Optimal. Leaf size=92 \[ \frac{166375}{3 x+2}+\frac{33275}{2 (3 x+2)^2}+\frac{6655}{3 (3 x+2)^3}+\frac{1331}{4 (3 x+2)^4}+\frac{7189}{135 (3 x+2)^5}+\frac{1421}{162 (3 x+2)^6}+\frac{49}{27 (3 x+2)^7}-831875 \log (3 x+2)+831875 \log (5 x+3) \]
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Rubi [A] time = 0.0384049, antiderivative size = 92, 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} \[ \frac{166375}{3 x+2}+\frac{33275}{2 (3 x+2)^2}+\frac{6655}{3 (3 x+2)^3}+\frac{1331}{4 (3 x+2)^4}+\frac{7189}{135 (3 x+2)^5}+\frac{1421}{162 (3 x+2)^6}+\frac{49}{27 (3 x+2)^7}-831875 \log (3 x+2)+831875 \log (5 x+3) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3}{(2+3 x)^8 (3+5 x)} \, dx &=\int \left (-\frac{343}{9 (2+3 x)^8}-\frac{1421}{9 (2+3 x)^7}-\frac{7189}{9 (2+3 x)^6}-\frac{3993}{(2+3 x)^5}-\frac{19965}{(2+3 x)^4}-\frac{99825}{(2+3 x)^3}-\frac{499125}{(2+3 x)^2}-\frac{2495625}{2+3 x}+\frac{4159375}{3+5 x}\right ) \, dx\\ &=\frac{49}{27 (2+3 x)^7}+\frac{1421}{162 (2+3 x)^6}+\frac{7189}{135 (2+3 x)^5}+\frac{1331}{4 (2+3 x)^4}+\frac{6655}{3 (2+3 x)^3}+\frac{33275}{2 (2+3 x)^2}+\frac{166375}{2+3 x}-831875 \log (2+3 x)+831875 \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0611, size = 84, normalized size = 0.91 \[ \frac{269527500 (3 x+2)^6+26952750 (3 x+2)^5+3593700 (3 x+2)^4+539055 (3 x+2)^3+86268 (3 x+2)^2+14210 (3 x+2)+2940}{1620 (3 x+2)^7}-831875 \log (5 (3 x+2))+831875 \log (5 x+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 81, normalized size = 0.9 \begin{align*}{\frac{49}{27\, \left ( 2+3\,x \right ) ^{7}}}+{\frac{1421}{162\, \left ( 2+3\,x \right ) ^{6}}}+{\frac{7189}{135\, \left ( 2+3\,x \right ) ^{5}}}+{\frac{1331}{4\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{6655}{3\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{33275}{2\, \left ( 2+3\,x \right ) ^{2}}}+166375\, \left ( 2+3\,x \right ) ^{-1}-831875\,\ln \left ( 2+3\,x \right ) +831875\,\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 = 1.59279, size = 116, normalized size = 1.26 \begin{align*} \frac{196485547500 \, x^{6} + 792491708250 \, x^{5} + 1332026467200 \, x^{4} + 1194258563685 \, x^{3} + 602391504582 \, x^{2} + 162081979026 \, x + 18174436072}{1620 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} + 831875 \, \log \left (5 \, x + 3\right ) - 831875 \, \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 = 1.20145, size = 598, normalized size = 6.5 \begin{align*} \frac{196485547500 \, x^{6} + 792491708250 \, x^{5} + 1332026467200 \, x^{4} + 1194258563685 \, x^{3} + 602391504582 \, x^{2} + 1347637500 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (5 \, x + 3\right ) - 1347637500 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )} \log \left (3 \, x + 2\right ) + 162081979026 \, x + 18174436072}{1620 \,{\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.213032, size = 82, normalized size = 0.89 \begin{align*} \frac{196485547500 x^{6} + 792491708250 x^{5} + 1332026467200 x^{4} + 1194258563685 x^{3} + 602391504582 x^{2} + 162081979026 x + 18174436072}{3542940 x^{7} + 16533720 x^{6} + 33067440 x^{5} + 36741600 x^{4} + 24494400 x^{3} + 9797760 x^{2} + 2177280 x + 207360} + 831875 \log{\left (x + \frac{3}{5} \right )} - 831875 \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 = 3.20228, size = 78, normalized size = 0.85 \begin{align*} \frac{196485547500 \, x^{6} + 792491708250 \, x^{5} + 1332026467200 \, x^{4} + 1194258563685 \, x^{3} + 602391504582 \, x^{2} + 162081979026 \, x + 18174436072}{1620 \,{\left (3 \, x + 2\right )}^{7}} + 831875 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 831875 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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