Integrand size = 18, antiderivative size = 34 \[ \int (1-2 x) (2+3 x)^6 (3+5 x) \, dx=-\frac {1}{27} (2+3 x)^7+\frac {37}{216} (2+3 x)^8-\frac {10}{243} (2+3 x)^9 \]
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Time = 0.01 (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} \[ \int (1-2 x) (2+3 x)^6 (3+5 x) \, dx=-\frac {10}{243} (3 x+2)^9+\frac {37}{216} (3 x+2)^8-\frac {1}{27} (3 x+2)^7 \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {7}{9} (2+3 x)^6+\frac {37}{9} (2+3 x)^7-\frac {10}{9} (2+3 x)^8\right ) \, dx \\ & = -\frac {1}{27} (2+3 x)^7+\frac {37}{216} (2+3 x)^8-\frac {10}{243} (2+3 x)^9 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.41 \[ \int (1-2 x) (2+3 x)^6 (3+5 x) \, dx=192 x+832 x^2+\frac {5264 x^3}{3}+1260 x^4-2268 x^5-6552 x^6-7047 x^7-\frac {29889 x^8}{8}-810 x^9 \]
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Time = 2.09 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.29
method | result | size |
gosper | \(-\frac {x \left (19440 x^{8}+89667 x^{7}+169128 x^{6}+157248 x^{5}+54432 x^{4}-30240 x^{3}-42112 x^{2}-19968 x -4608\right )}{24}\) | \(44\) |
default | \(-810 x^{9}-\frac {29889}{8} x^{8}-7047 x^{7}-6552 x^{6}-2268 x^{5}+1260 x^{4}+\frac {5264}{3} x^{3}+832 x^{2}+192 x\) | \(45\) |
norman | \(-810 x^{9}-\frac {29889}{8} x^{8}-7047 x^{7}-6552 x^{6}-2268 x^{5}+1260 x^{4}+\frac {5264}{3} x^{3}+832 x^{2}+192 x\) | \(45\) |
risch | \(-810 x^{9}-\frac {29889}{8} x^{8}-7047 x^{7}-6552 x^{6}-2268 x^{5}+1260 x^{4}+\frac {5264}{3} x^{3}+832 x^{2}+192 x\) | \(45\) |
parallelrisch | \(-810 x^{9}-\frac {29889}{8} x^{8}-7047 x^{7}-6552 x^{6}-2268 x^{5}+1260 x^{4}+\frac {5264}{3} x^{3}+832 x^{2}+192 x\) | \(45\) |
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Time = 0.22 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.29 \[ \int (1-2 x) (2+3 x)^6 (3+5 x) \, dx=-810 \, x^{9} - \frac {29889}{8} \, x^{8} - 7047 \, x^{7} - 6552 \, x^{6} - 2268 \, x^{5} + 1260 \, x^{4} + \frac {5264}{3} \, x^{3} + 832 \, x^{2} + 192 \, x \]
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Time = 0.02 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.35 \[ \int (1-2 x) (2+3 x)^6 (3+5 x) \, dx=- 810 x^{9} - \frac {29889 x^{8}}{8} - 7047 x^{7} - 6552 x^{6} - 2268 x^{5} + 1260 x^{4} + \frac {5264 x^{3}}{3} + 832 x^{2} + 192 x \]
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Time = 0.20 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.29 \[ \int (1-2 x) (2+3 x)^6 (3+5 x) \, dx=-810 \, x^{9} - \frac {29889}{8} \, x^{8} - 7047 \, x^{7} - 6552 \, x^{6} - 2268 \, x^{5} + 1260 \, x^{4} + \frac {5264}{3} \, x^{3} + 832 \, x^{2} + 192 \, x \]
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Time = 0.29 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.29 \[ \int (1-2 x) (2+3 x)^6 (3+5 x) \, dx=-810 \, x^{9} - \frac {29889}{8} \, x^{8} - 7047 \, x^{7} - 6552 \, x^{6} - 2268 \, x^{5} + 1260 \, x^{4} + \frac {5264}{3} \, x^{3} + 832 \, x^{2} + 192 \, x \]
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Time = 0.04 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.29 \[ \int (1-2 x) (2+3 x)^6 (3+5 x) \, dx=-810\,x^9-\frac {29889\,x^8}{8}-7047\,x^7-6552\,x^6-2268\,x^5+1260\,x^4+\frac {5264\,x^3}{3}+832\,x^2+192\,x \]
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