Integrand size = 32, antiderivative size = 15 \[ \int \frac {e^{-2+x-x^6} \left (-1+6 x^5\right )}{-1+e^{-2+x-x^6}} \, dx=-\log \left (-1+e^{-2+x-x^6}\right ) \]
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Time = 0.08 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.80, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {6816} \[ \int \frac {e^{-2+x-x^6} \left (-1+6 x^5\right )}{-1+e^{-2+x-x^6}} \, dx=-\log \left (-e^{-x^6-2} \left (e^x-e^{x^6+2}\right )\right ) \]
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Rule 6816
Rubi steps \begin{align*} \text {integral}& = -\log \left (-e^{-2-x^6} \left (e^x-e^{2+x^6}\right )\right ) \\ \end{align*}
Time = 0.57 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.33 \[ \int \frac {e^{-2+x-x^6} \left (-1+6 x^5\right )}{-1+e^{-2+x-x^6}} \, dx=x^6-\log \left (e^x-e^{2+x^6}\right ) \]
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Time = 0.08 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00
method | result | size |
norman | \(-\ln \left ({\mathrm e}^{-x^{6}+x -2}-1\right )\) | \(15\) |
parallelrisch | \(-\ln \left ({\mathrm e}^{-x^{6}+x -2}-1\right )\) | \(15\) |
risch | \(-2-\ln \left ({\mathrm e}^{-x^{6}+x -2}-1\right )\) | \(17\) |
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none
Time = 0.23 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {e^{-2+x-x^6} \left (-1+6 x^5\right )}{-1+e^{-2+x-x^6}} \, dx=-\log \left (e^{\left (-x^{6} + x - 2\right )} - 1\right ) \]
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Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \frac {e^{-2+x-x^6} \left (-1+6 x^5\right )}{-1+e^{-2+x-x^6}} \, dx=- \log {\left (e^{- x^{6} + x - 2} - 1 \right )} \]
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none
Time = 0.23 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.40 \[ \int \frac {e^{-2+x-x^6} \left (-1+6 x^5\right )}{-1+e^{-2+x-x^6}} \, dx=x^{6} - \log \left ({\left (e^{\left (x^{6} + 2\right )} - e^{x}\right )} e^{\left (-2\right )}\right ) \]
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none
Time = 0.25 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.07 \[ \int \frac {e^{-2+x-x^6} \left (-1+6 x^5\right )}{-1+e^{-2+x-x^6}} \, dx=-\log \left (-e^{\left (-x^{6} + x - 2\right )} + 1\right ) \]
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Time = 0.14 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \frac {e^{-2+x-x^6} \left (-1+6 x^5\right )}{-1+e^{-2+x-x^6}} \, dx=-\ln \left ({\mathrm {e}}^{-x^6+x-2}-1\right ) \]
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