Optimal. Leaf size=37 \[ \frac{27 x}{20}+\frac{343}{88 (1-2 x)}+\frac{392}{121} \log (1-2 x)+\frac{\log (5 x+3)}{3025} \]
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Rubi [A] time = 0.0160597, 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} \[ \frac{27 x}{20}+\frac{343}{88 (1-2 x)}+\frac{392}{121} \log (1-2 x)+\frac{\log (5 x+3)}{3025} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3}{(1-2 x)^2 (3+5 x)} \, dx &=\int \left (\frac{27}{20}+\frac{343}{44 (-1+2 x)^2}+\frac{784}{121 (-1+2 x)}+\frac{1}{605 (3+5 x)}\right ) \, dx\\ &=\frac{343}{88 (1-2 x)}+\frac{27 x}{20}+\frac{392}{121} \log (1-2 x)+\frac{\log (3+5 x)}{3025}\\ \end{align*}
Mathematica [A] time = 0.0209511, size = 37, normalized size = 1. \[ \frac{6534 (5 x+3)+\frac{94325}{1-2 x}+78400 \log (5-10 x)+8 \log (5 x+3)}{24200} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 30, normalized size = 0.8 \begin{align*}{\frac{27\,x}{20}}-{\frac{343}{176\,x-88}}+{\frac{392\,\ln \left ( 2\,x-1 \right ) }{121}}+{\frac{\ln \left ( 3+5\,x \right ) }{3025}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06979, size = 39, normalized size = 1.05 \begin{align*} \frac{27}{20} \, x - \frac{343}{88 \,{\left (2 \, x - 1\right )}} + \frac{1}{3025} \, \log \left (5 \, x + 3\right ) + \frac{392}{121} \, \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 = 1.30526, size = 144, normalized size = 3.89 \begin{align*} \frac{65340 \, x^{2} + 8 \,{\left (2 \, x - 1\right )} \log \left (5 \, x + 3\right ) + 78400 \,{\left (2 \, x - 1\right )} \log \left (2 \, x - 1\right ) - 32670 \, x - 94325}{24200 \,{\left (2 \, x - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.135291, size = 29, normalized size = 0.78 \begin{align*} \frac{27 x}{20} + \frac{392 \log{\left (x - \frac{1}{2} \right )}}{121} + \frac{\log{\left (x + \frac{3}{5} \right )}}{3025} - \frac{343}{176 x - 88} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.67309, size = 63, normalized size = 1.7 \begin{align*} \frac{27}{20} \, x - \frac{343}{88 \,{\left (2 \, x - 1\right )}} - \frac{81}{25} \, \log \left (\frac{{\left | 2 \, x - 1 \right |}}{2 \,{\left (2 \, x - 1\right )}^{2}}\right ) + \frac{1}{3025} \, \log \left ({\left | -\frac{11}{2 \, x - 1} - 5 \right |}\right ) - \frac{27}{40} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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