Optimal. Leaf size=44 \[ \frac{16}{9 (3 x+2)}-\frac{91}{54 (3 x+2)^2}+\frac{49}{243 (3 x+2)^3}+\frac{20}{81} \log (3 x+2) \]
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Rubi [A] time = 0.0170495, antiderivative size = 44, 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} \[ \frac{16}{9 (3 x+2)}-\frac{91}{54 (3 x+2)^2}+\frac{49}{243 (3 x+2)^3}+\frac{20}{81} \log (3 x+2) \]
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)^4} \, dx &=\int \left (-\frac{49}{27 (2+3 x)^4}+\frac{91}{9 (2+3 x)^3}-\frac{16}{3 (2+3 x)^2}+\frac{20}{27 (2+3 x)}\right ) \, dx\\ &=\frac{49}{243 (2+3 x)^3}-\frac{91}{54 (2+3 x)^2}+\frac{16}{9 (2+3 x)}+\frac{20}{81} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0132563, size = 36, normalized size = 0.82 \[ \frac{7776 x^2+7911 x+120 (3 x+2)^3 \log (3 x+2)+1916}{486 (3 x+2)^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 37, normalized size = 0.8 \begin{align*}{\frac{49}{243\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{91}{54\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{16}{18+27\,x}}+{\frac{20\,\ln \left ( 2+3\,x \right ) }{81}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.18492, size = 51, normalized size = 1.16 \begin{align*} \frac{7776 \, x^{2} + 7911 \, x + 1916}{486 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{20}{81} \, \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 = 1.54492, size = 150, normalized size = 3.41 \begin{align*} \frac{7776 \, x^{2} + 120 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) + 7911 \, x + 1916}{486 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.123864, size = 34, normalized size = 0.77 \begin{align*} \frac{7776 x^{2} + 7911 x + 1916}{13122 x^{3} + 26244 x^{2} + 17496 x + 3888} + \frac{20 \log{\left (3 x + 2 \right )}}{81} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.50807, size = 39, normalized size = 0.89 \begin{align*} \frac{7776 \, x^{2} + 7911 \, x + 1916}{486 \,{\left (3 \, x + 2\right )}^{3}} + \frac{20}{81} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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