Integrand size = 22, antiderivative size = 67 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=\frac {343 (2+3 x)^8}{5832}-\frac {3724 (2+3 x)^9}{6561}+\frac {11599 (2+3 x)^{10}}{7290}-\frac {8198 (2+3 x)^{11}}{8019}+\frac {545 (2+3 x)^{12}}{2187}-\frac {200 (2+3 x)^{13}}{9477} \]
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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} \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=-\frac {200 (3 x+2)^{13}}{9477}+\frac {545 (3 x+2)^{12}}{2187}-\frac {8198 (3 x+2)^{11}}{8019}+\frac {11599 (3 x+2)^{10}}{7290}-\frac {3724 (3 x+2)^9}{6561}+\frac {343 (3 x+2)^8}{5832} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {343}{243} (2+3 x)^7-\frac {3724}{243} (2+3 x)^8+\frac {11599}{243} (2+3 x)^9-\frac {8198}{243} (2+3 x)^{10}+\frac {2180}{243} (2+3 x)^{11}-\frac {200}{243} (2+3 x)^{12}\right ) \, dx \\ & = \frac {343 (2+3 x)^8}{5832}-\frac {3724 (2+3 x)^9}{6561}+\frac {11599 (2+3 x)^{10}}{7290}-\frac {8198 (2+3 x)^{11}}{8019}+\frac {545 (2+3 x)^{12}}{2187}-\frac {200 (2+3 x)^{13}}{9477} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 78, normalized size of antiderivative = 1.16 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=1152 x+4512 x^2+\frac {16160 x^3}{3}-13644 x^4-\frac {249864 x^5}{5}-\frac {90794 x^6}{3}+102378 x^7+\frac {1642815 x^8}{8}+69054 x^9-\frac {2005641 x^{10}}{10}-\frac {3168234 x^{11}}{11}-159165 x^{12}-\frac {437400 x^{13}}{13} \]
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Time = 2.38 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96
method | result | size |
gosper | \(-\frac {x \left (577368000 x^{12}+2731271400 x^{11}+4942445040 x^{10}+3441679956 x^{9}-1184966640 x^{8}-3523838175 x^{7}-1756806480 x^{6}+519341680 x^{5}+857533248 x^{4}+234131040 x^{3}-92435200 x^{2}-77425920 x -19768320\right )}{17160}\) | \(64\) |
default | \(-\frac {437400}{13} x^{13}-159165 x^{12}-\frac {3168234}{11} x^{11}-\frac {2005641}{10} x^{10}+69054 x^{9}+\frac {1642815}{8} x^{8}+102378 x^{7}-\frac {90794}{3} x^{6}-\frac {249864}{5} x^{5}-13644 x^{4}+\frac {16160}{3} x^{3}+4512 x^{2}+1152 x\) | \(65\) |
norman | \(-\frac {437400}{13} x^{13}-159165 x^{12}-\frac {3168234}{11} x^{11}-\frac {2005641}{10} x^{10}+69054 x^{9}+\frac {1642815}{8} x^{8}+102378 x^{7}-\frac {90794}{3} x^{6}-\frac {249864}{5} x^{5}-13644 x^{4}+\frac {16160}{3} x^{3}+4512 x^{2}+1152 x\) | \(65\) |
risch | \(-\frac {437400}{13} x^{13}-159165 x^{12}-\frac {3168234}{11} x^{11}-\frac {2005641}{10} x^{10}+69054 x^{9}+\frac {1642815}{8} x^{8}+102378 x^{7}-\frac {90794}{3} x^{6}-\frac {249864}{5} x^{5}-13644 x^{4}+\frac {16160}{3} x^{3}+4512 x^{2}+1152 x\) | \(65\) |
parallelrisch | \(-\frac {437400}{13} x^{13}-159165 x^{12}-\frac {3168234}{11} x^{11}-\frac {2005641}{10} x^{10}+69054 x^{9}+\frac {1642815}{8} x^{8}+102378 x^{7}-\frac {90794}{3} x^{6}-\frac {249864}{5} x^{5}-13644 x^{4}+\frac {16160}{3} x^{3}+4512 x^{2}+1152 x\) | \(65\) |
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Time = 0.21 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=-\frac {437400}{13} \, x^{13} - 159165 \, x^{12} - \frac {3168234}{11} \, x^{11} - \frac {2005641}{10} \, x^{10} + 69054 \, x^{9} + \frac {1642815}{8} \, x^{8} + 102378 \, x^{7} - \frac {90794}{3} \, x^{6} - \frac {249864}{5} \, x^{5} - 13644 \, x^{4} + \frac {16160}{3} \, x^{3} + 4512 \, x^{2} + 1152 \, x \]
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Time = 0.03 (sec) , antiderivative size = 75, normalized size of antiderivative = 1.12 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=- \frac {437400 x^{13}}{13} - 159165 x^{12} - \frac {3168234 x^{11}}{11} - \frac {2005641 x^{10}}{10} + 69054 x^{9} + \frac {1642815 x^{8}}{8} + 102378 x^{7} - \frac {90794 x^{6}}{3} - \frac {249864 x^{5}}{5} - 13644 x^{4} + \frac {16160 x^{3}}{3} + 4512 x^{2} + 1152 x \]
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Time = 0.20 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=-\frac {437400}{13} \, x^{13} - 159165 \, x^{12} - \frac {3168234}{11} \, x^{11} - \frac {2005641}{10} \, x^{10} + 69054 \, x^{9} + \frac {1642815}{8} \, x^{8} + 102378 \, x^{7} - \frac {90794}{3} \, x^{6} - \frac {249864}{5} \, x^{5} - 13644 \, x^{4} + \frac {16160}{3} \, x^{3} + 4512 \, x^{2} + 1152 \, x \]
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Time = 0.28 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=-\frac {437400}{13} \, x^{13} - 159165 \, x^{12} - \frac {3168234}{11} \, x^{11} - \frac {2005641}{10} \, x^{10} + 69054 \, x^{9} + \frac {1642815}{8} \, x^{8} + 102378 \, x^{7} - \frac {90794}{3} \, x^{6} - \frac {249864}{5} \, x^{5} - 13644 \, x^{4} + \frac {16160}{3} \, x^{3} + 4512 \, x^{2} + 1152 \, x \]
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Time = 0.08 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.96 \[ \int (1-2 x)^3 (2+3 x)^7 (3+5 x)^2 \, dx=-\frac {437400\,x^{13}}{13}-159165\,x^{12}-\frac {3168234\,x^{11}}{11}-\frac {2005641\,x^{10}}{10}+69054\,x^9+\frac {1642815\,x^8}{8}+102378\,x^7-\frac {90794\,x^6}{3}-\frac {249864\,x^5}{5}-13644\,x^4+\frac {16160\,x^3}{3}+4512\,x^2+1152\,x \]
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