Integrand size = 22, antiderivative size = 67 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x)^2 \, dx=\frac {343 (2+3 x)^9}{6561}-\frac {1862 (2+3 x)^{10}}{3645}+\frac {11599 (2+3 x)^{11}}{8019}-\frac {4099 (2+3 x)^{12}}{4374}+\frac {2180 (2+3 x)^{13}}{9477}-\frac {100 (2+3 x)^{14}}{5103} \]
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Time = 0.03 (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} \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x)^2 \, dx=-\frac {100 (3 x+2)^{14}}{5103}+\frac {2180 (3 x+2)^{13}}{9477}-\frac {4099 (3 x+2)^{12}}{4374}+\frac {11599 (3 x+2)^{11}}{8019}-\frac {1862 (3 x+2)^{10}}{3645}+\frac {343 (3 x+2)^9}{6561} \]
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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)^9+\frac {11599}{243} (2+3 x)^{10}-\frac {8198}{243} (2+3 x)^{11}+\frac {2180}{243} (2+3 x)^{12}-\frac {200}{243} (2+3 x)^{13}\right ) \, dx \\ & = \frac {343 (2+3 x)^9}{6561}-\frac {1862 (2+3 x)^{10}}{3645}+\frac {11599 (2+3 x)^{11}}{8019}-\frac {4099 (2+3 x)^{12}}{4374}+\frac {2180 (2+3 x)^{13}}{9477}-\frac {100 (2+3 x)^{14}}{5103} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 87, normalized size of antiderivative = 1.30 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x)^2 \, dx=2304 x+10752 x^2+\frac {59392 x^3}{3}-15168 x^4-\frac {663456 x^5}{5}-\frac {556384 x^6}{3}+\frac {888528 x^7}{7}+679446 x^8+685713 x^9-\frac {1073412 x^{10}}{5}-\frac {12353391 x^{11}}{11}-\frac {2220777 x^{12}}{2}-\frac {6604740 x^{13}}{13}-\frac {656100 x^{14}}{7} \]
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Time = 2.39 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.03
method | result | size |
gosper | \(-\frac {x \left (2814669000 x^{13}+15256949400 x^{12}+33344966655 x^{11}+33724757430 x^{10}+6446912472 x^{9}-20591961390 x^{8}-20403763380 x^{7}-3811785120 x^{6}+5569403840 x^{5}+3984716736 x^{4}+455495040 x^{3}-594513920 x^{2}-322882560 x -69189120\right )}{30030}\) | \(69\) |
default | \(-\frac {656100}{7} x^{14}-\frac {6604740}{13} x^{13}-\frac {2220777}{2} x^{12}-\frac {12353391}{11} x^{11}-\frac {1073412}{5} x^{10}+685713 x^{9}+679446 x^{8}+\frac {888528}{7} x^{7}-\frac {556384}{3} x^{6}-\frac {663456}{5} x^{5}-15168 x^{4}+\frac {59392}{3} x^{3}+10752 x^{2}+2304 x\) | \(70\) |
norman | \(-\frac {656100}{7} x^{14}-\frac {6604740}{13} x^{13}-\frac {2220777}{2} x^{12}-\frac {12353391}{11} x^{11}-\frac {1073412}{5} x^{10}+685713 x^{9}+679446 x^{8}+\frac {888528}{7} x^{7}-\frac {556384}{3} x^{6}-\frac {663456}{5} x^{5}-15168 x^{4}+\frac {59392}{3} x^{3}+10752 x^{2}+2304 x\) | \(70\) |
risch | \(-\frac {656100}{7} x^{14}-\frac {6604740}{13} x^{13}-\frac {2220777}{2} x^{12}-\frac {12353391}{11} x^{11}-\frac {1073412}{5} x^{10}+685713 x^{9}+679446 x^{8}+\frac {888528}{7} x^{7}-\frac {556384}{3} x^{6}-\frac {663456}{5} x^{5}-15168 x^{4}+\frac {59392}{3} x^{3}+10752 x^{2}+2304 x\) | \(70\) |
parallelrisch | \(-\frac {656100}{7} x^{14}-\frac {6604740}{13} x^{13}-\frac {2220777}{2} x^{12}-\frac {12353391}{11} x^{11}-\frac {1073412}{5} x^{10}+685713 x^{9}+679446 x^{8}+\frac {888528}{7} x^{7}-\frac {556384}{3} x^{6}-\frac {663456}{5} x^{5}-15168 x^{4}+\frac {59392}{3} x^{3}+10752 x^{2}+2304 x\) | \(70\) |
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Time = 0.22 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.03 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x)^2 \, dx=-\frac {656100}{7} \, x^{14} - \frac {6604740}{13} \, x^{13} - \frac {2220777}{2} \, x^{12} - \frac {12353391}{11} \, x^{11} - \frac {1073412}{5} \, x^{10} + 685713 \, x^{9} + 679446 \, x^{8} + \frac {888528}{7} \, x^{7} - \frac {556384}{3} \, x^{6} - \frac {663456}{5} \, x^{5} - 15168 \, x^{4} + \frac {59392}{3} \, x^{3} + 10752 \, x^{2} + 2304 \, x \]
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Time = 0.03 (sec) , antiderivative size = 83, normalized size of antiderivative = 1.24 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x)^2 \, dx=- \frac {656100 x^{14}}{7} - \frac {6604740 x^{13}}{13} - \frac {2220777 x^{12}}{2} - \frac {12353391 x^{11}}{11} - \frac {1073412 x^{10}}{5} + 685713 x^{9} + 679446 x^{8} + \frac {888528 x^{7}}{7} - \frac {556384 x^{6}}{3} - \frac {663456 x^{5}}{5} - 15168 x^{4} + \frac {59392 x^{3}}{3} + 10752 x^{2} + 2304 x \]
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Time = 0.19 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.03 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x)^2 \, dx=-\frac {656100}{7} \, x^{14} - \frac {6604740}{13} \, x^{13} - \frac {2220777}{2} \, x^{12} - \frac {12353391}{11} \, x^{11} - \frac {1073412}{5} \, x^{10} + 685713 \, x^{9} + 679446 \, x^{8} + \frac {888528}{7} \, x^{7} - \frac {556384}{3} \, x^{6} - \frac {663456}{5} \, x^{5} - 15168 \, x^{4} + \frac {59392}{3} \, x^{3} + 10752 \, x^{2} + 2304 \, x \]
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Time = 0.28 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.03 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x)^2 \, dx=-\frac {656100}{7} \, x^{14} - \frac {6604740}{13} \, x^{13} - \frac {2220777}{2} \, x^{12} - \frac {12353391}{11} \, x^{11} - \frac {1073412}{5} \, x^{10} + 685713 \, x^{9} + 679446 \, x^{8} + \frac {888528}{7} \, x^{7} - \frac {556384}{3} \, x^{6} - \frac {663456}{5} \, x^{5} - 15168 \, x^{4} + \frac {59392}{3} \, x^{3} + 10752 \, x^{2} + 2304 \, x \]
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Time = 0.10 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.03 \[ \int (1-2 x)^3 (2+3 x)^8 (3+5 x)^2 \, dx=-\frac {656100\,x^{14}}{7}-\frac {6604740\,x^{13}}{13}-\frac {2220777\,x^{12}}{2}-\frac {12353391\,x^{11}}{11}-\frac {1073412\,x^{10}}{5}+685713\,x^9+679446\,x^8+\frac {888528\,x^7}{7}-\frac {556384\,x^6}{3}-\frac {663456\,x^5}{5}-15168\,x^4+\frac {59392\,x^3}{3}+10752\,x^2+2304\,x \]
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