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 = 0.0222937, antiderivative size = 51, normalized size of antiderivative = 1., 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} \[ -\frac{500 x^6}{9}+\frac{220 x^5}{9}+\frac{2815 x^4}{54}-\frac{6427 x^3}{243}-\frac{8287 x^2}{486}+\frac{10013 x}{729}-\frac{343 \log (3 x+2)}{2187} \]
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*}
Mathematica [A] time = 0.0106253, size = 42, normalized size = 0.82 \[ \frac{-243000 x^6+106920 x^5+228015 x^4-115686 x^3-74583 x^2+60078 x-686 \log (3 x+2)+29296}{4374} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 38, normalized size = 0.8 \begin{align*}{\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\,\ln \left ( 2+3\,x \right ) }{2187}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02309, size = 50, normalized size = 0.98 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.24149, size = 143, normalized size = 2.8 \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.093385, size = 48, normalized size = 0.94 \begin{align*} - \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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.07905, size = 51, normalized size = 1. \begin{align*} -\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{align*}
Verification of antiderivative is not currently implemented for this CAS.
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