Integrand size = 22, antiderivative size = 78 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {49 (2+3 x)^7}{2187}+\frac {1813 (2+3 x)^8}{5832}-\frac {10073 (2+3 x)^9}{6561}+\frac {66193 (2+3 x)^{10}}{21870}-\frac {14390 (2+3 x)^{11}}{8019}+\frac {925 (2+3 x)^{12}}{2187}-\frac {1000 (2+3 x)^{13}}{28431} \]
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Time = 0.02 (sec) , antiderivative size = 78, 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} \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {1000 (3 x+2)^{13}}{28431}+\frac {925 (3 x+2)^{12}}{2187}-\frac {14390 (3 x+2)^{11}}{8019}+\frac {66193 (3 x+2)^{10}}{21870}-\frac {10073 (3 x+2)^9}{6561}+\frac {1813 (3 x+2)^8}{5832}-\frac {49 (3 x+2)^7}{2187} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {343}{729} (2+3 x)^6+\frac {1813}{243} (2+3 x)^7-\frac {10073}{243} (2+3 x)^8+\frac {66193}{729} (2+3 x)^9-\frac {14390}{243} (2+3 x)^{10}+\frac {3700}{243} (2+3 x)^{11}-\frac {1000}{729} (2+3 x)^{12}\right ) \, dx \\ & = -\frac {49 (2+3 x)^7}{2187}+\frac {1813 (2+3 x)^8}{5832}-\frac {10073 (2+3 x)^9}{6561}+\frac {66193 (2+3 x)^{10}}{21870}-\frac {14390 (2+3 x)^{11}}{8019}+\frac {925 (2+3 x)^{12}}{2187}-\frac {1000 (2+3 x)^{13}}{28431} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 74, normalized size of antiderivative = 0.95 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=1728 x+6912 x^2+8688 x^3-20140 x^4-\frac {390396 x^5}{5}-51908 x^6+155453 x^7+\frac {2623581 x^8}{8}+122655 x^9-\frac {3110589 x^{10}}{10}-\frac {5100570 x^{11}}{11}-261225 x^{12}-\frac {729000 x^{13}}{13} \]
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Time = 2.41 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.82
method | result | size |
gosper | \(-\frac {x \left (320760000 x^{12}+1494207000 x^{11}+2652296400 x^{10}+1779256908 x^{9}-701586600 x^{8}-1875860415 x^{7}-889191160 x^{6}+296913760 x^{5}+446613024 x^{4}+115200800 x^{3}-49695360 x^{2}-39536640 x -9884160\right )}{5720}\) | \(64\) |
default | \(-\frac {729000}{13} x^{13}-261225 x^{12}-\frac {5100570}{11} x^{11}-\frac {3110589}{10} x^{10}+122655 x^{9}+\frac {2623581}{8} x^{8}+155453 x^{7}-51908 x^{6}-\frac {390396}{5} x^{5}-20140 x^{4}+8688 x^{3}+6912 x^{2}+1728 x\) | \(65\) |
norman | \(-\frac {729000}{13} x^{13}-261225 x^{12}-\frac {5100570}{11} x^{11}-\frac {3110589}{10} x^{10}+122655 x^{9}+\frac {2623581}{8} x^{8}+155453 x^{7}-51908 x^{6}-\frac {390396}{5} x^{5}-20140 x^{4}+8688 x^{3}+6912 x^{2}+1728 x\) | \(65\) |
risch | \(-\frac {729000}{13} x^{13}-261225 x^{12}-\frac {5100570}{11} x^{11}-\frac {3110589}{10} x^{10}+122655 x^{9}+\frac {2623581}{8} x^{8}+155453 x^{7}-51908 x^{6}-\frac {390396}{5} x^{5}-20140 x^{4}+8688 x^{3}+6912 x^{2}+1728 x\) | \(65\) |
parallelrisch | \(-\frac {729000}{13} x^{13}-261225 x^{12}-\frac {5100570}{11} x^{11}-\frac {3110589}{10} x^{10}+122655 x^{9}+\frac {2623581}{8} x^{8}+155453 x^{7}-51908 x^{6}-\frac {390396}{5} x^{5}-20140 x^{4}+8688 x^{3}+6912 x^{2}+1728 x\) | \(65\) |
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Time = 0.21 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.82 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {729000}{13} \, x^{13} - 261225 \, x^{12} - \frac {5100570}{11} \, x^{11} - \frac {3110589}{10} \, x^{10} + 122655 \, x^{9} + \frac {2623581}{8} \, x^{8} + 155453 \, x^{7} - 51908 \, x^{6} - \frac {390396}{5} \, x^{5} - 20140 \, x^{4} + 8688 \, x^{3} + 6912 \, x^{2} + 1728 \, x \]
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Time = 0.03 (sec) , antiderivative size = 71, normalized size of antiderivative = 0.91 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=- \frac {729000 x^{13}}{13} - 261225 x^{12} - \frac {5100570 x^{11}}{11} - \frac {3110589 x^{10}}{10} + 122655 x^{9} + \frac {2623581 x^{8}}{8} + 155453 x^{7} - 51908 x^{6} - \frac {390396 x^{5}}{5} - 20140 x^{4} + 8688 x^{3} + 6912 x^{2} + 1728 x \]
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Time = 0.20 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.82 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {729000}{13} \, x^{13} - 261225 \, x^{12} - \frac {5100570}{11} \, x^{11} - \frac {3110589}{10} \, x^{10} + 122655 \, x^{9} + \frac {2623581}{8} \, x^{8} + 155453 \, x^{7} - 51908 \, x^{6} - \frac {390396}{5} \, x^{5} - 20140 \, x^{4} + 8688 \, x^{3} + 6912 \, x^{2} + 1728 \, x \]
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Time = 0.28 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.82 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {729000}{13} \, x^{13} - 261225 \, x^{12} - \frac {5100570}{11} \, x^{11} - \frac {3110589}{10} \, x^{10} + 122655 \, x^{9} + \frac {2623581}{8} \, x^{8} + 155453 \, x^{7} - 51908 \, x^{6} - \frac {390396}{5} \, x^{5} - 20140 \, x^{4} + 8688 \, x^{3} + 6912 \, x^{2} + 1728 \, x \]
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Time = 0.14 (sec) , antiderivative size = 64, normalized size of antiderivative = 0.82 \[ \int (1-2 x)^3 (2+3 x)^6 (3+5 x)^3 \, dx=-\frac {729000\,x^{13}}{13}-261225\,x^{12}-\frac {5100570\,x^{11}}{11}-\frac {3110589\,x^{10}}{10}+122655\,x^9+\frac {2623581\,x^8}{8}+155453\,x^7-51908\,x^6-\frac {390396\,x^5}{5}-20140\,x^4+8688\,x^3+6912\,x^2+1728\,x \]
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