Integrand size = 3, antiderivative size = 3 \[ \int e^x \, dx=e^x \]
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Time = 0.00 (sec) , antiderivative size = 3, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2225} \[ \int e^x \, dx=e^x \]
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Rule 2225
Rubi steps \begin{align*} \text {integral}& = e^x \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 3, normalized size of antiderivative = 1.00 \[ \int e^x \, dx=e^x \]
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Time = 0.05 (sec) , antiderivative size = 3, normalized size of antiderivative = 1.00
method | result | size |
gosper | \({\mathrm e}^{x}\) | \(3\) |
lookup | \({\mathrm e}^{x}\) | \(3\) |
derivativedivides | \({\mathrm e}^{x}\) | \(3\) |
default | \({\mathrm e}^{x}\) | \(3\) |
norman | \({\mathrm e}^{x}\) | \(3\) |
risch | \({\mathrm e}^{x}\) | \(3\) |
parallelrisch | \({\mathrm e}^{x}\) | \(3\) |
meijerg | \({\mathrm e}^{x}-1\) | \(5\) |
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none
Time = 0.23 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.67 \[ \int e^x \, dx=e^{x} \]
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Time = 0.04 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.67 \[ \int e^x \, dx=e^{x} \]
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none
Time = 0.18 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.67 \[ \int e^x \, dx=e^{x} \]
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none
Time = 0.27 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.67 \[ \int e^x \, dx=e^{x} \]
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Time = 0.01 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.67 \[ \int e^x \, dx={\mathrm {e}}^x \]
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