Optimal. Leaf size=43 \[ -\frac{407}{196 (1-2 x)}+\frac{121}{56 (1-2 x)^2}-\frac{1}{343} \log (1-2 x)+\frac{1}{343} \log (3 x+2) \]
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Rubi [A] time = 0.017587, antiderivative size = 43, 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} \[ -\frac{407}{196 (1-2 x)}+\frac{121}{56 (1-2 x)^2}-\frac{1}{343} \log (1-2 x)+\frac{1}{343} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^2}{(1-2 x)^3 (2+3 x)} \, dx &=\int \left (-\frac{121}{14 (-1+2 x)^3}-\frac{407}{98 (-1+2 x)^2}-\frac{2}{343 (-1+2 x)}+\frac{3}{343 (2+3 x)}\right ) \, dx\\ &=\frac{121}{56 (1-2 x)^2}-\frac{407}{196 (1-2 x)}-\frac{1}{343} \log (1-2 x)+\frac{1}{343} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0222259, size = 35, normalized size = 0.81 \[ \frac{\frac{77 (148 x+3)}{(1-2 x)^2}-8 \log (3-6 x)+8 \log (3 x+2)}{2744} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*}{\frac{121}{56\, \left ( 2\,x-1 \right ) ^{2}}}+{\frac{407}{392\,x-196}}-{\frac{\ln \left ( 2\,x-1 \right ) }{343}}+{\frac{\ln \left ( 2+3\,x \right ) }{343}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06975, size = 49, normalized size = 1.14 \begin{align*} \frac{11 \,{\left (148 \, x + 3\right )}}{392 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} + \frac{1}{343} \, \log \left (3 \, x + 2\right ) - \frac{1}{343} \, \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 = 1.65345, size = 151, normalized size = 3.51 \begin{align*} \frac{8 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (3 \, x + 2\right ) - 8 \,{\left (4 \, x^{2} - 4 \, x + 1\right )} \log \left (2 \, x - 1\right ) + 11396 \, x + 231}{2744 \,{\left (4 \, x^{2} - 4 \, x + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.138477, size = 31, normalized size = 0.72 \begin{align*} \frac{1628 x + 33}{1568 x^{2} - 1568 x + 392} - \frac{\log{\left (x - \frac{1}{2} \right )}}{343} + \frac{\log{\left (x + \frac{2}{3} \right )}}{343} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.98953, size = 45, normalized size = 1.05 \begin{align*} \frac{11 \,{\left (148 \, x + 3\right )}}{392 \,{\left (2 \, x - 1\right )}^{2}} + \frac{1}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{1}{343} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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