Integrand size = 20, antiderivative size = 45 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x) \, dx=-\frac {49}{405} (2+3 x)^5+\frac {91}{162} (2+3 x)^6-\frac {16}{63} (2+3 x)^7+\frac {5}{162} (2+3 x)^8 \]
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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} \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x) \, dx=\frac {5}{162} (3 x+2)^8-\frac {16}{63} (3 x+2)^7+\frac {91}{162} (3 x+2)^6-\frac {49}{405} (3 x+2)^5 \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {49}{27} (2+3 x)^4+\frac {91}{9} (2+3 x)^5-\frac {16}{3} (2+3 x)^6+\frac {20}{27} (2+3 x)^7\right ) \, dx \\ & = -\frac {49}{405} (2+3 x)^5+\frac {91}{162} (2+3 x)^6-\frac {16}{63} (2+3 x)^7+\frac {5}{162} (2+3 x)^8 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.09 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x) \, dx=48 x+88 x^2-\frac {152 x^3}{3}-328 x^4-\frac {1077 x^5}{5}+\frac {675 x^6}{2}+\frac {3672 x^7}{7}+\frac {405 x^8}{2} \]
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Time = 1.84 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.87
method | result | size |
gosper | \(\frac {x \left (42525 x^{7}+110160 x^{6}+70875 x^{5}-45234 x^{4}-68880 x^{3}-10640 x^{2}+18480 x +10080\right )}{210}\) | \(39\) |
default | \(\frac {405}{2} x^{8}+\frac {3672}{7} x^{7}+\frac {675}{2} x^{6}-\frac {1077}{5} x^{5}-328 x^{4}-\frac {152}{3} x^{3}+88 x^{2}+48 x\) | \(40\) |
norman | \(\frac {405}{2} x^{8}+\frac {3672}{7} x^{7}+\frac {675}{2} x^{6}-\frac {1077}{5} x^{5}-328 x^{4}-\frac {152}{3} x^{3}+88 x^{2}+48 x\) | \(40\) |
risch | \(\frac {405}{2} x^{8}+\frac {3672}{7} x^{7}+\frac {675}{2} x^{6}-\frac {1077}{5} x^{5}-328 x^{4}-\frac {152}{3} x^{3}+88 x^{2}+48 x\) | \(40\) |
parallelrisch | \(\frac {405}{2} x^{8}+\frac {3672}{7} x^{7}+\frac {675}{2} x^{6}-\frac {1077}{5} x^{5}-328 x^{4}-\frac {152}{3} x^{3}+88 x^{2}+48 x\) | \(40\) |
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Time = 0.21 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.87 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x) \, dx=\frac {405}{2} \, x^{8} + \frac {3672}{7} \, x^{7} + \frac {675}{2} \, x^{6} - \frac {1077}{5} \, x^{5} - 328 \, x^{4} - \frac {152}{3} \, x^{3} + 88 \, x^{2} + 48 \, x \]
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Time = 0.02 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.02 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x) \, dx=\frac {405 x^{8}}{2} + \frac {3672 x^{7}}{7} + \frac {675 x^{6}}{2} - \frac {1077 x^{5}}{5} - 328 x^{4} - \frac {152 x^{3}}{3} + 88 x^{2} + 48 x \]
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Time = 0.19 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.87 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x) \, dx=\frac {405}{2} \, x^{8} + \frac {3672}{7} \, x^{7} + \frac {675}{2} \, x^{6} - \frac {1077}{5} \, x^{5} - 328 \, x^{4} - \frac {152}{3} \, x^{3} + 88 \, x^{2} + 48 \, x \]
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Time = 0.26 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.87 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x) \, dx=\frac {405}{2} \, x^{8} + \frac {3672}{7} \, x^{7} + \frac {675}{2} \, x^{6} - \frac {1077}{5} \, x^{5} - 328 \, x^{4} - \frac {152}{3} \, x^{3} + 88 \, x^{2} + 48 \, x \]
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Time = 0.03 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.87 \[ \int (1-2 x)^2 (2+3 x)^4 (3+5 x) \, dx=\frac {405\,x^8}{2}+\frac {3672\,x^7}{7}+\frac {675\,x^6}{2}-\frac {1077\,x^5}{5}-328\,x^4-\frac {152\,x^3}{3}+88\,x^2+48\,x \]
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