189 (3 x+2)}-\frac{1331}{196} \log (1-2 x)+\frac{103 \log (3 x+2)}{1323} \]
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Rubi [A] time = 0.0158067, 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} \[ -\frac{125 x}{18}+\frac{1}{189 (3 x+2)}-\frac{1331}{196} \log (1-2 x)+\frac{103 \log (3 x+2)}{1323} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^3}{(1-2 x) (2+3 x)^2} \, dx &=\int \left (-\frac{125}{18}-\frac{1331}{98 (-1+2 x)}-\frac{1}{63 (2+3 x)^2}+\frac{103}{441 (2+3 x)}\right ) \, dx\\ &=-\frac{125 x}{18}+\frac{1}{189 (2+3 x)}-\frac{1331}{196} \log (1-2 x)+\frac{103 \log (2+3 x)}{1323}\\ \end{align*}
Mathematica [A] time = 0.0234478, size = 37, normalized size = 1. \[ \frac{18375 (1-2 x)+\frac{28}{3 x+2}-35937 \log (1-2 x)+412 \log (6 x+4)}{5292} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 30, normalized size = 0.8 \begin{align*} -{\frac{125\,x}{18}}-{\frac{1331\,\ln \left ( 2\,x-1 \right ) }{196}}+{\frac{1}{378+567\,x}}+{\frac{103\,\ln \left ( 2+3\,x \right ) }{1323}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.18441, size = 39, normalized size = 1.05 \begin{align*} -\frac{125}{18} \, x + \frac{1}{189 \,{\left (3 \, x + 2\right )}} + \frac{103}{1323} \, \log \left (3 \, x + 2\right ) - \frac{1331}{196} \, \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 = 1.25858, size = 144, normalized size = 3.89 \begin{align*} -\frac{110250 \, x^{2} - 412 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 35937 \,{\left (3 \, x + 2\right )} \log \left (2 \, x - 1\right ) + 73500 \, x - 28}{5292 \,{\left (3 \, x + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.140839, size = 31, normalized size = 0.84 \begin{align*} - \frac{125 x}{18} - \frac{1331 \log{\left (x - \frac{1}{2} \right )}}{196} + \frac{103 \log{\left (x + \frac{2}{3} \right )}}{1323} + \frac{1}{567 x + 378} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.8411, size = 63, normalized size = 1.7 \begin{align*} -\frac{125}{18} \, x + \frac{1}{189 \,{\left (3 \, x + 2\right )}} + \frac{725}{108} \, \log \left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) - \frac{1331}{196} \, \log \left ({\left | -\frac{7}{3 \, x + 2} + 2 \right |}\right ) - \frac{125}{27} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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