Optimal. Leaf size=56 \[ -\frac{100 x^2}{81}+\frac{1780 x}{243}-\frac{11599}{729 (3 x+2)}+\frac{1862}{729 (3 x+2)^2}-\frac{343}{2187 (3 x+2)^3}-\frac{8198}{729} \log (3 x+2) \]
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Rubi [A] time = 0.0248844, antiderivative size = 56, 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} \[ -\frac{100 x^2}{81}+\frac{1780 x}{243}-\frac{11599}{729 (3 x+2)}+\frac{1862}{729 (3 x+2)^2}-\frac{343}{2187 (3 x+2)^3}-\frac{8198}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^4} \, dx &=\int \left (\frac{1780}{243}-\frac{200 x}{81}+\frac{343}{243 (2+3 x)^4}-\frac{3724}{243 (2+3 x)^3}+\frac{11599}{243 (2+3 x)^2}-\frac{8198}{243 (2+3 x)}\right ) \, dx\\ &=\frac{1780 x}{243}-\frac{100 x^2}{81}-\frac{343}{2187 (2+3 x)^3}+\frac{1862}{729 (2+3 x)^2}-\frac{11599}{729 (2+3 x)}-\frac{8198}{729} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0304204, size = 51, normalized size = 0.91 \[ \frac{-72900 x^5+286740 x^4+1088640 x^3+883467 x^2+155034 x-24594 (3 x+2)^3 \log (30 x+20)-33319}{2187 (3 x+2)^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 45, normalized size = 0.8 \begin{align*}{\frac{1780\,x}{243}}-{\frac{100\,{x}^{2}}{81}}-{\frac{343}{2187\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{1862}{729\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{11599}{1458+2187\,x}}-{\frac{8198\,\ln \left ( 2+3\,x \right ) }{729}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0276, size = 62, normalized size = 1.11 \begin{align*} -\frac{100}{81} \, x^{2} + \frac{1780}{243} \, x - \frac{7 \,{\left (44739 \, x^{2} + 57258 \, x + 18337\right )}}{2187 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} - \frac{8198}{729} \, \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 = 1.2703, size = 215, normalized size = 3.84 \begin{align*} -\frac{72900 \, x^{5} - 286740 \, x^{4} - 767880 \, x^{3} - 241947 \, x^{2} + 24594 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 272646 \, x + 128359}{2187 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.137804, size = 46, normalized size = 0.82 \begin{align*} - \frac{100 x^{2}}{81} + \frac{1780 x}{243} - \frac{313173 x^{2} + 400806 x + 128359}{59049 x^{3} + 118098 x^{2} + 78732 x + 17496} - \frac{8198 \log{\left (3 x + 2 \right )}}{729} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.91719, size = 50, normalized size = 0.89 \begin{align*} -\frac{100}{81} \, x^{2} + \frac{1780}{243} \, x - \frac{7 \,{\left (44739 \, x^{2} + 57258 \, x + 18337\right )}}{2187 \,{\left (3 \, x + 2\right )}^{3}} - \frac{8198}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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