Integrand size = 20, antiderivative size = 45 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^7} \, dx=\frac {49}{486 (2+3 x)^6}-\frac {91}{135 (2+3 x)^5}+\frac {4}{9 (2+3 x)^4}-\frac {20}{243 (2+3 x)^3} \]
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Time = 0.01 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78} \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^7} \, dx=-\frac {20}{243 (3 x+2)^3}+\frac {4}{9 (3 x+2)^4}-\frac {91}{135 (3 x+2)^5}+\frac {49}{486 (3 x+2)^6} \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {49}{27 (2+3 x)^7}+\frac {91}{9 (2+3 x)^6}-\frac {16}{3 (2+3 x)^5}+\frac {20}{27 (2+3 x)^4}\right ) \, dx \\ & = \frac {49}{486 (2+3 x)^6}-\frac {91}{135 (2+3 x)^5}+\frac {4}{9 (2+3 x)^4}-\frac {20}{243 (2+3 x)^3} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.58 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^7} \, dx=-\frac {311-846 x+1080 x^2+5400 x^3}{2430 (2+3 x)^6} \]
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Time = 0.74 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.53
method | result | size |
norman | \(\frac {-\frac {20}{9} x^{3}-\frac {4}{9} x^{2}+\frac {47}{135} x -\frac {311}{2430}}{\left (2+3 x \right )^{6}}\) | \(24\) |
gosper | \(-\frac {5400 x^{3}+1080 x^{2}-846 x +311}{2430 \left (2+3 x \right )^{6}}\) | \(25\) |
risch | \(\frac {-\frac {20}{9} x^{3}-\frac {4}{9} x^{2}+\frac {47}{135} x -\frac {311}{2430}}{\left (2+3 x \right )^{6}}\) | \(25\) |
default | \(\frac {49}{486 \left (2+3 x \right )^{6}}-\frac {91}{135 \left (2+3 x \right )^{5}}+\frac {4}{9 \left (2+3 x \right )^{4}}-\frac {20}{243 \left (2+3 x \right )^{3}}\) | \(38\) |
parallelrisch | \(\frac {2799 x^{6}+11196 x^{5}+18660 x^{4}+12320 x^{3}+7440 x^{2}+2880 x}{1920 \left (2+3 x \right )^{6}}\) | \(39\) |
meijerg | \(\frac {x \left (\frac {243}{32} x^{5}+\frac {243}{8} x^{4}+\frac {405}{8} x^{3}+45 x^{2}+\frac {45}{2} x +6\right )}{256 \left (1+\frac {3 x}{2}\right )^{6}}-\frac {7 x^{2} \left (\frac {81}{16} x^{4}+\frac {81}{4} x^{3}+\frac {135}{4} x^{2}+30 x +15\right )}{3840 \left (1+\frac {3 x}{2}\right )^{6}}-\frac {x^{3} \left (\frac {27}{8} x^{3}+\frac {27}{2} x^{2}+\frac {45}{2} x +20\right )}{960 \left (1+\frac {3 x}{2}\right )^{6}}+\frac {x^{4} \left (\frac {9}{4} x^{2}+9 x +15\right )}{384 \left (1+\frac {3 x}{2}\right )^{6}}\) | \(118\) |
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Time = 0.22 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.09 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^7} \, dx=-\frac {5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 44, normalized size of antiderivative = 0.98 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^7} \, dx=\frac {- 5400 x^{3} - 1080 x^{2} + 846 x - 311}{1771470 x^{6} + 7085880 x^{5} + 11809800 x^{4} + 10497600 x^{3} + 5248800 x^{2} + 1399680 x + 155520} \]
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Time = 0.20 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.09 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^7} \, dx=-\frac {5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \]
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Time = 0.28 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.53 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^7} \, dx=-\frac {5400 \, x^{3} + 1080 \, x^{2} - 846 \, x + 311}{2430 \, {\left (3 \, x + 2\right )}^{6}} \]
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Time = 0.03 (sec) , antiderivative size = 37, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x)^2 (3+5 x)}{(2+3 x)^7} \, dx=\frac {4}{9\,{\left (3\,x+2\right )}^4}-\frac {20}{243\,{\left (3\,x+2\right )}^3}-\frac {91}{135\,{\left (3\,x+2\right )}^5}+\frac {49}{486\,{\left (3\,x+2\right )}^6} \]
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