Integrand size = 22, antiderivative size = 59 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx=216 x+378 x^2-534 x^3-\frac {8693 x^4}{4}-\frac {1419 x^5}{5}+\frac {10513 x^6}{2}+\frac {33013 x^7}{7}-\frac {14355 x^8}{4}-6900 x^9-2700 x^{10} \]
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Time = 0.02 (sec) , antiderivative size = 59, 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} \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx=-2700 x^{10}-6900 x^9-\frac {14355 x^8}{4}+\frac {33013 x^7}{7}+\frac {10513 x^6}{2}-\frac {1419 x^5}{5}-\frac {8693 x^4}{4}-534 x^3+378 x^2+216 x \]
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Rule 90
Rubi steps \begin{align*} \text {integral}& = \int \left (216+756 x-1602 x^2-8693 x^3-1419 x^4+31539 x^5+33013 x^6-28710 x^7-62100 x^8-27000 x^9\right ) \, dx \\ & = 216 x+378 x^2-534 x^3-\frac {8693 x^4}{4}-\frac {1419 x^5}{5}+\frac {10513 x^6}{2}+\frac {33013 x^7}{7}-\frac {14355 x^8}{4}-6900 x^9-2700 x^{10} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx=216 x+378 x^2-534 x^3-\frac {8693 x^4}{4}-\frac {1419 x^5}{5}+\frac {10513 x^6}{2}+\frac {33013 x^7}{7}-\frac {14355 x^8}{4}-6900 x^9-2700 x^{10} \]
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Time = 2.40 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.83
method | result | size |
gosper | \(-\frac {x \left (378000 x^{9}+966000 x^{8}+502425 x^{7}-660260 x^{6}-735910 x^{5}+39732 x^{4}+304255 x^{3}+74760 x^{2}-52920 x -30240\right )}{140}\) | \(49\) |
default | \(216 x +378 x^{2}-534 x^{3}-\frac {8693}{4} x^{4}-\frac {1419}{5} x^{5}+\frac {10513}{2} x^{6}+\frac {33013}{7} x^{7}-\frac {14355}{4} x^{8}-6900 x^{9}-2700 x^{10}\) | \(50\) |
norman | \(216 x +378 x^{2}-534 x^{3}-\frac {8693}{4} x^{4}-\frac {1419}{5} x^{5}+\frac {10513}{2} x^{6}+\frac {33013}{7} x^{7}-\frac {14355}{4} x^{8}-6900 x^{9}-2700 x^{10}\) | \(50\) |
risch | \(216 x +378 x^{2}-534 x^{3}-\frac {8693}{4} x^{4}-\frac {1419}{5} x^{5}+\frac {10513}{2} x^{6}+\frac {33013}{7} x^{7}-\frac {14355}{4} x^{8}-6900 x^{9}-2700 x^{10}\) | \(50\) |
parallelrisch | \(216 x +378 x^{2}-534 x^{3}-\frac {8693}{4} x^{4}-\frac {1419}{5} x^{5}+\frac {10513}{2} x^{6}+\frac {33013}{7} x^{7}-\frac {14355}{4} x^{8}-6900 x^{9}-2700 x^{10}\) | \(50\) |
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none
Time = 0.21 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx=-2700 \, x^{10} - 6900 \, x^{9} - \frac {14355}{4} \, x^{8} + \frac {33013}{7} \, x^{7} + \frac {10513}{2} \, x^{6} - \frac {1419}{5} \, x^{5} - \frac {8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \]
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Time = 0.02 (sec) , antiderivative size = 56, normalized size of antiderivative = 0.95 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx=- 2700 x^{10} - 6900 x^{9} - \frac {14355 x^{8}}{4} + \frac {33013 x^{7}}{7} + \frac {10513 x^{6}}{2} - \frac {1419 x^{5}}{5} - \frac {8693 x^{4}}{4} - 534 x^{3} + 378 x^{2} + 216 x \]
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none
Time = 0.21 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx=-2700 \, x^{10} - 6900 \, x^{9} - \frac {14355}{4} \, x^{8} + \frac {33013}{7} \, x^{7} + \frac {10513}{2} \, x^{6} - \frac {1419}{5} \, x^{5} - \frac {8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \]
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Time = 0.29 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx=-2700 \, x^{10} - 6900 \, x^{9} - \frac {14355}{4} \, x^{8} + \frac {33013}{7} \, x^{7} + \frac {10513}{2} \, x^{6} - \frac {1419}{5} \, x^{5} - \frac {8693}{4} \, x^{4} - 534 \, x^{3} + 378 \, x^{2} + 216 \, x \]
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Time = 0.07 (sec) , antiderivative size = 49, normalized size of antiderivative = 0.83 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x)^3 \, dx=-2700\,x^{10}-6900\,x^9-\frac {14355\,x^8}{4}+\frac {33013\,x^7}{7}+\frac {10513\,x^6}{2}-\frac {1419\,x^5}{5}-\frac {8693\,x^4}{4}-534\,x^3+378\,x^2+216\,x \]
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