Optimal. Leaf size=55 \[ -\frac {200 x^5}{9}+\frac {775 x^4}{27}-\frac {190 x^3}{81}-\frac {5287 x^2}{486}+\frac {2287 x}{729}+\frac {343}{2187 (3 x+2)}+\frac {1813}{729} \log (3 x+2) \]
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Rubi [A] time = 0.03, antiderivative size = 55, 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 {200 x^5}{9}+\frac {775 x^4}{27}-\frac {190 x^3}{81}-\frac {5287 x^2}{486}+\frac {2287 x}{729}+\frac {343}{2187 (3 x+2)}+\frac {1813}{729} \log (3 x+2) \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)^2} \, dx &=\int \left (\frac {2287}{729}-\frac {5287 x}{243}-\frac {190 x^2}{27}+\frac {3100 x^3}{27}-\frac {1000 x^4}{9}-\frac {343}{729 (2+3 x)^2}+\frac {1813}{243 (2+3 x)}\right ) \, dx\\ &=\frac {2287 x}{729}-\frac {5287 x^2}{486}-\frac {190 x^3}{81}+\frac {775 x^4}{27}-\frac {200 x^5}{9}+\frac {343}{2187 (2+3 x)}+\frac {1813}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.02, size = 54, normalized size = 0.98 \begin {gather*} -\frac {291600 x^6-182250 x^5-220320 x^4+163269 x^3+54000 x^2+3588 x-10878 (3 x+2) \log (3 x+2)+20002}{4374 (3 x+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 (3+5 x)^3}{(2+3 x)^2} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.74, size = 52, normalized size = 0.95 \begin {gather*} -\frac {291600 \, x^{6} - 182250 \, x^{5} - 220320 \, x^{4} + 163269 \, x^{3} + 54000 \, x^{2} - 10878 \, {\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 27444 \, x - 686}{4374 \, {\left (3 \, x + 2\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.91, size = 75, normalized size = 1.36 \begin {gather*} \frac {1}{4374} \, {\left (3 \, x + 2\right )}^{5} {\left (\frac {5550}{3 \, x + 2} - \frac {28780}{{\left (3 \, x + 2\right )}^{2}} + \frac {66193}{{\left (3 \, x + 2\right )}^{3}} - \frac {60438}{{\left (3 \, x + 2\right )}^{4}} - 400\right )} + \frac {343}{2187 \, {\left (3 \, x + 2\right )}} - \frac {1813}{729} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 42, normalized size = 0.76 \begin {gather*} -\frac {200 x^{5}}{9}+\frac {775 x^{4}}{27}-\frac {190 x^{3}}{81}-\frac {5287 x^{2}}{486}+\frac {2287 x}{729}+\frac {1813 \ln \left (3 x +2\right )}{729}+\frac {343}{2187 \left (3 x +2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 41, normalized size = 0.75 \begin {gather*} -\frac {200}{9} \, x^{5} + \frac {775}{27} \, x^{4} - \frac {190}{81} \, x^{3} - \frac {5287}{486} \, x^{2} + \frac {2287}{729} \, x + \frac {343}{2187 \, {\left (3 \, x + 2\right )}} + \frac {1813}{729} \, \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 = 39, normalized size = 0.71 \begin {gather*} \frac {2287\,x}{729}+\frac {1813\,\ln \left (x+\frac {2}{3}\right )}{729}+\frac {343}{6561\,\left (x+\frac {2}{3}\right )}-\frac {5287\,x^2}{486}-\frac {190\,x^3}{81}+\frac {775\,x^4}{27}-\frac {200\,x^5}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 48, normalized size = 0.87 \begin {gather*} - \frac {200 x^{5}}{9} + \frac {775 x^{4}}{27} - \frac {190 x^{3}}{81} - \frac {5287 x^{2}}{486} + \frac {2287 x}{729} + \frac {1813 \log {\left (3 x + 2 \right )}}{729} + \frac {343}{6561 x + 4374} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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