Integrand size = 22, antiderivative size = 35 \[ \int x \left (a+8 x-8 x^2+4 x^3-x^4\right ) \, dx=\frac {a x^2}{2}+\frac {8 x^3}{3}-2 x^4+\frac {4 x^5}{5}-\frac {x^6}{6} \]
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Time = 0.01 (sec) , antiderivative size = 35, 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 = {14} \[ \int x \left (a+8 x-8 x^2+4 x^3-x^4\right ) \, dx=\frac {a x^2}{2}-\frac {x^6}{6}+\frac {4 x^5}{5}-2 x^4+\frac {8 x^3}{3} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (a x+8 x^2-8 x^3+4 x^4-x^5\right ) \, dx \\ & = \frac {a x^2}{2}+\frac {8 x^3}{3}-2 x^4+\frac {4 x^5}{5}-\frac {x^6}{6} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.00 \[ \int x \left (a+8 x-8 x^2+4 x^3-x^4\right ) \, dx=\frac {a x^2}{2}+\frac {8 x^3}{3}-2 x^4+\frac {4 x^5}{5}-\frac {x^6}{6} \]
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Time = 0.02 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.80
method | result | size |
gosper | \(\frac {1}{2} a \,x^{2}+\frac {8}{3} x^{3}-2 x^{4}+\frac {4}{5} x^{5}-\frac {1}{6} x^{6}\) | \(28\) |
default | \(\frac {1}{2} a \,x^{2}+\frac {8}{3} x^{3}-2 x^{4}+\frac {4}{5} x^{5}-\frac {1}{6} x^{6}\) | \(28\) |
norman | \(\frac {1}{2} a \,x^{2}+\frac {8}{3} x^{3}-2 x^{4}+\frac {4}{5} x^{5}-\frac {1}{6} x^{6}\) | \(28\) |
risch | \(\frac {1}{2} a \,x^{2}+\frac {8}{3} x^{3}-2 x^{4}+\frac {4}{5} x^{5}-\frac {1}{6} x^{6}\) | \(28\) |
parallelrisch | \(\frac {1}{2} a \,x^{2}+\frac {8}{3} x^{3}-2 x^{4}+\frac {4}{5} x^{5}-\frac {1}{6} x^{6}\) | \(28\) |
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none
Time = 0.25 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.77 \[ \int x \left (a+8 x-8 x^2+4 x^3-x^4\right ) \, dx=-\frac {1}{6} \, x^{6} + \frac {4}{5} \, x^{5} - 2 \, x^{4} + \frac {1}{2} \, a x^{2} + \frac {8}{3} \, x^{3} \]
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Time = 0.02 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.83 \[ \int x \left (a+8 x-8 x^2+4 x^3-x^4\right ) \, dx=\frac {a x^{2}}{2} - \frac {x^{6}}{6} + \frac {4 x^{5}}{5} - 2 x^{4} + \frac {8 x^{3}}{3} \]
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none
Time = 0.20 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.77 \[ \int x \left (a+8 x-8 x^2+4 x^3-x^4\right ) \, dx=-\frac {1}{6} \, x^{6} + \frac {4}{5} \, x^{5} - 2 \, x^{4} + \frac {1}{2} \, a x^{2} + \frac {8}{3} \, x^{3} \]
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none
Time = 0.26 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.77 \[ \int x \left (a+8 x-8 x^2+4 x^3-x^4\right ) \, dx=-\frac {1}{6} \, x^{6} + \frac {4}{5} \, x^{5} - 2 \, x^{4} + \frac {1}{2} \, a x^{2} + \frac {8}{3} \, x^{3} \]
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Time = 0.01 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.77 \[ \int x \left (a+8 x-8 x^2+4 x^3-x^4\right ) \, dx=-\frac {x^6}{6}+\frac {4\,x^5}{5}-2\,x^4+\frac {8\,x^3}{3}+\frac {a\,x^2}{2} \]
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