Integrand size = 14, antiderivative size = 11 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=e^{625 x^8}-x \]
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Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {2240} \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=e^{625 x^8}-x \]
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Rule 2240
Rubi steps \begin{align*} \text {integral}& = -x+5000 \int e^{625 x^8} x^7 \, dx \\ & = e^{625 x^8}-x \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=e^{625 x^8}-x \]
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Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00
method | result | size |
default | \(-x +{\mathrm e}^{625 x^{8}}\) | \(11\) |
norman | \(-x +{\mathrm e}^{625 x^{8}}\) | \(11\) |
risch | \(-x +{\mathrm e}^{625 x^{8}}\) | \(11\) |
parallelrisch | \(-x +{\mathrm e}^{625 x^{8}}\) | \(11\) |
parts | \(-x +{\mathrm e}^{625 x^{8}}\) | \(11\) |
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none
Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=-x + e^{\left (625 \, x^{8}\right )} \]
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Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=- x + e^{625 x^{8}} \]
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none
Time = 0.18 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=-x + e^{\left (625 \, x^{8}\right )} \]
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none
Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx=-x + e^{\left (625 \, x^{8}\right )} \]
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Time = 0.06 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \left (-1+5000 e^{625 x^8} x^7\right ) \, dx={\mathrm {e}}^{625\,x^8}-x \]
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