Optimal. Leaf size=38 \[ \frac{20 x}{27}-\frac{91}{27 (3 x+2)}+\frac{49}{162 (3 x+2)^2}-\frac{16}{9} \log (3 x+2) \]
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Rubi [A] time = 0.0151843, antiderivative size = 38, 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} \[ \frac{20 x}{27}-\frac{91}{27 (3 x+2)}+\frac{49}{162 (3 x+2)^2}-\frac{16}{9} \log (3 x+2) \]
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)^3} \, dx &=\int \left (\frac{20}{27}-\frac{49}{27 (2+3 x)^3}+\frac{91}{9 (2+3 x)^2}-\frac{16}{3 (2+3 x)}\right ) \, dx\\ &=\frac{20 x}{27}+\frac{49}{162 (2+3 x)^2}-\frac{91}{27 (2+3 x)}-\frac{16}{9} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0139426, size = 41, normalized size = 1.08 \[ \frac{1080 x^3+900 x^2-1878 x-288 (3 x+2)^2 \log (6 x+4)-1283}{162 (3 x+2)^2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 31, normalized size = 0.8 \begin{align*}{\frac{20\,x}{27}}+{\frac{49}{162\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{91}{54+81\,x}}-{\frac{16\,\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 = 1.076, size = 42, normalized size = 1.11 \begin{align*} \frac{20}{27} \, x - \frac{7 \,{\left (234 \, x + 149\right )}}{162 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} - \frac{16}{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 = 1.45406, size = 138, normalized size = 3.63 \begin{align*} \frac{1080 \, x^{3} + 1440 \, x^{2} - 288 \,{\left (9 \, x^{2} + 12 \, x + 4\right )} \log \left (3 \, x + 2\right ) - 1158 \, x - 1043}{162 \,{\left (9 \, x^{2} + 12 \, x + 4\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.112872, size = 29, normalized size = 0.76 \begin{align*} \frac{20 x}{27} - \frac{1638 x + 1043}{1458 x^{2} + 1944 x + 648} - \frac{16 \log{\left (3 x + 2 \right )}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.7328, size = 36, normalized size = 0.95 \begin{align*} \frac{20}{27} \, x - \frac{7 \,{\left (234 \, x + 149\right )}}{162 \,{\left (3 \, x + 2\right )}^{2}} - \frac{16}{9} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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