Integrand size = 11, antiderivative size = 22 \[ \int x \left (1-x^3\right )^2 \, dx=\frac {x^2}{2}-\frac {2 x^5}{5}+\frac {x^8}{8} \]
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Time = 0.00 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {276} \[ \int x \left (1-x^3\right )^2 \, dx=\frac {x^8}{8}-\frac {2 x^5}{5}+\frac {x^2}{2} \]
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Rule 276
Rubi steps \begin{align*} \text {integral}& = \int \left (x-2 x^4+x^7\right ) \, dx \\ & = \frac {x^2}{2}-\frac {2 x^5}{5}+\frac {x^8}{8} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int x \left (1-x^3\right )^2 \, dx=\frac {x^2}{2}-\frac {2 x^5}{5}+\frac {x^8}{8} \]
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Time = 0.81 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77
method | result | size |
default | \(\frac {1}{2} x^{2}-\frac {2}{5} x^{5}+\frac {1}{8} x^{8}\) | \(17\) |
norman | \(\frac {1}{2} x^{2}-\frac {2}{5} x^{5}+\frac {1}{8} x^{8}\) | \(17\) |
risch | \(\frac {1}{2} x^{2}-\frac {2}{5} x^{5}+\frac {1}{8} x^{8}\) | \(17\) |
parallelrisch | \(\frac {1}{2} x^{2}-\frac {2}{5} x^{5}+\frac {1}{8} x^{8}\) | \(17\) |
gosper | \(\frac {x^{2} \left (5 x^{6}-16 x^{3}+20\right )}{40}\) | \(18\) |
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none
Time = 0.24 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.73 \[ \int x \left (1-x^3\right )^2 \, dx=\frac {1}{8} \, x^{8} - \frac {2}{5} \, x^{5} + \frac {1}{2} \, x^{2} \]
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Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.68 \[ \int x \left (1-x^3\right )^2 \, dx=\frac {x^{8}}{8} - \frac {2 x^{5}}{5} + \frac {x^{2}}{2} \]
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none
Time = 0.19 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.73 \[ \int x \left (1-x^3\right )^2 \, dx=\frac {1}{8} \, x^{8} - \frac {2}{5} \, x^{5} + \frac {1}{2} \, x^{2} \]
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none
Time = 0.29 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.73 \[ \int x \left (1-x^3\right )^2 \, dx=\frac {1}{8} \, x^{8} - \frac {2}{5} \, x^{5} + \frac {1}{2} \, x^{2} \]
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Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77 \[ \int x \left (1-x^3\right )^2 \, dx=\frac {x^2\,\left (5\,x^6-16\,x^3+20\right )}{40} \]
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