Integrand size = 7, antiderivative size = 9 \[ \int -5 e^{-x} \, dx=-4+5 e^{-x} \]
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Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 2225} \[ \int -5 e^{-x} \, dx=5 e^{-x} \]
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Rule 12
Rule 2225
Rubi steps \begin{align*} \text {integral}& = -\left (5 \int e^{-x} \, dx\right ) \\ & = 5 e^{-x} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int -5 e^{-x} \, dx=5 e^{-x} \]
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Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78
method | result | size |
gosper | \(5 \,{\mathrm e}^{-x}\) | \(7\) |
derivativedivides | \(5 \,{\mathrm e}^{-x}\) | \(7\) |
default | \(5 \,{\mathrm e}^{-x}\) | \(7\) |
norman | \(5 \,{\mathrm e}^{-x}\) | \(7\) |
risch | \(5 \,{\mathrm e}^{-x}\) | \(7\) |
parallelrisch | \(5 \,{\mathrm e}^{-x}\) | \(7\) |
meijerg | \(-5+5 \,{\mathrm e}^{-x}\) | \(9\) |
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none
Time = 0.25 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -5 e^{-x} \, dx=5 \, e^{\left (-x\right )} \]
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Time = 0.03 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.33 \[ \int -5 e^{-x} \, dx=5 e^{- x} \]
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none
Time = 0.18 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -5 e^{-x} \, dx=5 \, e^{\left (-x\right )} \]
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none
Time = 0.24 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -5 e^{-x} \, dx=5 \, e^{\left (-x\right )} \]
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Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -5 e^{-x} \, dx=5\,{\mathrm {e}}^{-x} \]
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