Optimal. Leaf size=49 \[ -\frac{40 x}{81}+\frac{518}{81 (3 x+2)}-\frac{2009}{486 (3 x+2)^2}+\frac{343}{729 (3 x+2)^3}+\frac{428}{243} \log (3 x+2) \]
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Rubi [A] time = 0.0202781, antiderivative size = 49, 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} \[ -\frac{40 x}{81}+\frac{518}{81 (3 x+2)}-\frac{2009}{486 (3 x+2)^2}+\frac{343}{729 (3 x+2)^3}+\frac{428}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 77
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (3+5 x)}{(2+3 x)^4} \, dx &=\int \left (-\frac{40}{81}-\frac{343}{81 (2+3 x)^4}+\frac{2009}{81 (2+3 x)^3}-\frac{518}{27 (2+3 x)^2}+\frac{428}{81 (2+3 x)}\right ) \, dx\\ &=-\frac{40 x}{81}+\frac{343}{729 (2+3 x)^3}-\frac{2009}{486 (2+3 x)^2}+\frac{518}{81 (2+3 x)}+\frac{428}{243} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0147109, size = 46, normalized size = 0.94 \[ \frac{-19440 x^4-51840 x^3+32076 x^2+70767 x+2568 (3 x+2)^3 \log (3 x+2)+22088}{1458 (3 x+2)^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 40, normalized size = 0.8 \begin{align*} -{\frac{40\,x}{81}}+{\frac{343}{729\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{2009}{486\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{518}{162+243\,x}}+{\frac{428\,\ln \left ( 2+3\,x \right ) }{243}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04761, size = 55, normalized size = 1.12 \begin{align*} -\frac{40}{81} \, x + \frac{7 \,{\left (11988 \, x^{2} + 13401 \, x + 3704\right )}}{1458 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{428}{243} \, \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 = 1.32111, size = 190, normalized size = 3.88 \begin{align*} -\frac{19440 \, x^{4} + 38880 \, x^{3} - 57996 \, x^{2} - 2568 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 88047 \, x - 25928}{1458 \,{\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 = 0.129777, size = 39, normalized size = 0.8 \begin{align*} - \frac{40 x}{81} + \frac{83916 x^{2} + 93807 x + 25928}{39366 x^{3} + 78732 x^{2} + 52488 x + 11664} + \frac{428 \log{\left (3 x + 2 \right )}}{243} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 3.22229, size = 43, normalized size = 0.88 \begin{align*} -\frac{40}{81} \, x + \frac{7 \,{\left (11988 \, x^{2} + 13401 \, x + 3704\right )}}{1458 \,{\left (3 \, x + 2\right )}^{3}} + \frac{428}{243} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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