Optimal. Leaf size=41 \[ -\frac{250 x^3}{27}+\frac{25 x^2}{54}+\frac{55 x}{9}+\frac{7}{243 (3 x+2)}+\frac{107}{243} \log (3 x+2) \]
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Rubi [A] time = 0.0180203, antiderivative size = 41, 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} \[ -\frac{250 x^3}{27}+\frac{25 x^2}{54}+\frac{55 x}{9}+\frac{7}{243 (3 x+2)}+\frac{107}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (3+5 x)^3}{(2+3 x)^2} \, dx &=\int \left (\frac{55}{9}+\frac{25 x}{27}-\frac{250 x^2}{9}-\frac{7}{81 (2+3 x)^2}+\frac{107}{81 (2+3 x)}\right ) \, dx\\ &=\frac{55 x}{9}+\frac{25 x^2}{54}-\frac{250 x^3}{27}+\frac{7}{243 (2+3 x)}+\frac{107}{243} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0106505, size = 44, normalized size = 1.07 \[ \frac{-40500 x^4-24975 x^3+28080 x^2+22740 x+642 (3 x+2) \log (3 x+2)+3322}{1458 (3 x+2)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 32, normalized size = 0.8 \begin{align*}{\frac{55\,x}{9}}+{\frac{25\,{x}^{2}}{54}}-{\frac{250\,{x}^{3}}{27}}+{\frac{7}{486+729\,x}}+{\frac{107\,\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 = 1.14508, size = 42, normalized size = 1.02 \begin{align*} -\frac{250}{27} \, x^{3} + \frac{25}{54} \, x^{2} + \frac{55}{9} \, x + \frac{7}{243 \,{\left (3 \, x + 2\right )}} + \frac{107}{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 = 1.69136, size = 128, normalized size = 3.12 \begin{align*} -\frac{13500 \, x^{4} + 8325 \, x^{3} - 9360 \, x^{2} - 214 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 5940 \, x - 14}{486 \,{\left (3 \, x + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.101294, size = 34, normalized size = 0.83 \begin{align*} - \frac{250 x^{3}}{27} + \frac{25 x^{2}}{54} + \frac{55 x}{9} + \frac{107 \log{\left (3 x + 2 \right )}}{243} + \frac{7}{729 x + 486} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.92006, size = 77, normalized size = 1.88 \begin{align*} \frac{5}{1458} \,{\left (3 \, x + 2\right )}^{3}{\left (\frac{615}{3 \, x + 2} - \frac{666}{{\left (3 \, x + 2\right )}^{2}} - 100\right )} + \frac{7}{243 \,{\left (3 \, x + 2\right )}} - \frac{107}{243} \, \log \left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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