Optimal. Leaf size=43 \[ \frac{68}{441 (3 x+2)}-\frac{1}{126 (3 x+2)^2}-\frac{121}{343} \log (1-2 x)+\frac{121}{343} \log (3 x+2) \]
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Rubi [A] time = 0.0191789, 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} \[ \frac{68}{441 (3 x+2)}-\frac{1}{126 (3 x+2)^2}-\frac{121}{343} \log (1-2 x)+\frac{121}{343} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(3+5 x)^2}{(1-2 x) (2+3 x)^3} \, dx &=\int \left (-\frac{242}{343 (-1+2 x)}+\frac{1}{21 (2+3 x)^3}-\frac{68}{147 (2+3 x)^2}+\frac{363}{343 (2+3 x)}\right ) \, dx\\ &=-\frac{1}{126 (2+3 x)^2}+\frac{68}{441 (2+3 x)}-\frac{121}{343} \log (1-2 x)+\frac{121}{343} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0187307, size = 35, normalized size = 0.81 \[ \frac{\frac{7 (408 x+265)}{(3 x+2)^2}-2178 \log (1-2 x)+2178 \log (6 x+4)}{6174} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 36, normalized size = 0.8 \begin{align*} -{\frac{121\,\ln \left ( 2\,x-1 \right ) }{343}}-{\frac{1}{126\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{68}{882+1323\,x}}+{\frac{121\,\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 = 1.10738, size = 49, normalized size = 1.14 \begin{align*} \frac{408 \, x + 265}{882 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} + \frac{121}{343} \, \log \left (3 \, x + 2\right ) - \frac{121}{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 = 1.25566, size = 163, normalized size = 3.79 \begin{align*} \frac{2178 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 2178 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (2 \, x - 1\right ) + 2856 \, x + 1855}{6174 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.143161, size = 34, normalized size = 0.79 \begin{align*} \frac{408 x + 265}{7938 x^{2} + 10584 x + 3528} - \frac{121 \log{\left (x - \frac{1}{2} \right )}}{343} + \frac{121 \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 = 1.27075, size = 45, normalized size = 1.05 \begin{align*} \frac{408 \, x + 265}{882 \,{\left (3 \, x + 2\right )}^{2}} + \frac{121}{343} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{121}{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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