Integrand size = 22, antiderivative size = 60 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^5} \, dx=\frac {500 x}{243}+\frac {49}{2916 (2+3 x)^4}-\frac {763}{2187 (2+3 x)^3}+\frac {4099}{1458 (2+3 x)^2}-\frac {8285}{729 (2+3 x)}-\frac {3800}{729} \log (2+3 x) \]
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Time = 0.02 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90} \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^5} \, dx=\frac {500 x}{243}-\frac {8285}{729 (3 x+2)}+\frac {4099}{1458 (3 x+2)^2}-\frac {763}{2187 (3 x+2)^3}+\frac {49}{2916 (3 x+2)^4}-\frac {3800}{729} \log (3 x+2) \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \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*}
Time = 0.03 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.85 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^5} \, dx=\frac {-510941-1853148 x-827334 x^2+3795660 x^3+4860000 x^4+1458000 x^5-45600 (2+3 x)^4 \log (20+30 x)}{8748 (2+3 x)^4} \]
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Time = 2.46 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.62
method | result | size |
risch | \(\frac {500 x}{243}+\frac {-\frac {8285}{27} x^{3}-\frac {95321}{162} x^{2}-\frac {274429}{729} x -\frac {702941}{8748}}{\left (2+3 x \right )^{4}}-\frac {3800 \ln \left (2+3 x \right )}{729}\) | \(37\) |
norman | \(\frac {\frac {449657}{648} x^{2}+\frac {792101}{648} x^{3}+\frac {67361}{486} x +\frac {1470941}{1728} x^{4}+\frac {500}{3} x^{5}}{\left (2+3 x \right )^{4}}-\frac {3800 \ln \left (2+3 x \right )}{729}\) | \(42\) |
default | \(\frac {500 x}{243}+\frac {49}{2916 \left (2+3 x \right )^{4}}-\frac {763}{2187 \left (2+3 x \right )^{3}}+\frac {4099}{1458 \left (2+3 x \right )^{2}}-\frac {8285}{729 \left (2+3 x \right )}-\frac {3800 \ln \left (2+3 x \right )}{729}\) | \(49\) |
parallelrisch | \(-\frac {19699200 \ln \left (\frac {2}{3}+x \right ) x^{4}-7776000 x^{5}+52531200 \ln \left (\frac {2}{3}+x \right ) x^{3}-39715407 x^{4}+52531200 \ln \left (\frac {2}{3}+x \right ) x^{2}-57031272 x^{3}+23347200 \ln \left (\frac {2}{3}+x \right ) x -32375304 x^{2}+3891200 \ln \left (\frac {2}{3}+x \right )-6466656 x}{46656 \left (2+3 x \right )^{4}}\) | \(74\) |
meijerg | \(\frac {27 x \left (\frac {27}{8} x^{3}+9 x^{2}+9 x +4\right )}{128 \left (1+\frac {3 x}{2}\right )^{4}}+\frac {9 x^{2} \left (\frac {9}{4} x^{2}+6 x +6\right )}{128 \left (1+\frac {3 x}{2}\right )^{4}}-\frac {69 x^{3} \left (\frac {3 x}{2}+4\right )}{128 \left (1+\frac {3 x}{2}\right )^{4}}-\frac {235 x^{4}}{128 \left (1+\frac {3 x}{2}\right )^{4}}-\frac {10 x \left (\frac {3375}{8} x^{3}+585 x^{2}+315 x +60\right )}{243 \left (1+\frac {3 x}{2}\right )^{4}}-\frac {3800 \ln \left (1+\frac {3 x}{2}\right )}{729}+\frac {125 x \left (\frac {243}{4} x^{4}+\frac {3375}{8} x^{3}+585 x^{2}+315 x +60\right )}{729 \left (1+\frac {3 x}{2}\right )^{4}}\) | \(141\) |
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none
Time = 0.22 (sec) , antiderivative size = 77, normalized size of antiderivative = 1.28 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^5} \, dx=\frac {1458000 \, x^{5} + 3888000 \, x^{4} + 1203660 \, x^{3} - 3419334 \, x^{2} - 45600 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )} \log \left (3 \, x + 2\right ) - 3005148 \, x - 702941}{8748 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.85 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^5} \, dx=\frac {500 x}{243} + \frac {- 2684340 x^{3} - 5147334 x^{2} - 3293148 x - 702941}{708588 x^{4} + 1889568 x^{3} + 1889568 x^{2} + 839808 x + 139968} - \frac {3800 \log {\left (3 x + 2 \right )}}{729} \]
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Time = 0.20 (sec) , antiderivative size = 51, normalized size of antiderivative = 0.85 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^5} \, dx=\frac {500}{243} \, x - \frac {2684340 \, x^{3} + 5147334 \, x^{2} + 3293148 \, x + 702941}{8748 \, {\left (81 \, x^{4} + 216 \, x^{3} + 216 \, x^{2} + 96 \, x + 16\right )}} - \frac {3800}{729} \, \log \left (3 \, x + 2\right ) \]
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Time = 0.28 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.98 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^5} \, dx=\frac {500}{243} \, x - \frac {8285}{729 \, {\left (3 \, x + 2\right )}} + \frac {4099}{1458 \, {\left (3 \, x + 2\right )}^{2}} - \frac {763}{2187 \, {\left (3 \, x + 2\right )}^{3}} + \frac {49}{2916 \, {\left (3 \, x + 2\right )}^{4}} + \frac {3800}{729} \, \log \left (\frac {{\left | 3 \, x + 2 \right |}}{3 \, {\left (3 \, x + 2\right )}^{2}}\right ) + \frac {1000}{729} \]
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Time = 0.04 (sec) , antiderivative size = 47, normalized size of antiderivative = 0.78 \[ \int \frac {(1-2 x)^2 (3+5 x)^3}{(2+3 x)^5} \, dx=\frac {500\,x}{243}-\frac {3800\,\ln \left (x+\frac {2}{3}\right )}{729}-\frac {\frac {8285\,x^3}{2187}+\frac {95321\,x^2}{13122}+\frac {274429\,x}{59049}+\frac {702941}{708588}}{x^4+\frac {8\,x^3}{3}+\frac {8\,x^2}{3}+\frac {32\,x}{27}+\frac {16}{81}} \]
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