Optimal. Leaf size=80 \[ -\frac {5832 x^7}{875}-\frac {3402 x^6}{625}+\frac {134622 x^5}{15625}+\frac {74223 x^4}{12500}-\frac {81747 x^3}{15625}-\frac {915777 x^2}{390625}+\frac {4571416 x}{1953125}-\frac {23232}{9765625 (5 x+3)}-\frac {1331}{19531250 (5 x+3)^2}+\frac {166749 \log (5 x+3)}{9765625} \]
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Rubi [A] time = 0.04, antiderivative size = 80, 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 {5832 x^7}{875}-\frac {3402 x^6}{625}+\frac {134622 x^5}{15625}+\frac {74223 x^4}{12500}-\frac {81747 x^3}{15625}-\frac {915777 x^2}{390625}+\frac {4571416 x}{1953125}-\frac {23232}{9765625 (5 x+3)}-\frac {1331}{19531250 (5 x+3)^2}+\frac {166749 \log (5 x+3)}{9765625} \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)^6}{(3+5 x)^3} \, dx &=\int \left (\frac {4571416}{1953125}-\frac {1831554 x}{390625}-\frac {245241 x^2}{15625}+\frac {74223 x^3}{3125}+\frac {134622 x^4}{3125}-\frac {20412 x^5}{625}-\frac {5832 x^6}{125}+\frac {1331}{1953125 (3+5 x)^3}+\frac {23232}{1953125 (3+5 x)^2}+\frac {166749}{1953125 (3+5 x)}\right ) \, dx\\ &=\frac {4571416 x}{1953125}-\frac {915777 x^2}{390625}-\frac {81747 x^3}{15625}+\frac {74223 x^4}{12500}+\frac {134622 x^5}{15625}-\frac {3402 x^6}{625}-\frac {5832 x^7}{875}-\frac {1331}{19531250 (3+5 x)^2}-\frac {23232}{9765625 (3+5 x)}+\frac {166749 \log (3+5 x)}{9765625}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 73, normalized size = 0.91 \begin {gather*} \frac {-227812500000 x^9-459421875000 x^8-10783125000 x^7+489359390625 x^6+170737481250 x^5-221653096875 x^4-80532567500 x^3+104273484075 x^2+73328526690 x+23344860 (5 x+3)^2 \log (6 (5 x+3))+13353609877}{1367187500 (5 x+3)^2} \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)^6}{(3+5 x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.27, size = 77, normalized size = 0.96 \begin {gather*} -\frac {45562500000 \, x^{9} + 91884375000 \, x^{8} + 2156625000 \, x^{7} - 97871878125 \, x^{6} - 34147496250 \, x^{5} + 44330619375 \, x^{4} + 16106513500 \, x^{3} - 13430552100 \, x^{2} - 4668972 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 5756731680 \, x + 1970122}{273437500 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.16, size = 57, normalized size = 0.71 \begin {gather*} -\frac {5832}{875} \, x^{7} - \frac {3402}{625} \, x^{6} + \frac {134622}{15625} \, x^{5} + \frac {74223}{12500} \, x^{4} - \frac {81747}{15625} \, x^{3} - \frac {915777}{390625} \, x^{2} + \frac {4571416}{1953125} \, x - \frac {121 \, {\left (1920 \, x + 1163\right )}}{19531250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {166749}{9765625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 61, normalized size = 0.76 \begin {gather*} -\frac {5832 x^{7}}{875}-\frac {3402 x^{6}}{625}+\frac {134622 x^{5}}{15625}+\frac {74223 x^{4}}{12500}-\frac {81747 x^{3}}{15625}-\frac {915777 x^{2}}{390625}+\frac {4571416 x}{1953125}+\frac {166749 \ln \left (5 x +3\right )}{9765625}-\frac {1331}{19531250 \left (5 x +3\right )^{2}}-\frac {23232}{9765625 \left (5 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 61, normalized size = 0.76 \begin {gather*} -\frac {5832}{875} \, x^{7} - \frac {3402}{625} \, x^{6} + \frac {134622}{15625} \, x^{5} + \frac {74223}{12500} \, x^{4} - \frac {81747}{15625} \, x^{3} - \frac {915777}{390625} \, x^{2} + \frac {4571416}{1953125} \, x - \frac {121 \, {\left (1920 \, x + 1163\right )}}{19531250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {166749}{9765625} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 57, normalized size = 0.71 \begin {gather*} \frac {4571416\,x}{1953125}+\frac {166749\,\ln \left (x+\frac {3}{5}\right )}{9765625}-\frac {\frac {23232\,x}{48828125}+\frac {140723}{488281250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {915777\,x^2}{390625}-\frac {81747\,x^3}{15625}+\frac {74223\,x^4}{12500}+\frac {134622\,x^5}{15625}-\frac {3402\,x^6}{625}-\frac {5832\,x^7}{875} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 70, normalized size = 0.88 \begin {gather*} - \frac {5832 x^{7}}{875} - \frac {3402 x^{6}}{625} + \frac {134622 x^{5}}{15625} + \frac {74223 x^{4}}{12500} - \frac {81747 x^{3}}{15625} - \frac {915777 x^{2}}{390625} + \frac {4571416 x}{1953125} - \frac {232320 x + 140723}{488281250 x^{2} + 585937500 x + 175781250} + \frac {166749 \log {\left (5 x + 3 \right )}}{9765625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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