Optimal. Leaf size=54 \[ \frac{14}{1331 (1-2 x)}-\frac{1}{1331 (5 x+3)}+\frac{49}{484 (1-2 x)^2}-\frac{72 \log (1-2 x)}{14641}+\frac{72 \log (5 x+3)}{14641} \]
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Rubi [A] time = 0.0240991, antiderivative size = 54, 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} \[ \frac{14}{1331 (1-2 x)}-\frac{1}{1331 (5 x+3)}+\frac{49}{484 (1-2 x)^2}-\frac{72 \log (1-2 x)}{14641}+\frac{72 \log (5 x+3)}{14641} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^2}{(1-2 x)^3 (3+5 x)^2} \, dx &=\int \left (-\frac{49}{121 (-1+2 x)^3}+\frac{28}{1331 (-1+2 x)^2}-\frac{144}{14641 (-1+2 x)}+\frac{5}{1331 (3+5 x)^2}+\frac{360}{14641 (3+5 x)}\right ) \, dx\\ &=\frac{49}{484 (1-2 x)^2}+\frac{14}{1331 (1-2 x)}-\frac{1}{1331 (3+5 x)}-\frac{72 \log (1-2 x)}{14641}+\frac{72 \log (3+5 x)}{14641}\\ \end{align*}
Mathematica [A] time = 0.0292258, size = 48, normalized size = 0.89 \[ \frac{\frac{616}{1-2 x}-\frac{44}{5 x+3}+\frac{5929}{(1-2 x)^2}-288 \log (1-2 x)+288 \log (10 x+6)}{58564} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 45, normalized size = 0.8 \begin{align*}{\frac{49}{484\, \left ( 2\,x-1 \right ) ^{2}}}-{\frac{14}{2662\,x-1331}}-{\frac{72\,\ln \left ( 2\,x-1 \right ) }{14641}}-{\frac{1}{3993+6655\,x}}+{\frac{72\,\ln \left ( 3+5\,x \right ) }{14641}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.06428, size = 62, normalized size = 1.15 \begin{align*} -\frac{576 \, x^{2} - 2655 \, x - 1781}{5324 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} + \frac{72}{14641} \, \log \left (5 \, x + 3\right ) - \frac{72}{14641} \, \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 = 1.58147, size = 213, normalized size = 3.94 \begin{align*} -\frac{6336 \, x^{2} - 288 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (5 \, x + 3\right ) + 288 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )} \log \left (2 \, x - 1\right ) - 29205 \, x - 19591}{58564 \,{\left (20 \, x^{3} - 8 \, x^{2} - 7 \, x + 3\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.156859, size = 44, normalized size = 0.81 \begin{align*} - \frac{576 x^{2} - 2655 x - 1781}{106480 x^{3} - 42592 x^{2} - 37268 x + 15972} - \frac{72 \log{\left (x - \frac{1}{2} \right )}}{14641} + \frac{72 \log{\left (x + \frac{3}{5} \right )}}{14641} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.17162, size = 69, normalized size = 1.28 \begin{align*} -\frac{1}{1331 \,{\left (5 \, x + 3\right )}} + \frac{35 \,{\left (\frac{429}{5 \, x + 3} - 43\right )}}{14641 \,{\left (\frac{11}{5 \, x + 3} - 2\right )}^{2}} - \frac{72}{14641} \, \log \left ({\left | -\frac{11}{5 \, x + 3} + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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