Integrand size = 18, antiderivative size = 34 \[ \int (1-2 x) (2+3 x)^7 (3+5 x) \, dx=-\frac {7}{216} (2+3 x)^8+\frac {37}{243} (2+3 x)^9-\frac {1}{27} (2+3 x)^{10} \]
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Time = 0.02 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {78} \[ \int (1-2 x) (2+3 x)^7 (3+5 x) \, dx=-\frac {1}{27} (3 x+2)^{10}+\frac {37}{243} (3 x+2)^9-\frac {7}{216} (3 x+2)^8 \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {7}{9} (2+3 x)^7+\frac {37}{9} (2+3 x)^8-\frac {10}{9} (2+3 x)^9\right ) \, dx \\ & = -\frac {7}{216} (2+3 x)^8+\frac {37}{243} (2+3 x)^9-\frac {1}{27} (2+3 x)^{10} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.56 \[ \int (1-2 x) (2+3 x)^7 (3+5 x) \, dx=384 x+1952 x^2+\frac {15520 x^3}{3}+6468 x^4-1512 x^5-18774 x^6-30942 x^7-\frac {207765 x^8}{8}-11583 x^9-2187 x^{10} \]
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Time = 0.68 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.44
method | result | size |
gosper | \(-\frac {x \left (52488 x^{9}+277992 x^{8}+623295 x^{7}+742608 x^{6}+450576 x^{5}+36288 x^{4}-155232 x^{3}-124160 x^{2}-46848 x -9216\right )}{24}\) | \(49\) |
default | \(-2187 x^{10}-11583 x^{9}-\frac {207765}{8} x^{8}-30942 x^{7}-18774 x^{6}-1512 x^{5}+6468 x^{4}+\frac {15520}{3} x^{3}+1952 x^{2}+384 x\) | \(50\) |
norman | \(-2187 x^{10}-11583 x^{9}-\frac {207765}{8} x^{8}-30942 x^{7}-18774 x^{6}-1512 x^{5}+6468 x^{4}+\frac {15520}{3} x^{3}+1952 x^{2}+384 x\) | \(50\) |
risch | \(-2187 x^{10}-11583 x^{9}-\frac {207765}{8} x^{8}-30942 x^{7}-18774 x^{6}-1512 x^{5}+6468 x^{4}+\frac {15520}{3} x^{3}+1952 x^{2}+384 x\) | \(50\) |
parallelrisch | \(-2187 x^{10}-11583 x^{9}-\frac {207765}{8} x^{8}-30942 x^{7}-18774 x^{6}-1512 x^{5}+6468 x^{4}+\frac {15520}{3} x^{3}+1952 x^{2}+384 x\) | \(50\) |
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Time = 0.22 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.44 \[ \int (1-2 x) (2+3 x)^7 (3+5 x) \, dx=-2187 \, x^{10} - 11583 \, x^{9} - \frac {207765}{8} \, x^{8} - 30942 \, x^{7} - 18774 \, x^{6} - 1512 \, x^{5} + 6468 \, x^{4} + \frac {15520}{3} \, x^{3} + 1952 \, x^{2} + 384 \, x \]
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Time = 0.02 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.50 \[ \int (1-2 x) (2+3 x)^7 (3+5 x) \, dx=- 2187 x^{10} - 11583 x^{9} - \frac {207765 x^{8}}{8} - 30942 x^{7} - 18774 x^{6} - 1512 x^{5} + 6468 x^{4} + \frac {15520 x^{3}}{3} + 1952 x^{2} + 384 x \]
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Time = 0.19 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.44 \[ \int (1-2 x) (2+3 x)^7 (3+5 x) \, dx=-2187 \, x^{10} - 11583 \, x^{9} - \frac {207765}{8} \, x^{8} - 30942 \, x^{7} - 18774 \, x^{6} - 1512 \, x^{5} + 6468 \, x^{4} + \frac {15520}{3} \, x^{3} + 1952 \, x^{2} + 384 \, x \]
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Time = 0.28 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.44 \[ \int (1-2 x) (2+3 x)^7 (3+5 x) \, dx=-2187 \, x^{10} - 11583 \, x^{9} - \frac {207765}{8} \, x^{8} - 30942 \, x^{7} - 18774 \, x^{6} - 1512 \, x^{5} + 6468 \, x^{4} + \frac {15520}{3} \, x^{3} + 1952 \, x^{2} + 384 \, x \]
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Time = 0.04 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.44 \[ \int (1-2 x) (2+3 x)^7 (3+5 x) \, dx=-2187\,x^{10}-11583\,x^9-\frac {207765\,x^8}{8}-30942\,x^7-18774\,x^6-1512\,x^5+6468\,x^4+\frac {15520\,x^3}{3}+1952\,x^2+384\,x \]
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