Integrand size = 22, antiderivative size = 67 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^3 \, dx=-\frac {49 (2+3 x)^9}{6561}+\frac {763 (2+3 x)^{10}}{7290}-\frac {4099 (2+3 x)^{11}}{8019}+\frac {8285 (2+3 x)^{12}}{8748}-\frac {3800 (2+3 x)^{13}}{9477}+\frac {250 (2+3 x)^{14}}{5103} \]
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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} \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^3 \, dx=\frac {250 (3 x+2)^{14}}{5103}-\frac {3800 (3 x+2)^{13}}{9477}+\frac {8285 (3 x+2)^{12}}{8748}-\frac {4099 (3 x+2)^{11}}{8019}+\frac {763 (3 x+2)^{10}}{7290}-\frac {49 (3 x+2)^9}{6561} \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {49}{243} (2+3 x)^8+\frac {763}{243} (2+3 x)^9-\frac {4099}{243} (2+3 x)^{10}+\frac {8285}{243} (2+3 x)^{11}-\frac {3800}{243} (2+3 x)^{12}+\frac {500}{243} (2+3 x)^{13}\right ) \, dx \\ & = -\frac {49 (2+3 x)^9}{6561}+\frac {763 (2+3 x)^{10}}{7290}-\frac {4099 (2+3 x)^{11}}{8019}+\frac {8285 (2+3 x)^{12}}{8748}-\frac {3800 (2+3 x)^{13}}{9477}+\frac {250 (2+3 x)^{14}}{5103} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 85, normalized size of antiderivative = 1.27 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^3 \, dx=6912 x+44928 x^2+155136 x^3+261440 x^4-\frac {202208 x^5}{5}-\frac {3530000 x^6}{3}-\frac {17018256 x^7}{7}-1660896 x^8+2124195 x^9+\frac {62652123 x^{10}}{10}+\frac {77509953 x^{11}}{11}+\frac {17759655 x^{12}}{4}+\frac {20120400 x^{13}}{13}+\frac {1640250 x^{14}}{7} \]
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Time = 2.29 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.03
method | result | size |
gosper | \(\frac {x \left (14073345000 x^{13}+92956248000 x^{12}+266661219825 x^{11}+423204343380 x^{10}+376288650738 x^{9}+127579151700 x^{8}-99753413760 x^{7}-146016636480 x^{6}-70670600000 x^{5}-2428922496 x^{4}+15702086400 x^{3}+9317468160 x^{2}+2698375680 x +415134720\right )}{60060}\) | \(69\) |
default | \(6912 x +44928 x^{2}+155136 x^{3}+261440 x^{4}-\frac {202208}{5} x^{5}-\frac {3530000}{3} x^{6}-\frac {17018256}{7} x^{7}-1660896 x^{8}+2124195 x^{9}+\frac {62652123}{10} x^{10}+\frac {77509953}{11} x^{11}+\frac {17759655}{4} x^{12}+\frac {20120400}{13} x^{13}+\frac {1640250}{7} x^{14}\) | \(70\) |
norman | \(6912 x +44928 x^{2}+155136 x^{3}+261440 x^{4}-\frac {202208}{5} x^{5}-\frac {3530000}{3} x^{6}-\frac {17018256}{7} x^{7}-1660896 x^{8}+2124195 x^{9}+\frac {62652123}{10} x^{10}+\frac {77509953}{11} x^{11}+\frac {17759655}{4} x^{12}+\frac {20120400}{13} x^{13}+\frac {1640250}{7} x^{14}\) | \(70\) |
risch | \(6912 x +44928 x^{2}+155136 x^{3}+261440 x^{4}-\frac {202208}{5} x^{5}-\frac {3530000}{3} x^{6}-\frac {17018256}{7} x^{7}-1660896 x^{8}+2124195 x^{9}+\frac {62652123}{10} x^{10}+\frac {77509953}{11} x^{11}+\frac {17759655}{4} x^{12}+\frac {20120400}{13} x^{13}+\frac {1640250}{7} x^{14}\) | \(70\) |
parallelrisch | \(6912 x +44928 x^{2}+155136 x^{3}+261440 x^{4}-\frac {202208}{5} x^{5}-\frac {3530000}{3} x^{6}-\frac {17018256}{7} x^{7}-1660896 x^{8}+2124195 x^{9}+\frac {62652123}{10} x^{10}+\frac {77509953}{11} x^{11}+\frac {17759655}{4} x^{12}+\frac {20120400}{13} x^{13}+\frac {1640250}{7} x^{14}\) | \(70\) |
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Time = 0.21 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.03 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^3 \, dx=\frac {1640250}{7} \, x^{14} + \frac {20120400}{13} \, x^{13} + \frac {17759655}{4} \, x^{12} + \frac {77509953}{11} \, x^{11} + \frac {62652123}{10} \, x^{10} + 2124195 \, x^{9} - 1660896 \, x^{8} - \frac {17018256}{7} \, x^{7} - \frac {3530000}{3} \, x^{6} - \frac {202208}{5} \, x^{5} + 261440 \, x^{4} + 155136 \, x^{3} + 44928 \, x^{2} + 6912 \, x \]
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Time = 0.03 (sec) , antiderivative size = 82, normalized size of antiderivative = 1.22 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^3 \, dx=\frac {1640250 x^{14}}{7} + \frac {20120400 x^{13}}{13} + \frac {17759655 x^{12}}{4} + \frac {77509953 x^{11}}{11} + \frac {62652123 x^{10}}{10} + 2124195 x^{9} - 1660896 x^{8} - \frac {17018256 x^{7}}{7} - \frac {3530000 x^{6}}{3} - \frac {202208 x^{5}}{5} + 261440 x^{4} + 155136 x^{3} + 44928 x^{2} + 6912 x \]
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Time = 0.19 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.03 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^3 \, dx=\frac {1640250}{7} \, x^{14} + \frac {20120400}{13} \, x^{13} + \frac {17759655}{4} \, x^{12} + \frac {77509953}{11} \, x^{11} + \frac {62652123}{10} \, x^{10} + 2124195 \, x^{9} - 1660896 \, x^{8} - \frac {17018256}{7} \, x^{7} - \frac {3530000}{3} \, x^{6} - \frac {202208}{5} \, x^{5} + 261440 \, x^{4} + 155136 \, x^{3} + 44928 \, x^{2} + 6912 \, x \]
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Time = 0.27 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.03 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^3 \, dx=\frac {1640250}{7} \, x^{14} + \frac {20120400}{13} \, x^{13} + \frac {17759655}{4} \, x^{12} + \frac {77509953}{11} \, x^{11} + \frac {62652123}{10} \, x^{10} + 2124195 \, x^{9} - 1660896 \, x^{8} - \frac {17018256}{7} \, x^{7} - \frac {3530000}{3} \, x^{6} - \frac {202208}{5} \, x^{5} + 261440 \, x^{4} + 155136 \, x^{3} + 44928 \, x^{2} + 6912 \, x \]
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Time = 0.10 (sec) , antiderivative size = 69, normalized size of antiderivative = 1.03 \[ \int (1-2 x)^2 (2+3 x)^8 (3+5 x)^3 \, dx=\frac {1640250\,x^{14}}{7}+\frac {20120400\,x^{13}}{13}+\frac {17759655\,x^{12}}{4}+\frac {77509953\,x^{11}}{11}+\frac {62652123\,x^{10}}{10}+2124195\,x^9-1660896\,x^8-\frac {17018256\,x^7}{7}-\frac {3530000\,x^6}{3}-\frac {202208\,x^5}{5}+261440\,x^4+155136\,x^3+44928\,x^2+6912\,x \]
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