Optimal. Leaf size=60 \[ \frac {500 x}{243}-\frac {8285}{729 (3 x+2)}+\frac {4099}{1458 (3 x+2)^2}-\frac {763}{2187 (3 x+2)^3}+\frac {49}{2916 (3 x+2)^4}-\frac {3800}{729} \log (3 x+2) \]
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Rubi [A] time = 0.03, antiderivative size = 60, 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} \[ \frac {500 x}{243}-\frac {8285}{729 (3 x+2)}+\frac {4099}{1458 (3 x+2)^2}-\frac {763}{2187 (3 x+2)^3}+\frac {49}{2916 (3 x+2)^4}-\frac {3800}{729} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^5} \, dx &=\int \left (\frac {500}{243}-\frac {49}{243 (2+3 x)^5}+\frac {763}{243 (2+3 x)^4}-\frac {4099}{243 (2+3 x)^3}+\frac {8285}{243 (2+3 x)^2}-\frac {3800}{243 (2+3 x)}\right ) \, dx\\ &=\frac {500 x}{243}+\frac {49}{2916 (2+3 x)^4}-\frac {763}{2187 (2+3 x)^3}+\frac {4099}{1458 (2+3 x)^2}-\frac {8285}{729 (2+3 x)}-\frac {3800}{729} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.04, size = 51, normalized size = 0.85 \[ \frac {1458000 x^5+4860000 x^4+3795660 x^3-827334 x^2-1853148 x-45600 (3 x+2)^4 \log (30 x+20)-510941}{8748 (3 x+2)^4} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 77, normalized size = 1.28 \[ \frac {1458000 \, x^{5} + 3888000 \, x^{4} + 1203660 \, x^{3} - 3419334 \, x^{2} - 45600 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) - 3005148 \, x - 702941}{8748 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.13, size = 59, normalized size = 0.98 \[ \frac {500}{243} \, x - \frac {8285}{729 \, {\left (3 \, x + 2\right )}} + \frac {4099}{1458 \, {\left (3 \, x + 2\right )}^{2}} - \frac {763}{2187 \, {\left (3 \, x + 2\right )}^{3}} + \frac {49}{2916 \, {\left (3 \, x + 2\right )}^{4}} + \frac {3800}{729} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) + \frac {1000}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 49, normalized size = 0.82 \[ \frac {500 x}{243}-\frac {3800 \ln \left (3 x +2\right )}{729}+\frac {49}{2916 \left (3 x +2\right )^{4}}-\frac {763}{2187 \left (3 x +2\right )^{3}}+\frac {4099}{1458 \left (3 x +2\right )^{2}}-\frac {8285}{729 \left (3 x +2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 51, normalized size = 0.85 \[ \frac {500}{243} \, x - \frac {2684340 \, x^{3} + 5147334 \, x^{2} + 3293148 \, x + 702941}{8748 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} - \frac {3800}{729} \, \log \left (3 \, x + 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 47, normalized size = 0.78 \[ \frac {500\,x}{243}-\frac {3800\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {\frac {8285\,x^3}{2187}+\frac {95321\,x^2}{13122}+\frac {274429\,x}{59049}+\frac {702941}{708588}}{x^4+\frac {8\,x^3}{3}+\frac {8\,x^2}{3}+\frac {32\,x}{27}+\frac {16}{81}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 51, normalized size = 0.85 \[ \frac {500 x}{243} + \frac {- 2684340 x^{3} - 5147334 x^{2} - 3293148 x - 702941}{708588 x^{4} + 1889568 x^{3} + 1889568 x^{2} + 839808 x + 139968} - \frac {3800 \log {\left (3 x + 2 \right )}}{729} \]
Verification of antiderivative is not currently implemented for this CAS.
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