Optimal. Leaf size=67 \[ -\frac{500 x^2}{243}+\frac{9100 x}{729}-\frac{66193}{2187 (3 x+2)}+\frac{10073}{1458 (3 x+2)^2}-\frac{1813}{2187 (3 x+2)^3}+\frac{343}{8748 (3 x+2)^4}-\frac{14390}{729} \log (3 x+2) \]
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Rubi [A] time = 0.0303992, antiderivative size = 67, 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} \[ -\frac{500 x^2}{243}+\frac{9100 x}{729}-\frac{66193}{2187 (3 x+2)}+\frac{10073}{1458 (3 x+2)^2}-\frac{1813}{2187 (3 x+2)^3}+\frac{343}{8748 (3 x+2)^4}-\frac{14390}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin{align*} \int \frac{(1-2 x)^3 (3+5 x)^3}{(2+3 x)^5} \, dx &=\int \left (\frac{9100}{729}-\frac{1000 x}{243}-\frac{343}{729 (2+3 x)^5}+\frac{1813}{243 (2+3 x)^4}-\frac{10073}{243 (2+3 x)^3}+\frac{66193}{729 (2+3 x)^2}-\frac{14390}{243 (2+3 x)}\right ) \, dx\\ &=\frac{9100 x}{729}-\frac{500 x^2}{243}+\frac{343}{8748 (2+3 x)^4}-\frac{1813}{2187 (2+3 x)^3}+\frac{10073}{1458 (2+3 x)^2}-\frac{66193}{2187 (2+3 x)}-\frac{14390}{729} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0171684, size = 56, normalized size = 0.84 \[ \frac{-1458000 x^6+4957200 x^5+26244000 x^4+32163156 x^3+13894254 x^2+675708 x-172680 (3 x+2)^4 \log (3 x+2)-597785}{8748 (3 x+2)^4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 54, normalized size = 0.8 \begin{align*}{\frac{9100\,x}{729}}-{\frac{500\,{x}^{2}}{243}}+{\frac{343}{8748\, \left ( 2+3\,x \right ) ^{4}}}-{\frac{1813}{2187\, \left ( 2+3\,x \right ) ^{3}}}+{\frac{10073}{1458\, \left ( 2+3\,x \right ) ^{2}}}-{\frac{66193}{4374+6561\,x}}-{\frac{14390\,\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 = 2.46738, size = 76, normalized size = 1.13 \begin{align*} -\frac{500}{243} \, x^{2} + \frac{9100}{729} \, x - \frac{2382948 \, x^{3} + 4584582 \, x^{2} + 2942764 \, x + 630195}{2916 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} - \frac{14390}{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 = 1.35123, size = 273, normalized size = 4.07 \begin{align*} -\frac{486000 \, x^{6} - 1652400 \, x^{5} - 6566400 \, x^{4} - 4903452 \, x^{3} + 1186182 \, x^{2} + 57560 \,{\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 2360364 \, x + 630195}{2916 \,{\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 = 0.148324, size = 56, normalized size = 0.84 \begin{align*} - \frac{500 x^{2}}{243} + \frac{9100 x}{729} - \frac{2382948 x^{3} + 4584582 x^{2} + 2942764 x + 630195}{236196 x^{4} + 629856 x^{3} + 629856 x^{2} + 279936 x + 46656} - \frac{14390 \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 = 3.08148, size = 101, normalized size = 1.51 \begin{align*} \frac{100}{2187} \,{\left (3 \, x + 2\right )}^{2}{\left (\frac{111}{3 \, x + 2} - 5\right )} - \frac{66193}{2187 \,{\left (3 \, x + 2\right )}} + \frac{10073}{1458 \,{\left (3 \, x + 2\right )}^{2}} - \frac{1813}{2187 \,{\left (3 \, x + 2\right )}^{3}} + \frac{343}{8748 \,{\left (3 \, x + 2\right )}^{4}} + \frac{14390}{729} \, \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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