Optimal. Leaf size=27 \[ -\frac{10 x}{9}+\frac{7}{27 (3 x+2)}+\frac{37}{27} \log (3 x+2) \]
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Rubi [A] time = 0.012331, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {77} \[ -\frac{10 x}{9}+\frac{7}{27 (3 x+2)}+\frac{37}{27} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x) (3+5 x)}{(2+3 x)^2} \, dx &=\int \left (-\frac{10}{9}-\frac{7}{9 (2+3 x)^2}+\frac{37}{9 (2+3 x)}\right ) \, dx\\ &=-\frac{10 x}{9}+\frac{7}{27 (2+3 x)}+\frac{37}{27} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0099498, size = 26, normalized size = 0.96 \[ \frac{1}{27} \left (-30 x+\frac{7}{3 x+2}+37 \log (3 x+2)-20\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 22, normalized size = 0.8 \begin{align*} -{\frac{10\,x}{9}}+{\frac{7}{54+81\,x}}+{\frac{37\,\ln \left ( 2+3\,x \right ) }{27}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.13441, size = 28, normalized size = 1.04 \begin{align*} -\frac{10}{9} \, x + \frac{7}{27 \,{\left (3 \, x + 2\right )}} + \frac{37}{27} \, \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 = 1.4763, size = 88, normalized size = 3.26 \begin{align*} -\frac{90 \, x^{2} - 37 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 60 \, x - 7}{27 \,{\left (3 \, x + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.091926, size = 20, normalized size = 0.74 \begin{align*} - \frac{10 x}{9} + \frac{37 \log{\left (3 x + 2 \right )}}{27} + \frac{7}{81 x + 54} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.95895, size = 43, normalized size = 1.59 \begin{align*} -\frac{10}{9} \, x + \frac{7}{27 \,{\left (3 \, x + 2\right )}} - \frac{37}{27} \, \log \left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) - \frac{20}{27} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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