Optimal. Leaf size=57 \[ \frac{1617}{3 x+2}+\frac{2541}{5 x+3}+\frac{343}{6 (3 x+2)^2}-\frac{1331}{10 (5 x+3)^2}-15708 \log (3 x+2)+15708 \log (5 x+3) \]
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Rubi [A] time = 0.0275684, antiderivative size = 57, 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} \[ \frac{1617}{3 x+2}+\frac{2541}{5 x+3}+\frac{343}{6 (3 x+2)^2}-\frac{1331}{10 (5 x+3)^2}-15708 \log (3 x+2)+15708 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3}{(2+3 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac{343}{(2+3 x)^3}-\frac{4851}{(2+3 x)^2}-\frac{47124}{2+3 x}+\frac{1331}{(3+5 x)^3}-\frac{12705}{(3+5 x)^2}+\frac{78540}{3+5 x}\right ) \, dx\\ &=\frac{343}{6 (2+3 x)^2}+\frac{1617}{2+3 x}-\frac{1331}{10 (3+5 x)^2}+\frac{2541}{3+5 x}-15708 \log (2+3 x)+15708 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.032289, size = 59, normalized size = 1.04 \[ \frac{1617}{3 x+2}+\frac{2541}{5 x+3}+\frac{343}{6 (3 x+2)^2}-\frac{1331}{10 (5 x+3)^2}-15708 \log (5 (3 x+2))+15708 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.008, size = 54, normalized size = 1. \begin{align*}{\frac{343}{6\, \left ( 2+3\,x \right ) ^{2}}}+1617\, \left ( 2+3\,x \right ) ^{-1}-{\frac{1331}{10\, \left ( 3+5\,x \right ) ^{2}}}+2541\, \left ( 3+5\,x \right ) ^{-1}-15708\,\ln \left ( 2+3\,x \right ) +15708\,\ln \left ( 3+5\,x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03618, size = 76, normalized size = 1.33 \begin{align*} \frac{7068600 \, x^{3} + 13430348 \, x^{2} + 8492784 \, x + 1787403}{30 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} + 15708 \, \log \left (5 \, x + 3\right ) - 15708 \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.25191, size = 311, normalized size = 5.46 \begin{align*} \frac{7068600 \, x^{3} + 13430348 \, x^{2} + 471240 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (5 \, x + 3\right ) - 471240 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )} \log \left (3 \, x + 2\right ) + 8492784 \, x + 1787403}{30 \,{\left (225 \, x^{4} + 570 \, x^{3} + 541 \, x^{2} + 228 \, x + 36\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.166293, size = 51, normalized size = 0.89 \begin{align*} \frac{7068600 x^{3} + 13430348 x^{2} + 8492784 x + 1787403}{6750 x^{4} + 17100 x^{3} + 16230 x^{2} + 6840 x + 1080} + 15708 \log{\left (x + \frac{3}{5} \right )} - 15708 \log{\left (x + \frac{2}{3} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.50146, size = 65, normalized size = 1.14 \begin{align*} \frac{7068600 \, x^{3} + 13430348 \, x^{2} + 8492784 \, x + 1787403}{30 \,{\left (15 \, x^{2} + 19 \, x + 6\right )}^{2}} + 15708 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 15708 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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