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 = 0.03, antiderivative size = 67, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.02, 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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fricas [A] time = 0.61, size = 82, normalized size = 1.22 \[ -\frac {486000 \, x^{6} - 1652400 \, x^{5} - 6566400 \, x^{4} - 4903452 \, x^{3} + 1186182 \, x^{2} + 57560 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) + 2360364 \, x + 630195}{2916 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.87, size = 75, normalized size = 1.12 \[ \frac {100}{2187} \, {\left (3 \, x + 2\right )}^{2} {\left (\frac {111}{3 \, x + 2} - 5\right )} - \frac {66193}{2187 \, {\left (3 \, x + 2\right )}} + \frac {10073}{1458 \, {\left (3 \, x + 2\right )}^{2}} - \frac {1813}{2187 \, {\left (3 \, x + 2\right )}^{3}} + \frac {343}{8748 \, {\left (3 \, x + 2\right )}^{4}} + \frac {14390}{729} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 54, normalized size = 0.81 \[ -\frac {500 x^{2}}{243}+\frac {9100 x}{729}-\frac {14390 \ln \left (3 x +2\right )}{729}+\frac {343}{8748 \left (3 x +2\right )^{4}}-\frac {1813}{2187 \left (3 x +2\right )^{3}}+\frac {10073}{1458 \left (3 x +2\right )^{2}}-\frac {66193}{2187 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 56, normalized size = 0.84 \[ -\frac {500}{243} \, x^{2} + \frac {9100}{729} \, x - \frac {2382948 \, x^{3} + 4584582 \, x^{2} + 2942764 \, x + 630195}{2916 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} - \frac {14390}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 52, normalized size = 0.78 \[ \frac {9100\,x}{729}-\frac {14390\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {500\,x^2}{243}-\frac {\frac {66193\,x^3}{6561}+\frac {254699\,x^2}{13122}+\frac {735691\,x}{59049}+\frac {210065}{78732}}{x^4+\frac {8\,x^3}{3}+\frac {8\,x^2}{3}+\frac {32\,x}{27}+\frac {16}{81}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 56, normalized size = 0.84 \[ - \frac {500 x^{2}}{243} + \frac {9100 x}{729} - \frac {2382948 x^{3} + 4584582 x^{2} + 2942764 x + 630195}{236196 x^{4} + 629856 x^{3} + 629856 x^{2} + 279936 x + 46656} - \frac {14390 \log {\left (3 x + 2 \right )}}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
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