Optimal. Leaf size=34 \[ -\frac{25 x^2}{9}+\frac{95 x}{27}-\frac{7}{81 (3 x+2)}-\frac{8}{9} \log (3 x+2) \]
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Rubi [A] time = 0.0153246, antiderivative size = 34, 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} \[ -\frac{25 x^2}{9}+\frac{95 x}{27}-\frac{7}{81 (3 x+2)}-\frac{8}{9} \log (3 x+2) \]
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)^2} \, dx &=\int \left (\frac{95}{27}-\frac{50 x}{9}+\frac{7}{27 (2+3 x)^2}-\frac{8}{3 (2+3 x)}\right ) \, dx\\ &=\frac{95 x}{27}-\frac{25 x^2}{9}-\frac{7}{81 (2+3 x)}-\frac{8}{9} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0098726, size = 36, normalized size = 1.06 \[ \frac{-225 x^3+135 x^2+480 x-24 (3 x+2) \log (3 x+2)+191}{81 x+54} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 27, normalized size = 0.8 \begin{align*}{\frac{95\,x}{27}}-{\frac{25\,{x}^{2}}{9}}-{\frac{7}{162+243\,x}}-{\frac{8\,\ln \left ( 2+3\,x \right ) }{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08661, size = 35, normalized size = 1.03 \begin{align*} -\frac{25}{9} \, x^{2} + \frac{95}{27} \, x - \frac{7}{81 \,{\left (3 \, x + 2\right )}} - \frac{8}{9} \, \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 = 1.73467, size = 104, normalized size = 3.06 \begin{align*} -\frac{675 \, x^{3} - 405 \, x^{2} + 72 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 570 \, x + 7}{81 \,{\left (3 \, x + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.096711, size = 27, normalized size = 0.79 \begin{align*} - \frac{25 x^{2}}{9} + \frac{95 x}{27} - \frac{8 \log{\left (3 x + 2 \right )}}{9} - \frac{7}{243 x + 162} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.36877, size = 65, normalized size = 1.91 \begin{align*} \frac{5}{81} \,{\left (3 \, x + 2\right )}^{2}{\left (\frac{39}{3 \, x + 2} - 5\right )} - \frac{7}{81 \,{\left (3 \, x + 2\right )}} + \frac{8}{9} \, \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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