Integrand size = 13, antiderivative size = 11 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{e^{\frac {1}{e^4}}-x} \]
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Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {2225} \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{e^{\frac {1}{e^4}}-x} \]
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Rule 2225
Rubi steps \begin{align*} \text {integral}& = e^{e^{\frac {1}{e^4}}-x} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{e^{\frac {1}{e^4}}-x} \]
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Time = 0.04 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\) | \(9\) |
gosper | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\) | \(11\) |
derivativedivides | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\) | \(11\) |
default | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\) | \(11\) |
norman | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\) | \(11\) |
parallelrisch | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\) | \(11\) |
parts | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}-x}\) | \(11\) |
meijerg | \(-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{-4}}} \left (1-{\mathrm e}^{-x}\right )\) | \(15\) |
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none
Time = 0.24 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{\left (-x + e^{\left (e^{\left (-4\right )}\right )}\right )} \]
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Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{- x + e^{e^{-4}}} \]
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none
Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{\left (-x + e^{\left (e^{\left (-4\right )}\right )}\right )} \]
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none
Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx=e^{\left (-x + e^{\left (e^{\left (-4\right )}\right )}\right )} \]
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Time = 0.04 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int -e^{e^{\frac {1}{e^4}}-x} \, dx={\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{-4}}}\,{\mathrm {e}}^{-x} \]
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