Integrand size = 20, antiderivative size = 56 \[ \int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx=-\frac {7 (2+3 x)^9}{2187}+\frac {107 (2+3 x)^{10}}{2430}-\frac {185}{891} (2+3 x)^{11}+\frac {1025 (2+3 x)^{12}}{2916}-\frac {250 (2+3 x)^{13}}{3159} \]
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Time = 0.02 (sec) , antiderivative size = 56, 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} \[ \int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx=-\frac {250 (3 x+2)^{13}}{3159}+\frac {1025 (3 x+2)^{12}}{2916}-\frac {185}{891} (3 x+2)^{11}+\frac {107 (3 x+2)^{10}}{2430}-\frac {7 (3 x+2)^9}{2187} \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {7}{81} (2+3 x)^8+\frac {107}{81} (2+3 x)^9-\frac {185}{27} (2+3 x)^{10}+\frac {1025}{81} (2+3 x)^{11}-\frac {250}{81} (2+3 x)^{12}\right ) \, dx \\ & = -\frac {7 (2+3 x)^9}{2187}+\frac {107 (2+3 x)^{10}}{2430}-\frac {185}{891} (2+3 x)^{11}+\frac {1025 (2+3 x)^{12}}{2916}-\frac {250 (2+3 x)^{13}}{3159} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 74, normalized size of antiderivative = 1.32 \[ \int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx=6912 x+51840 x^2+224256 x^3+597824 x^4+\frac {4580384 x^5}{5}+350128 x^6-1830960 x^7-4865076 x^8-6524829 x^9-\frac {54794799 x^{10}}{10}-\frac {32079645 x^{11}}{11}-\frac {3626775 x^{12}}{4}-\frac {1640250 x^{13}}{13} \]
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Time = 2.18 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14
method | result | size |
gosper | \(-\frac {x \left (360855000 x^{12}+2593144125 x^{11}+8340707700 x^{10}+15671312514 x^{9}+18661010940 x^{8}+13914117360 x^{7}+5236545600 x^{6}-1001366080 x^{5}-2619979648 x^{4}-1709776640 x^{3}-641372160 x^{2}-148262400 x -19768320\right )}{2860}\) | \(64\) |
default | \(-\frac {1640250}{13} x^{13}-\frac {3626775}{4} x^{12}-\frac {32079645}{11} x^{11}-\frac {54794799}{10} x^{10}-6524829 x^{9}-4865076 x^{8}-1830960 x^{7}+350128 x^{6}+\frac {4580384}{5} x^{5}+597824 x^{4}+224256 x^{3}+51840 x^{2}+6912 x\) | \(65\) |
norman | \(-\frac {1640250}{13} x^{13}-\frac {3626775}{4} x^{12}-\frac {32079645}{11} x^{11}-\frac {54794799}{10} x^{10}-6524829 x^{9}-4865076 x^{8}-1830960 x^{7}+350128 x^{6}+\frac {4580384}{5} x^{5}+597824 x^{4}+224256 x^{3}+51840 x^{2}+6912 x\) | \(65\) |
risch | \(-\frac {1640250}{13} x^{13}-\frac {3626775}{4} x^{12}-\frac {32079645}{11} x^{11}-\frac {54794799}{10} x^{10}-6524829 x^{9}-4865076 x^{8}-1830960 x^{7}+350128 x^{6}+\frac {4580384}{5} x^{5}+597824 x^{4}+224256 x^{3}+51840 x^{2}+6912 x\) | \(65\) |
parallelrisch | \(-\frac {1640250}{13} x^{13}-\frac {3626775}{4} x^{12}-\frac {32079645}{11} x^{11}-\frac {54794799}{10} x^{10}-6524829 x^{9}-4865076 x^{8}-1830960 x^{7}+350128 x^{6}+\frac {4580384}{5} x^{5}+597824 x^{4}+224256 x^{3}+51840 x^{2}+6912 x\) | \(65\) |
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Time = 0.22 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14 \[ \int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx=-\frac {1640250}{13} \, x^{13} - \frac {3626775}{4} \, x^{12} - \frac {32079645}{11} \, x^{11} - \frac {54794799}{10} \, x^{10} - 6524829 \, x^{9} - 4865076 \, x^{8} - 1830960 \, x^{7} + 350128 \, x^{6} + \frac {4580384}{5} \, x^{5} + 597824 \, x^{4} + 224256 \, x^{3} + 51840 \, x^{2} + 6912 \, x \]
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Time = 0.03 (sec) , antiderivative size = 71, normalized size of antiderivative = 1.27 \[ \int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx=- \frac {1640250 x^{13}}{13} - \frac {3626775 x^{12}}{4} - \frac {32079645 x^{11}}{11} - \frac {54794799 x^{10}}{10} - 6524829 x^{9} - 4865076 x^{8} - 1830960 x^{7} + 350128 x^{6} + \frac {4580384 x^{5}}{5} + 597824 x^{4} + 224256 x^{3} + 51840 x^{2} + 6912 x \]
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Time = 0.19 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14 \[ \int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx=-\frac {1640250}{13} \, x^{13} - \frac {3626775}{4} \, x^{12} - \frac {32079645}{11} \, x^{11} - \frac {54794799}{10} \, x^{10} - 6524829 \, x^{9} - 4865076 \, x^{8} - 1830960 \, x^{7} + 350128 \, x^{6} + \frac {4580384}{5} \, x^{5} + 597824 \, x^{4} + 224256 \, x^{3} + 51840 \, x^{2} + 6912 \, x \]
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Time = 0.29 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14 \[ \int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx=-\frac {1640250}{13} \, x^{13} - \frac {3626775}{4} \, x^{12} - \frac {32079645}{11} \, x^{11} - \frac {54794799}{10} \, x^{10} - 6524829 \, x^{9} - 4865076 \, x^{8} - 1830960 \, x^{7} + 350128 \, x^{6} + \frac {4580384}{5} \, x^{5} + 597824 \, x^{4} + 224256 \, x^{3} + 51840 \, x^{2} + 6912 \, x \]
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Time = 0.09 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.14 \[ \int (1-2 x) (2+3 x)^8 (3+5 x)^3 \, dx=-\frac {1640250\,x^{13}}{13}-\frac {3626775\,x^{12}}{4}-\frac {32079645\,x^{11}}{11}-\frac {54794799\,x^{10}}{10}-6524829\,x^9-4865076\,x^8-1830960\,x^7+350128\,x^6+\frac {4580384\,x^5}{5}+597824\,x^4+224256\,x^3+51840\,x^2+6912\,x \]
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