Integrand size = 20, antiderivative size = 45 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx=24 x+2 x^2-86 x^3-\frac {117 x^4}{4}+\frac {949 x^5}{5}+111 x^6-\frac {1188 x^7}{7}-135 x^8 \]
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Time = 0.01 (sec) , antiderivative size = 45, 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} \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx=-135 x^8-\frac {1188 x^7}{7}+111 x^6+\frac {949 x^5}{5}-\frac {117 x^4}{4}-86 x^3+2 x^2+24 x \]
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Rule 78
Rubi steps \begin{align*} \text {integral}& = \int \left (24+4 x-258 x^2-117 x^3+949 x^4+666 x^5-1188 x^6-1080 x^7\right ) \, dx \\ & = 24 x+2 x^2-86 x^3-\frac {117 x^4}{4}+\frac {949 x^5}{5}+111 x^6-\frac {1188 x^7}{7}-135 x^8 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.00 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx=24 x+2 x^2-86 x^3-\frac {117 x^4}{4}+\frac {949 x^5}{5}+111 x^6-\frac {1188 x^7}{7}-135 x^8 \]
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Time = 2.36 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.87
method | result | size |
gosper | \(-\frac {x \left (18900 x^{7}+23760 x^{6}-15540 x^{5}-26572 x^{4}+4095 x^{3}+12040 x^{2}-280 x -3360\right )}{140}\) | \(39\) |
default | \(24 x +2 x^{2}-86 x^{3}-\frac {117}{4} x^{4}+\frac {949}{5} x^{5}+111 x^{6}-\frac {1188}{7} x^{7}-135 x^{8}\) | \(40\) |
norman | \(24 x +2 x^{2}-86 x^{3}-\frac {117}{4} x^{4}+\frac {949}{5} x^{5}+111 x^{6}-\frac {1188}{7} x^{7}-135 x^{8}\) | \(40\) |
risch | \(24 x +2 x^{2}-86 x^{3}-\frac {117}{4} x^{4}+\frac {949}{5} x^{5}+111 x^{6}-\frac {1188}{7} x^{7}-135 x^{8}\) | \(40\) |
parallelrisch | \(24 x +2 x^{2}-86 x^{3}-\frac {117}{4} x^{4}+\frac {949}{5} x^{5}+111 x^{6}-\frac {1188}{7} x^{7}-135 x^{8}\) | \(40\) |
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Time = 0.22 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.87 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx=-135 \, x^{8} - \frac {1188}{7} \, x^{7} + 111 \, x^{6} + \frac {949}{5} \, x^{5} - \frac {117}{4} \, x^{4} - 86 \, x^{3} + 2 \, x^{2} + 24 \, x \]
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Time = 0.02 (sec) , antiderivative size = 42, normalized size of antiderivative = 0.93 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx=- 135 x^{8} - \frac {1188 x^{7}}{7} + 111 x^{6} + \frac {949 x^{5}}{5} - \frac {117 x^{4}}{4} - 86 x^{3} + 2 x^{2} + 24 x \]
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Time = 0.19 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.87 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx=-135 \, x^{8} - \frac {1188}{7} \, x^{7} + 111 \, x^{6} + \frac {949}{5} \, x^{5} - \frac {117}{4} \, x^{4} - 86 \, x^{3} + 2 \, x^{2} + 24 \, x \]
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Time = 0.27 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.87 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx=-135 \, x^{8} - \frac {1188}{7} \, x^{7} + 111 \, x^{6} + \frac {949}{5} \, x^{5} - \frac {117}{4} \, x^{4} - 86 \, x^{3} + 2 \, x^{2} + 24 \, x \]
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Time = 0.03 (sec) , antiderivative size = 39, normalized size of antiderivative = 0.87 \[ \int (1-2 x)^3 (2+3 x)^3 (3+5 x) \, dx=-135\,x^8-\frac {1188\,x^7}{7}+111\,x^6+\frac {949\,x^5}{5}-\frac {117\,x^4}{4}-86\,x^3+2\,x^2+24\,x \]
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