Optimal. Leaf size=60 \[ -\frac{200 x}{243}+\frac{8198}{729 (3 x+2)}-\frac{11599}{1458 (3 x+2)^2}+\frac{3724}{2187 (3 x+2)^3}-\frac{343}{2916 (3 x+2)^4}+\frac{2180}{729} \log (3 x+2) \]
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Rubi [A] time = 0.0250564, antiderivative size = 60, 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} \[ -\frac{200 x}{243}+\frac{8198}{729 (3 x+2)}-\frac{11599}{1458 (3 x+2)^2}+\frac{3724}{2187 (3 x+2)^3}-\frac{343}{2916 (3 x+2)^4}+\frac{2180}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (3+5 x)^2}{(2+3 x)^5} \, dx &=\int \left (-\frac{200}{243}+\frac{343}{243 (2+3 x)^5}-\frac{3724}{243 (2+3 x)^4}+\frac{11599}{243 (2+3 x)^3}-\frac{8198}{243 (2+3 x)^2}+\frac{2180}{243 (2+3 x)}\right ) \, dx\\ &=-\frac{200 x}{243}-\frac{343}{2916 (2+3 x)^4}+\frac{3724}{2187 (2+3 x)^3}-\frac{11599}{1458 (2+3 x)^2}+\frac{8198}{729 (2+3 x)}+\frac{2180}{729} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0308321, size = 51, normalized size = 0.85 \[ \frac{-583200 x^5-1944000 x^4+64152 x^3+2957958 x^2+2175096 x+26160 (3 x+2)^4 \log (30 x+20)+460595}{8748 (3 x+2)^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 49, normalized size = 0.8 \begin{align*} -{\frac{200\,x}{243}}-{\frac{343}{2916\, \left ( 2+3\,x \right ) ^{4}}}+{\frac{3724}{2187\, \left ( 2+3\,x \right ) ^{3}}}-{\frac{11599}{1458\, \left ( 2+3\,x \right ) ^{2}}}+{\frac{8198}{1458+2187\,x}}+{\frac{2180\,\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 = 1.00035, size = 69, normalized size = 1.15 \begin{align*} -\frac{200}{243} \, x + \frac{2656152 \, x^{3} + 4685958 \, x^{2} + 2751096 \, x + 537395}{8748 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} + \frac{2180}{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 = 1.2749, size = 254, normalized size = 4.23 \begin{align*} -\frac{583200 \, x^{5} + 1555200 \, x^{4} - 1100952 \, x^{3} - 3994758 \, x^{2} - 26160 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) - 2635896 \, x - 537395}{8748 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.146456, size = 49, normalized size = 0.82 \begin{align*} - \frac{200 x}{243} + \frac{2656152 x^{3} + 4685958 x^{2} + 2751096 x + 537395}{708588 x^{4} + 1889568 x^{3} + 1889568 x^{2} + 839808 x + 139968} + \frac{2180 \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 = 2.93062, size = 80, normalized size = 1.33 \begin{align*} -\frac{200}{243} \, x + \frac{8198}{729 \,{\left (3 \, x + 2\right )}} - \frac{11599}{1458 \,{\left (3 \, x + 2\right )}^{2}} + \frac{3724}{2187 \,{\left (3 \, x + 2\right )}^{3}} - \frac{343}{2916 \,{\left (3 \, x + 2\right )}^{4}} - \frac{2180}{729} \, \log \left (\frac{{\left | 3 \, x + 2 \right |}}{3 \,{\left (3 \, x + 2\right )}^{2}}\right ) - \frac{400}{729} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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