Integrand size = 22, antiderivative size = 67 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^8} \, dx=-\frac {49}{729 (2+3 x)^7}+\frac {1862}{2187 (2+3 x)^6}-\frac {11599}{3645 (2+3 x)^5}+\frac {4099}{1458 (2+3 x)^4}-\frac {2180}{2187 (2+3 x)^3}+\frac {100}{729 (2+3 x)^2} \]
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Time = 0.02 (sec) , antiderivative size = 67, 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} \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^8} \, dx=\frac {100}{729 (3 x+2)^2}-\frac {2180}{2187 (3 x+2)^3}+\frac {4099}{1458 (3 x+2)^4}-\frac {11599}{3645 (3 x+2)^5}+\frac {1862}{2187 (3 x+2)^6}-\frac {49}{729 (3 x+2)^7} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {343}{243 (2+3 x)^8}-\frac {3724}{243 (2+3 x)^7}+\frac {11599}{243 (2+3 x)^6}-\frac {8198}{243 (2+3 x)^5}+\frac {2180}{243 (2+3 x)^4}-\frac {200}{243 (2+3 x)^3}\right ) \, dx \\ & = -\frac {49}{729 (2+3 x)^7}+\frac {1862}{2187 (2+3 x)^6}-\frac {11599}{3645 (2+3 x)^5}+\frac {4099}{1458 (2+3 x)^4}-\frac {2180}{2187 (2+3 x)^3}+\frac {100}{729 (2+3 x)^2} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 36, normalized size of antiderivative = 0.54 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^8} \, dx=\frac {-3526+61392 x+145044 x^2+191295 x^3+664200 x^4+729000 x^5}{21870 (2+3 x)^7} \]
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Time = 2.41 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.51
method | result | size |
norman | \(\frac {\frac {100}{3} x^{5}+\frac {820}{27} x^{4}+\frac {1417}{162} x^{3}+\frac {2686}{405} x^{2}+\frac {10232}{3645} x -\frac {1763}{10935}}{\left (2+3 x \right )^{7}}\) | \(34\) |
gosper | \(\frac {729000 x^{5}+664200 x^{4}+191295 x^{3}+145044 x^{2}+61392 x -3526}{21870 \left (2+3 x \right )^{7}}\) | \(35\) |
risch | \(\frac {\frac {100}{3} x^{5}+\frac {820}{27} x^{4}+\frac {1417}{162} x^{3}+\frac {2686}{405} x^{2}+\frac {10232}{3645} x -\frac {1763}{10935}}{\left (2+3 x \right )^{7}}\) | \(35\) |
parallelrisch | \(\frac {5289 x^{7}+24682 x^{6}+113364 x^{5}+113160 x^{4}+53360 x^{3}+27360 x^{2}+8640 x}{1920 \left (2+3 x \right )^{7}}\) | \(44\) |
default | \(-\frac {49}{729 \left (2+3 x \right )^{7}}+\frac {1862}{2187 \left (2+3 x \right )^{6}}-\frac {11599}{3645 \left (2+3 x \right )^{5}}+\frac {4099}{1458 \left (2+3 x \right )^{4}}-\frac {2180}{2187 \left (2+3 x \right )^{3}}+\frac {100}{729 \left (2+3 x \right )^{2}}\) | \(56\) |
meijerg | \(\frac {9 x \left (\frac {729}{64} x^{6}+\frac {1701}{32} x^{5}+\frac {1701}{16} x^{4}+\frac {945}{8} x^{3}+\frac {315}{4} x^{2}+\frac {63}{2} x +7\right )}{1792 \left (1+\frac {3 x}{2}\right )^{7}}-\frac {x^{2} \left (\frac {243}{32} x^{5}+\frac {567}{16} x^{4}+\frac {567}{8} x^{3}+\frac {315}{4} x^{2}+\frac {105}{2} x +21\right )}{448 \left (1+\frac {3 x}{2}\right )^{7}}-\frac {47 x^{3} \left (\frac {81}{16} x^{4}+\frac {189}{8} x^{3}+\frac {189}{4} x^{2}+\frac {105}{2} x +35\right )}{26880 \left (1+\frac {3 x}{2}\right )^{7}}+\frac {69 x^{4} \left (\frac {27}{8} x^{3}+\frac {63}{4} x^{2}+\frac {63}{2} x +35\right )}{17920 \left (1+\frac {3 x}{2}\right )^{7}}+\frac {x^{5} \left (\frac {9}{4} x^{2}+\frac {21}{2} x +21\right )}{448 \left (1+\frac {3 x}{2}\right )^{7}}-\frac {25 x^{6} \left (\frac {3 x}{2}+7\right )}{1344 \left (1+\frac {3 x}{2}\right )^{7}}\) | \(177\) |
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Time = 0.22 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^8} \, dx=\frac {729000 \, x^{5} + 664200 \, x^{4} + 191295 \, x^{3} + 145044 \, x^{2} + 61392 \, x - 3526}{21870 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
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Time = 0.08 (sec) , antiderivative size = 61, normalized size of antiderivative = 0.91 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^8} \, dx=- \frac {- 729000 x^{5} - 664200 x^{4} - 191295 x^{3} - 145044 x^{2} - 61392 x + 3526}{47829690 x^{7} + 223205220 x^{6} + 446410440 x^{5} + 496011600 x^{4} + 330674400 x^{3} + 132269760 x^{2} + 29393280 x + 2799360} \]
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Time = 0.21 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^8} \, dx=\frac {729000 \, x^{5} + 664200 \, x^{4} + 191295 \, x^{3} + 145044 \, x^{2} + 61392 \, x - 3526}{21870 \, {\left (2187 \, x^{7} + 10206 \, x^{6} + 20412 \, x^{5} + 22680 \, x^{4} + 15120 \, x^{3} + 6048 \, x^{2} + 1344 \, x + 128\right )}} \]
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Time = 0.29 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.51 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^8} \, dx=\frac {729000 \, x^{5} + 664200 \, x^{4} + 191295 \, x^{3} + 145044 \, x^{2} + 61392 \, x - 3526}{21870 \, {\left (3 \, x + 2\right )}^{7}} \]
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Time = 0.04 (sec) , antiderivative size = 55, normalized size of antiderivative = 0.82 \[ \int \frac {(1-2 x)^3 (3+5 x)^2}{(2+3 x)^8} \, dx=\frac {100}{729\,{\left (3\,x+2\right )}^2}-\frac {2180}{2187\,{\left (3\,x+2\right )}^3}+\frac {4099}{1458\,{\left (3\,x+2\right )}^4}-\frac {11599}{3645\,{\left (3\,x+2\right )}^5}+\frac {1862}{2187\,{\left (3\,x+2\right )}^6}-\frac {49}{729\,{\left (3\,x+2\right )}^7} \]
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