Optimal. Leaf size=65 \[ \frac{147}{14641 (1-2 x)}-\frac{21}{14641 (5 x+3)}+\frac{343}{5324 (1-2 x)^2}-\frac{1}{13310 (5 x+3)^2}-\frac{777 \log (1-2 x)}{161051}+\frac{777 \log (5 x+3)}{161051} \]
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Rubi [A] time = 0.0299482, antiderivative size = 65, 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} \[ \frac{147}{14641 (1-2 x)}-\frac{21}{14641 (5 x+3)}+\frac{343}{5324 (1-2 x)^2}-\frac{1}{13310 (5 x+3)^2}-\frac{777 \log (1-2 x)}{161051}+\frac{777 \log (5 x+3)}{161051} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(2+3 x)^3}{(1-2 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac{343}{1331 (-1+2 x)^3}+\frac{294}{14641 (-1+2 x)^2}-\frac{1554}{161051 (-1+2 x)}+\frac{1}{1331 (3+5 x)^3}+\frac{105}{14641 (3+5 x)^2}+\frac{3885}{161051 (3+5 x)}\right ) \, dx\\ &=\frac{343}{5324 (1-2 x)^2}+\frac{147}{14641 (1-2 x)}-\frac{1}{13310 (3+5 x)^2}-\frac{21}{14641 (3+5 x)}-\frac{777 \log (1-2 x)}{161051}+\frac{777 \log (3+5 x)}{161051}\\ \end{align*}
Mathematica [A] time = 0.0289584, size = 48, normalized size = 0.74 \[ \frac{-\frac{11 \left (155400 x^3-371997 x^2-604258 x-194963\right )}{\left (10 x^2+x-3\right )^2}+15540 \log (-5 x-3)-15540 \log (1-2 x)}{3221020} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 54, normalized size = 0.8 \begin{align*}{\frac{343}{5324\, \left ( 2\,x-1 \right ) ^{2}}}-{\frac{147}{29282\,x-14641}}-{\frac{777\,\ln \left ( 2\,x-1 \right ) }{161051}}-{\frac{1}{13310\, \left ( 3+5\,x \right ) ^{2}}}-{\frac{21}{43923+73205\,x}}+{\frac{777\,\ln \left ( 3+5\,x \right ) }{161051}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04597, size = 76, normalized size = 1.17 \begin{align*} -\frac{155400 \, x^{3} - 371997 \, x^{2} - 604258 \, x - 194963}{292820 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac{777}{161051} \, \log \left (5 \, x + 3\right ) - \frac{777}{161051} \, \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 = 1.51202, size = 294, normalized size = 4.52 \begin{align*} -\frac{1709400 \, x^{3} - 4091967 \, x^{2} - 15540 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 15540 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 6646838 \, x - 2144593}{3221020 \,{\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.170407, size = 54, normalized size = 0.83 \begin{align*} - \frac{155400 x^{3} - 371997 x^{2} - 604258 x - 194963}{29282000 x^{4} + 5856400 x^{3} - 17276380 x^{2} - 1756920 x + 2635380} - \frac{777 \log{\left (x - \frac{1}{2} \right )}}{161051} + \frac{777 \log{\left (x + \frac{3}{5} \right )}}{161051} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.72418, size = 62, normalized size = 0.95 \begin{align*} -\frac{155400 \, x^{3} - 371997 \, x^{2} - 604258 \, x - 194963}{292820 \,{\left (10 \, x^{2} + x - 3\right )}^{2}} + \frac{777}{161051} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{777}{161051} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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