Optimal. Leaf size=37 \[ -\frac{10 x^4}{3}+\frac{188 x^3}{27}-\frac{161 x^2}{27}+\frac{293 x}{81}-\frac{343}{243} \log (3 x+2) \]
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Rubi [A] time = 0.0133814, antiderivative size = 37, 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} \[ -\frac{10 x^4}{3}+\frac{188 x^3}{27}-\frac{161 x^2}{27}+\frac{293 x}{81}-\frac{343}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (3+5 x)}{2+3 x} \, dx &=\int \left (\frac{293}{81}-\frac{322 x}{27}+\frac{188 x^2}{9}-\frac{40 x^3}{3}-\frac{343}{81 (2+3 x)}\right ) \, dx\\ &=\frac{293 x}{81}-\frac{161 x^2}{27}+\frac{188 x^3}{27}-\frac{10 x^4}{3}-\frac{343}{243} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0114267, size = 32, normalized size = 0.86 \[ \frac{1}{729} \left (-2430 x^4+5076 x^3-4347 x^2+2637 x-1029 \log (3 x+2)+5674\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 28, normalized size = 0.8 \begin{align*}{\frac{293\,x}{81}}-{\frac{161\,{x}^{2}}{27}}+{\frac{188\,{x}^{3}}{27}}-{\frac{10\,{x}^{4}}{3}}-{\frac{343\,\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 = 1.03237, size = 36, normalized size = 0.97 \begin{align*} -\frac{10}{3} \, x^{4} + \frac{188}{27} \, x^{3} - \frac{161}{27} \, x^{2} + \frac{293}{81} \, x - \frac{343}{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 = 1.26892, size = 96, normalized size = 2.59 \begin{align*} -\frac{10}{3} \, x^{4} + \frac{188}{27} \, x^{3} - \frac{161}{27} \, x^{2} + \frac{293}{81} \, x - \frac{343}{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 = 0.087991, size = 34, normalized size = 0.92 \begin{align*} - \frac{10 x^{4}}{3} + \frac{188 x^{3}}{27} - \frac{161 x^{2}}{27} + \frac{293 x}{81} - \frac{343 \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 = 2.73058, size = 38, normalized size = 1.03 \begin{align*} -\frac{10}{3} \, x^{4} + \frac{188}{27} \, x^{3} - \frac{161}{27} \, x^{2} + \frac{293}{81} \, x - \frac{343}{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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