Optimal. Leaf size=41 \[ \frac{100 x^3}{27}-\frac{170 x^2}{27}+\frac{143 x}{27}-\frac{49}{243 (3 x+2)}-\frac{518}{243} \log (3 x+2) \]
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Rubi [A] time = 0.0201524, antiderivative size = 41, 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} \[ \frac{100 x^3}{27}-\frac{170 x^2}{27}+\frac{143 x}{27}-\frac{49}{243 (3 x+2)}-\frac{518}{243} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^2 (3+5 x)^2}{(2+3 x)^2} \, dx &=\int \left (\frac{143}{27}-\frac{340 x}{27}+\frac{100 x^2}{9}+\frac{49}{81 (2+3 x)^2}-\frac{518}{81 (2+3 x)}\right ) \, dx\\ &=\frac{143 x}{27}-\frac{170 x^2}{27}+\frac{100 x^3}{27}-\frac{49}{243 (2+3 x)}-\frac{518}{243} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0124739, size = 44, normalized size = 1.07 \[ \frac{8100 x^4-8370 x^3+2403 x^2+23964 x-1554 (3 x+2) \log (3 x+2)+10681}{729 (3 x+2)} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 32, normalized size = 0.8 \begin{align*}{\frac{143\,x}{27}}-{\frac{170\,{x}^{2}}{27}}+{\frac{100\,{x}^{3}}{27}}-{\frac{49}{486+729\,x}}-{\frac{518\,\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 = 1.00288, size = 42, normalized size = 1.02 \begin{align*} \frac{100}{27} \, x^{3} - \frac{170}{27} \, x^{2} + \frac{143}{27} \, x - \frac{49}{243 \,{\left (3 \, x + 2\right )}} - \frac{518}{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 = 1.53674, size = 124, normalized size = 3.02 \begin{align*} \frac{2700 \, x^{4} - 2790 \, x^{3} + 801 \, x^{2} - 518 \,{\left (3 \, x + 2\right )} \log \left (3 \, x + 2\right ) + 2574 \, x - 49}{243 \,{\left (3 \, x + 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.099565, size = 34, normalized size = 0.83 \begin{align*} \frac{100 x^{3}}{27} - \frac{170 x^{2}}{27} + \frac{143 x}{27} - \frac{518 \log{\left (3 x + 2 \right )}}{243} - \frac{49}{729 x + 486} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.88793, size = 77, normalized size = 1.88 \begin{align*} -\frac{1}{729} \,{\left (3 \, x + 2\right )}^{3}{\left (\frac{1110}{3 \, x + 2} - \frac{4527}{{\left (3 \, x + 2\right )}^{2}} - 100\right )} - \frac{49}{243 \,{\left (3 \, x + 2\right )}} + \frac{518}{243} \, \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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