Optimal. Leaf size=49 \[ \frac{100 x}{81}-\frac{503}{81 (3 x+2)}+\frac{259}{243 (3 x+2)^2}-\frac{49}{729 (3 x+2)^3}-\frac{740}{243} \log (3 x+2) \]
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Rubi [A] time = 0.0190883, antiderivative size = 49, 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} \[ \frac{100 x}{81}-\frac{503}{81 (3 x+2)}+\frac{259}{243 (3 x+2)^2}-\frac{49}{729 (3 x+2)^3}-\frac{740}{243} \log (3 x+2) \]
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)^4} \, dx &=\int \left (\frac{100}{81}+\frac{49}{81 (2+3 x)^4}-\frac{518}{81 (2+3 x)^3}+\frac{503}{27 (2+3 x)^2}-\frac{740}{81 (2+3 x)}\right ) \, dx\\ &=\frac{100 x}{81}-\frac{49}{729 (2+3 x)^3}+\frac{259}{243 (2+3 x)^2}-\frac{503}{81 (2+3 x)}-\frac{740}{243} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0147521, size = 46, normalized size = 0.94 \[ \frac{24300 x^4+64800 x^3+24057 x^2-23193 x-2220 (3 x+2)^3 \log (3 x+2)-11803}{729 (3 x+2)^3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 40, normalized size = 0.8 \begin{align*}{\frac{100\,x}{81}}-{\frac{49}{729\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{259}{243\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{503}{162+243\,x}}-{\frac{740\,\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 = 1.04763, size = 55, normalized size = 1.12 \begin{align*} \frac{100}{81} \, x - \frac{40743 \, x^{2} + 51993 \, x + 16603}{729 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )}} - \frac{740}{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 = 1.51867, size = 186, normalized size = 3.8 \begin{align*} \frac{24300 \, x^{4} + 48600 \, x^{3} - 8343 \, x^{2} - 2220 \,{\left (27 \, x^{3} + 54 \, x^{2} + 36 \, x + 8\right )} \log \left (3 \, x + 2\right ) - 44793 \, x - 16603}{729 \,{\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 = 0.130502, size = 39, normalized size = 0.8 \begin{align*} \frac{100 x}{81} - \frac{40743 x^{2} + 51993 x + 16603}{19683 x^{3} + 39366 x^{2} + 26244 x + 5832} - \frac{740 \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 = 1.89968, size = 43, normalized size = 0.88 \begin{align*} \frac{100}{81} \, x - \frac{40743 \, x^{2} + 51993 \, x + 16603}{729 \,{\left (3 \, x + 2\right )}^{3}} - \frac{740}{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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