Optimal. Leaf size=87 \[ -\frac {2187 x^8}{125}-\frac {119556 x^7}{4375}+\frac {33291 x^6}{3125}+\frac {491913 x^5}{15625}+\frac {6507 x^4}{62500}-\frac {5918904 x^3}{390625}-\frac {2300646 x^2}{1953125}+\frac {46214407 x}{9765625}-\frac {1089}{1953125 (5 x+3)}-\frac {1331}{97656250 (5 x+3)^2}+\frac {47289 \log (5 x+3)}{9765625} \]
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Rubi [A] time = 0.05, antiderivative size = 87, 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 {2187 x^8}{125}-\frac {119556 x^7}{4375}+\frac {33291 x^6}{3125}+\frac {491913 x^5}{15625}+\frac {6507 x^4}{62500}-\frac {5918904 x^3}{390625}-\frac {2300646 x^2}{1953125}+\frac {46214407 x}{9765625}-\frac {1089}{1953125 (5 x+3)}-\frac {1331}{97656250 (5 x+3)^2}+\frac {47289 \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)^7}{(3+5 x)^3} \, dx &=\int \left (\frac {46214407}{9765625}-\frac {4601292 x}{1953125}-\frac {17756712 x^2}{390625}+\frac {6507 x^3}{15625}+\frac {491913 x^4}{3125}+\frac {199746 x^5}{3125}-\frac {119556 x^6}{625}-\frac {17496 x^7}{125}+\frac {1331}{9765625 (3+5 x)^3}+\frac {1089}{390625 (3+5 x)^2}+\frac {47289}{1953125 (3+5 x)}\right ) \, dx\\ &=\frac {46214407 x}{9765625}-\frac {2300646 x^2}{1953125}-\frac {5918904 x^3}{390625}+\frac {6507 x^4}{62500}+\frac {491913 x^5}{15625}+\frac {33291 x^6}{3125}-\frac {119556 x^7}{4375}-\frac {2187 x^8}{125}-\frac {1331}{97656250 (3+5 x)^2}-\frac {1089}{1953125 (3+5 x)}+\frac {47289 \log (3+5 x)}{9765625}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 76, normalized size = 0.87 \begin {gather*} \frac {-598007812500 x^{10}-1651640625000 x^9-972000000000 x^8+1176752812500 x^7+1425913453125 x^6-126252393750 x^5-660465159375 x^4-73008617500 x^3+229405636575 x^2+117985377690 x+6620460 (5 x+3)^2 \log (5 x+3)+17925405377}{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)^7}{(3+5 x)^3} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.46, size = 82, normalized size = 0.94 \begin {gather*} -\frac {598007812500 \, x^{10} + 1651640625000 \, x^{9} + 972000000000 \, x^{8} - 1176752812500 \, x^{7} - 1425913453125 \, x^{6} + 126252393750 \, x^{5} + 660465159375 \, x^{4} + 73008617500 \, x^{3} - 179606439600 \, x^{2} - 6620460 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) - 58226341320 \, x + 2305534}{1367187500 \, {\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 = 0.94, size = 62, normalized size = 0.71 \begin {gather*} -\frac {2187}{125} \, x^{8} - \frac {119556}{4375} \, x^{7} + \frac {33291}{3125} \, x^{6} + \frac {491913}{15625} \, x^{5} + \frac {6507}{62500} \, x^{4} - \frac {5918904}{390625} \, x^{3} - \frac {2300646}{1953125} \, x^{2} + \frac {46214407}{9765625} \, x - \frac {121 \, {\left (2250 \, x + 1361\right )}}{97656250 \, {\left (5 \, x + 3\right )}^{2}} + \frac {47289}{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 = 66, normalized size = 0.76 \begin {gather*} -\frac {2187 x^{8}}{125}-\frac {119556 x^{7}}{4375}+\frac {33291 x^{6}}{3125}+\frac {491913 x^{5}}{15625}+\frac {6507 x^{4}}{62500}-\frac {5918904 x^{3}}{390625}-\frac {2300646 x^{2}}{1953125}+\frac {46214407 x}{9765625}+\frac {47289 \ln \left (5 x +3\right )}{9765625}-\frac {1331}{97656250 \left (5 x +3\right )^{2}}-\frac {1089}{1953125 \left (5 x +3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.69, size = 66, normalized size = 0.76 \begin {gather*} -\frac {2187}{125} \, x^{8} - \frac {119556}{4375} \, x^{7} + \frac {33291}{3125} \, x^{6} + \frac {491913}{15625} \, x^{5} + \frac {6507}{62500} \, x^{4} - \frac {5918904}{390625} \, x^{3} - \frac {2300646}{1953125} \, x^{2} + \frac {46214407}{9765625} \, x - \frac {121 \, {\left (2250 \, x + 1361\right )}}{97656250 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {47289}{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 = 1.16, size = 62, normalized size = 0.71 \begin {gather*} \frac {46214407\,x}{9765625}+\frac {47289\,\ln \left (x+\frac {3}{5}\right )}{9765625}-\frac {\frac {1089\,x}{9765625}+\frac {164681}{2441406250}}{x^2+\frac {6\,x}{5}+\frac {9}{25}}-\frac {2300646\,x^2}{1953125}-\frac {5918904\,x^3}{390625}+\frac {6507\,x^4}{62500}+\frac {491913\,x^5}{15625}+\frac {33291\,x^6}{3125}-\frac {119556\,x^7}{4375}-\frac {2187\,x^8}{125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 76, normalized size = 0.87 \begin {gather*} - \frac {2187 x^{8}}{125} - \frac {119556 x^{7}}{4375} + \frac {33291 x^{6}}{3125} + \frac {491913 x^{5}}{15625} + \frac {6507 x^{4}}{62500} - \frac {5918904 x^{3}}{390625} - \frac {2300646 x^{2}}{1953125} + \frac {46214407 x}{9765625} - \frac {272250 x + 164681}{2441406250 x^{2} + 2929687500 x + 878906250} + \frac {47289 \log {\left (5 x + 3 \right )}}{9765625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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