Optimal. Leaf size=56 \[ \frac{250 x^2}{81}-\frac{2800 x}{243}+\frac{4099}{729 (3 x+2)}-\frac{763}{1458 (3 x+2)^2}+\frac{49}{2187 (3 x+2)^3}+\frac{8285}{729} \log (3 x+2) \]
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Rubi [A] time = 0.0240618, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {88} \[ \frac{250 x^2}{81}-\frac{2800 x}{243}+\frac{4099}{729 (3 x+2)}-\frac{763}{1458 (3 x+2)^2}+\frac{49}{2187 (3 x+2)^3}+\frac{8285}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (3+5 x)^3}{(2+3 x)^4} \, dx &=\int \left (-\frac{2800}{243}+\frac{500 x}{81}-\frac{49}{243 (2+3 x)^4}+\frac{763}{243 (2+3 x)^3}-\frac{4099}{243 (2+3 x)^2}+\frac{8285}{243 (2+3 x)}\right ) \, dx\\ &=-\frac{2800 x}{243}+\frac{250 x^2}{81}+\frac{49}{2187 (2+3 x)^3}-\frac{763}{1458 (2+3 x)^2}+\frac{4099}{729 (2+3 x)}+\frac{8285}{729} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0330625, size = 51, normalized size = 0.91 \[ -\frac{-364500 x^5+631800 x^4+3304800 x^3+3623454 x^2+1540539 x-49710 (3 x+2)^3 \log (30 x+20)+222904}{4374 (3 x+2)^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 45, normalized size = 0.8 \begin{align*} -{\frac{2800\,x}{243}}+{\frac{250\,{x}^{2}}{81}}+{\frac{49}{2187\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{763}{1458\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{4099}{1458+2187\,x}}+{\frac{8285\,\ln \left ( 2+3\,x \right ) }{729}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.568, size = 62, normalized size = 1.11 \begin{align*} \frac{250}{81} \, x^{2} - \frac{2800}{243} \, x + \frac{221346 \, x^{2} + 288261 \, x + 93896}{4374 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} + \frac{8285}{729} \, \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 = 1.49909, size = 216, normalized size = 3.86 \begin{align*} \frac{364500 \, x^{5} - 631800 \, x^{4} - 2235600 \, x^{3} - 1485054 \, x^{2} + 49710 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 114939 \, x + 93896}{4374 \,{\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 = 0.133162, size = 46, normalized size = 0.82 \begin{align*} \frac{250 x^{2}}{81} - \frac{2800 x}{243} + \frac{221346 x^{2} + 288261 x + 93896}{118098 x^{3} + 236196 x^{2} + 157464 x + 34992} + \frac{8285 \log{\left (3 x + 2 \right )}}{729} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.90835, size = 50, normalized size = 0.89 \begin{align*} \frac{250}{81} \, x^{2} - \frac{2800}{243} \, x + \frac{221346 \, x^{2} + 288261 \, x + 93896}{4374 \,{\left (3 \, x + 2\right )}^{3}} + \frac{8285}{729} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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