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 = 0.04, antiderivative size = 92, normalized size of antiderivative = 1.00, 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} \begin {gather*} \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) \end {gather*}
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*}
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Mathematica [A] time = 0.11, size = 84, normalized size = 0.91 \begin {gather*} \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) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {(1-2 x)^3}{(2+3 x)^8 (3+5 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.20, size = 155, normalized size = 1.68 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.07, size = 58, normalized size = 0.63 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 81, normalized size = 0.88 \begin {gather*} -831875 \ln \left (3 x +2\right )+831875 \ln \left (5 x +3\right )+\frac {49}{27 \left (3 x +2\right )^{7}}+\frac {1421}{162 \left (3 x +2\right )^{6}}+\frac {7189}{135 \left (3 x +2\right )^{5}}+\frac {1331}{4 \left (3 x +2\right )^{4}}+\frac {6655}{3 \left (3 x +2\right )^{3}}+\frac {33275}{2 \left (3 x +2\right )^{2}}+\frac {166375}{3 x +2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 86, normalized size = 0.93 \begin {gather*} \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.14, size = 75, normalized size = 0.82 \begin {gather*} \frac {\frac {166375\,x^6}{3}+\frac {4026275\,x^5}{18}+\frac {30453280\,x^4}{81}+\frac {327642953\,x^3}{972}+\frac {11155398233\,x^2}{65610}+\frac {27013663171\,x}{590490}+\frac {4543609018}{885735}}{x^7+\frac {14\,x^6}{3}+\frac {28\,x^5}{3}+\frac {280\,x^4}{27}+\frac {560\,x^3}{81}+\frac {224\,x^2}{81}+\frac {448\,x}{729}+\frac {128}{2187}}-1663750\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.23, size = 83, normalized size = 0.90 \begin {gather*} - \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 {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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