Integrand size = 22, antiderivative size = 67 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx=\frac {49}{729} (2+3 x)^7-\frac {931 (2+3 x)^8}{1458}+\frac {11599 (2+3 x)^9}{6561}-\frac {4099 (2+3 x)^{10}}{3645}+\frac {2180 (2+3 x)^{11}}{8019}-\frac {50 (2+3 x)^{12}}{2187} \]
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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} \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx=-\frac {50 (3 x+2)^{12}}{2187}+\frac {2180 (3 x+2)^{11}}{8019}-\frac {4099 (3 x+2)^{10}}{3645}+\frac {11599 (3 x+2)^9}{6561}-\frac {931 (3 x+2)^8}{1458}+\frac {49}{729} (3 x+2)^7 \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {343}{243} (2+3 x)^6-\frac {3724}{243} (2+3 x)^7+\frac {11599}{243} (2+3 x)^8-\frac {8198}{243} (2+3 x)^9+\frac {2180}{243} (2+3 x)^{10}-\frac {200}{243} (2+3 x)^{11}\right ) \, dx \\ & = \frac {49}{729} (2+3 x)^7-\frac {931 (2+3 x)^8}{1458}+\frac {11599 (2+3 x)^9}{6561}-\frac {4099 (2+3 x)^{10}}{3645}+\frac {2180 (2+3 x)^{11}}{8019}-\frac {50 (2+3 x)^{12}}{2187} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 71, normalized size of antiderivative = 1.06 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx=576 x+1824 x^2+\frac {2608 x^3}{3}-7800 x^4-\frac {78132 x^5}{5}+\frac {13202 x^6}{3}+45531 x^7+\frac {85833 x^8}{2}-22695 x^9-\frac {348219 x^{10}}{5}-\frac {539460 x^{11}}{11}-12150 x^{12} \]
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Time = 2.39 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.88
method | result | size |
gosper | \(-\frac {x \left (4009500 x^{11}+16183800 x^{10}+22982454 x^{9}+7489350 x^{8}-14162445 x^{7}-15025230 x^{6}-1452220 x^{5}+5156712 x^{4}+2574000 x^{3}-286880 x^{2}-601920 x -190080\right )}{330}\) | \(59\) |
default | \(-12150 x^{12}-\frac {539460}{11} x^{11}-\frac {348219}{5} x^{10}-22695 x^{9}+\frac {85833}{2} x^{8}+45531 x^{7}+\frac {13202}{3} x^{6}-\frac {78132}{5} x^{5}-7800 x^{4}+\frac {2608}{3} x^{3}+1824 x^{2}+576 x\) | \(60\) |
norman | \(-12150 x^{12}-\frac {539460}{11} x^{11}-\frac {348219}{5} x^{10}-22695 x^{9}+\frac {85833}{2} x^{8}+45531 x^{7}+\frac {13202}{3} x^{6}-\frac {78132}{5} x^{5}-7800 x^{4}+\frac {2608}{3} x^{3}+1824 x^{2}+576 x\) | \(60\) |
risch | \(-12150 x^{12}-\frac {539460}{11} x^{11}-\frac {348219}{5} x^{10}-22695 x^{9}+\frac {85833}{2} x^{8}+45531 x^{7}+\frac {13202}{3} x^{6}-\frac {78132}{5} x^{5}-7800 x^{4}+\frac {2608}{3} x^{3}+1824 x^{2}+576 x\) | \(60\) |
parallelrisch | \(-12150 x^{12}-\frac {539460}{11} x^{11}-\frac {348219}{5} x^{10}-22695 x^{9}+\frac {85833}{2} x^{8}+45531 x^{7}+\frac {13202}{3} x^{6}-\frac {78132}{5} x^{5}-7800 x^{4}+\frac {2608}{3} x^{3}+1824 x^{2}+576 x\) | \(60\) |
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Time = 0.22 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx=-12150 \, x^{12} - \frac {539460}{11} \, x^{11} - \frac {348219}{5} \, x^{10} - 22695 \, x^{9} + \frac {85833}{2} \, x^{8} + 45531 \, x^{7} + \frac {13202}{3} \, x^{6} - \frac {78132}{5} \, x^{5} - 7800 \, x^{4} + \frac {2608}{3} \, x^{3} + 1824 \, x^{2} + 576 \, x \]
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Time = 0.03 (sec) , antiderivative size = 68, normalized size of antiderivative = 1.01 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx=- 12150 x^{12} - \frac {539460 x^{11}}{11} - \frac {348219 x^{10}}{5} - 22695 x^{9} + \frac {85833 x^{8}}{2} + 45531 x^{7} + \frac {13202 x^{6}}{3} - \frac {78132 x^{5}}{5} - 7800 x^{4} + \frac {2608 x^{3}}{3} + 1824 x^{2} + 576 x \]
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Time = 0.20 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx=-12150 \, x^{12} - \frac {539460}{11} \, x^{11} - \frac {348219}{5} \, x^{10} - 22695 \, x^{9} + \frac {85833}{2} \, x^{8} + 45531 \, x^{7} + \frac {13202}{3} \, x^{6} - \frac {78132}{5} \, x^{5} - 7800 \, x^{4} + \frac {2608}{3} \, x^{3} + 1824 \, x^{2} + 576 \, x \]
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Time = 0.30 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx=-12150 \, x^{12} - \frac {539460}{11} \, x^{11} - \frac {348219}{5} \, x^{10} - 22695 \, x^{9} + \frac {85833}{2} \, x^{8} + 45531 \, x^{7} + \frac {13202}{3} \, x^{6} - \frac {78132}{5} \, x^{5} - 7800 \, x^{4} + \frac {2608}{3} \, x^{3} + 1824 \, x^{2} + 576 \, x \]
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Time = 0.06 (sec) , antiderivative size = 59, normalized size of antiderivative = 0.88 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^2 \, dx=-12150\,x^{12}-\frac {539460\,x^{11}}{11}-\frac {348219\,x^{10}}{5}-22695\,x^9+\frac {85833\,x^8}{2}+45531\,x^7+\frac {13202\,x^6}{3}-\frac {78132\,x^5}{5}-7800\,x^4+\frac {2608\,x^3}{3}+1824\,x^2+576\,x \]
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