Optimal. Leaf size=37 \[ \frac{25 x^4}{3}-\frac{140 x^3}{27}-\frac{251 x^2}{54}+\frac{340 x}{81}+\frac{49}{243} \log (3 x+2) \]
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Rubi [A] time = 0.0157756, antiderivative size = 37, 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} \[ \frac{25 x^4}{3}-\frac{140 x^3}{27}-\frac{251 x^2}{54}+\frac{340 x}{81}+\frac{49}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (3+5 x)^2}{2+3 x} \, dx &=\int \left (\frac{340}{81}-\frac{251 x}{27}-\frac{140 x^2}{9}+\frac{100 x^3}{3}+\frac{49}{81 (2+3 x)}\right ) \, dx\\ &=\frac{340 x}{81}-\frac{251 x^2}{54}-\frac{140 x^3}{27}+\frac{25 x^4}{3}+\frac{49}{243} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0086873, size = 32, normalized size = 0.86 \[ \frac{12150 x^4-7560 x^3-6777 x^2+6120 x+294 \log (3 x+2)+2452}{1458} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 28, normalized size = 0.8 \begin{align*}{\frac{340\,x}{81}}-{\frac{251\,{x}^{2}}{54}}-{\frac{140\,{x}^{3}}{27}}+{\frac{25\,{x}^{4}}{3}}+{\frac{49\,\ln \left ( 2+3\,x \right ) }{243}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.00507, size = 36, normalized size = 0.97 \begin{align*} \frac{25}{3} \, x^{4} - \frac{140}{27} \, x^{3} - \frac{251}{54} \, x^{2} + \frac{340}{81} \, x + \frac{49}{243} \, \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 = 1.57954, size = 93, normalized size = 2.51 \begin{align*} \frac{25}{3} \, x^{4} - \frac{140}{27} \, x^{3} - \frac{251}{54} \, x^{2} + \frac{340}{81} \, x + \frac{49}{243} \, \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 = 0.086662, size = 34, normalized size = 0.92 \begin{align*} \frac{25 x^{4}}{3} - \frac{140 x^{3}}{27} - \frac{251 x^{2}}{54} + \frac{340 x}{81} + \frac{49 \log{\left (3 x + 2 \right )}}{243} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.69126, size = 38, normalized size = 1.03 \begin{align*} \frac{25}{3} \, x^{4} - \frac{140}{27} \, x^{3} - \frac{251}{54} \, x^{2} + \frac{340}{81} \, x + \frac{49}{243} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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