Optimal. Leaf size=51 \[ -\frac {500 x^6}{9}+\frac {220 x^5}{9}+\frac {2815 x^4}{54}-\frac {6427 x^3}{243}-\frac {8287 x^2}{486}+\frac {10013 x}{729}-\frac {343 \log (3 x+2)}{2187} \]
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Rubi [A] time = 0.02, antiderivative size = 51, 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 {500 x^6}{9}+\frac {220 x^5}{9}+\frac {2815 x^4}{54}-\frac {6427 x^3}{243}-\frac {8287 x^2}{486}+\frac {10013 x}{729}-\frac {343 \log (3 x+2)}{2187} \end {gather*}
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3 (3+5 x)^3}{2+3 x} \, dx &=\int \left (\frac {10013}{729}-\frac {8287 x}{243}-\frac {6427 x^2}{81}+\frac {5630 x^3}{27}+\frac {1100 x^4}{9}-\frac {1000 x^5}{3}-\frac {343}{729 (2+3 x)}\right ) \, dx\\ &=\frac {10013 x}{729}-\frac {8287 x^2}{486}-\frac {6427 x^3}{243}+\frac {2815 x^4}{54}+\frac {220 x^5}{9}-\frac {500 x^6}{9}-\frac {343 \log (2+3 x)}{2187}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 42, normalized size = 0.82 \begin {gather*} \frac {-243000 x^6+106920 x^5+228015 x^4-115686 x^3-74583 x^2+60078 x-686 \log (3 x+2)+29296}{4374} \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 (3+5 x)^3}{2+3 x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.29, size = 37, normalized size = 0.73 \begin {gather*} -\frac {500}{9} \, x^{6} + \frac {220}{9} \, x^{5} + \frac {2815}{54} \, x^{4} - \frac {6427}{243} \, x^{3} - \frac {8287}{486} \, x^{2} + \frac {10013}{729} \, x - \frac {343}{2187} \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.92, size = 38, normalized size = 0.75 \begin {gather*} -\frac {500}{9} \, x^{6} + \frac {220}{9} \, x^{5} + \frac {2815}{54} \, x^{4} - \frac {6427}{243} \, x^{3} - \frac {8287}{486} \, x^{2} + \frac {10013}{729} \, x - \frac {343}{2187} \, \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 = 0.00, size = 38, normalized size = 0.75 \begin {gather*} -\frac {500 x^{6}}{9}+\frac {220 x^{5}}{9}+\frac {2815 x^{4}}{54}-\frac {6427 x^{3}}{243}-\frac {8287 x^{2}}{486}+\frac {10013 x}{729}-\frac {343 \ln \left (3 x +2\right )}{2187} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 37, normalized size = 0.73 \begin {gather*} -\frac {500}{9} \, x^{6} + \frac {220}{9} \, x^{5} + \frac {2815}{54} \, x^{4} - \frac {6427}{243} \, x^{3} - \frac {8287}{486} \, x^{2} + \frac {10013}{729} \, x - \frac {343}{2187} \, \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 = 0.03, size = 35, normalized size = 0.69 \begin {gather*} \frac {10013\,x}{729}-\frac {343\,\ln \left (x+\frac {2}{3}\right )}{2187}-\frac {8287\,x^2}{486}-\frac {6427\,x^3}{243}+\frac {2815\,x^4}{54}+\frac {220\,x^5}{9}-\frac {500\,x^6}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 48, normalized size = 0.94 \begin {gather*} - \frac {500 x^{6}}{9} + \frac {220 x^{5}}{9} + \frac {2815 x^{4}}{54} - \frac {6427 x^{3}}{243} - \frac {8287 x^{2}}{486} + \frac {10013 x}{729} - \frac {343 \log {\left (3 x + 2 \right )}}{2187} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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