Optimal. Leaf size=30 \[ -\frac{50 x^3}{9}-\frac{5 x^2}{18}+\frac{118 x}{27}+\frac{7}{81} \log (3 x+2) \]
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Rubi [A] time = 0.0126983, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {77} \[ -\frac{50 x^3}{9}-\frac{5 x^2}{18}+\frac{118 x}{27}+\frac{7}{81} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (3+5 x)^2}{2+3 x} \, dx &=\int \left (\frac{118}{27}-\frac{5 x}{9}-\frac{50 x^2}{3}+\frac{7}{27 (2+3 x)}\right ) \, dx\\ &=\frac{118 x}{27}-\frac{5 x^2}{18}-\frac{50 x^3}{9}+\frac{7}{81} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0094917, size = 27, normalized size = 0.9 \[ \frac{1}{486} \left (-2700 x^3-135 x^2+2124 x+42 \log (3 x+2)+676\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 23, normalized size = 0.8 \begin{align*}{\frac{118\,x}{27}}-{\frac{5\,{x}^{2}}{18}}-{\frac{50\,{x}^{3}}{9}}+{\frac{7\,\ln \left ( 2+3\,x \right ) }{81}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.10636, size = 30, normalized size = 1. \begin{align*} -\frac{50}{9} \, x^{3} - \frac{5}{18} \, x^{2} + \frac{118}{27} \, x + \frac{7}{81} \, \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 = 1.74567, size = 72, normalized size = 2.4 \begin{align*} -\frac{50}{9} \, x^{3} - \frac{5}{18} \, x^{2} + \frac{118}{27} \, x + \frac{7}{81} \, \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 = 0.08637, size = 27, normalized size = 0.9 \begin{align*} - \frac{50 x^{3}}{9} - \frac{5 x^{2}}{18} + \frac{118 x}{27} + \frac{7 \log{\left (3 x + 2 \right )}}{81} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.86205, size = 31, normalized size = 1.03 \begin{align*} -\frac{50}{9} \, x^{3} - \frac{5}{18} \, x^{2} + \frac{118}{27} \, x + \frac{7}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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