Integrand size = 9, antiderivative size = 7 \[ \int -e^{-2-x} \, dx=e^{-2-x} \]
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Time = 0.01 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2225} \[ \int -e^{-2-x} \, dx=e^{-x-2} \]
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Rule 2225
Rubi steps \begin{align*} \text {integral}& = e^{-2-x} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int -e^{-2-x} \, dx=e^{-2-x} \]
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Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00
method | result | size |
gosper | \({\mathrm e}^{-2-x}\) | \(7\) |
derivativedivides | \({\mathrm e}^{-2-x}\) | \(7\) |
default | \({\mathrm e}^{-2-x}\) | \(7\) |
norman | \({\mathrm e}^{-2-x}\) | \(7\) |
risch | \({\mathrm e}^{-2-x}\) | \(7\) |
parallelrisch | \({\mathrm e}^{-2-x}\) | \(7\) |
parts | \({\mathrm e}^{-2-x}\) | \(7\) |
meijerg | \(-{\mathrm e}^{-2} \left (1-{\mathrm e}^{-x}\right )\) | \(13\) |
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none
Time = 0.22 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int -e^{-2-x} \, dx=e^{\left (-x - 2\right )} \]
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Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int -e^{-2-x} \, dx=e^{- x - 2} \]
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none
Time = 0.17 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int -e^{-2-x} \, dx=e^{\left (-x - 2\right )} \]
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none
Time = 0.28 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int -e^{-2-x} \, dx=e^{\left (-x - 2\right )} \]
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Time = 0.04 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int -e^{-2-x} \, dx={\mathrm {e}}^{-x-2} \]
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