Optimal. Leaf size=34 \[ \frac{10 x^2}{9}-\frac{104 x}{27}+\frac{49}{81 (3 x+2)}+\frac{91}{27} \log (3 x+2) \]
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Rubi [A] time = 0.0142177, 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} \[ \frac{10 x^2}{9}-\frac{104 x}{27}+\frac{49}{81 (3 x+2)}+\frac{91}{27} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (3+5 x)}{(2+3 x)^2} \, dx &=\int \left (-\frac{104}{27}+\frac{20 x}{9}-\frac{49}{27 (2+3 x)^2}+\frac{91}{9 (2+3 x)}\right ) \, dx\\ &=-\frac{104 x}{27}+\frac{10 x^2}{9}+\frac{49}{81 (2+3 x)}+\frac{91}{27} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0126663, size = 39, normalized size = 1.15 \[ \frac{540 x^3-1512 x^2-447 x+546 (3 x+2) \log (6 x+4)+632}{162 (3 x+2)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 27, normalized size = 0.8 \begin{align*} -{\frac{104\,x}{27}}+{\frac{10\,{x}^{2}}{9}}+{\frac{49}{162+243\,x}}+{\frac{91\,\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 = 1.02621, size = 35, normalized size = 1.03 \begin{align*} \frac{10}{9} \, x^{2} - \frac{104}{27} \, x + \frac{49}{81 \,{\left (3 \, x + 2\right )}} + \frac{91}{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 = 1.4733, size = 105, normalized size = 3.09 \begin{align*} \frac{270 \, x^{3} - 756 \, x^{2} + 273 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) - 624 \, x + 49}{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 = 0.097296, size = 27, normalized size = 0.79 \begin{align*} \frac{10 x^{2}}{9} - \frac{104 x}{27} + \frac{91 \log{\left (3 x + 2 \right )}}{27} + \frac{49}{243 x + 162} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.9648, size = 65, normalized size = 1.91 \begin{align*} -\frac{2}{81} \,{\left (3 \, x + 2\right )}^{2}{\left (\frac{72}{3 \, x + 2} - 5\right )} + \frac{49}{81 \,{\left (3 \, x + 2\right )}} - \frac{91}{27} \, \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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