Integrand size = 7, antiderivative size = 24 \[ \int e^{\sqrt {x}} \, dx=-2 e^{\sqrt {x}}+2 e^{\sqrt {x}} \sqrt {x} \]
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Time = 0.01 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.429, Rules used = {2238, 2207, 2225} \[ \int e^{\sqrt {x}} \, dx=2 e^{\sqrt {x}} \sqrt {x}-2 e^{\sqrt {x}} \]
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Rule 2207
Rule 2225
Rule 2238
Rubi steps \begin{align*} \text {integral}& = 2 \text {Subst}\left (\int e^x x \, dx,x,\sqrt {x}\right ) \\ & = 2 e^{\sqrt {x}} \sqrt {x}-2 \text {Subst}\left (\int e^x \, dx,x,\sqrt {x}\right ) \\ & = -2 e^{\sqrt {x}}+2 e^{\sqrt {x}} \sqrt {x} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67 \[ \int e^{\sqrt {x}} \, dx=2 e^{\sqrt {x}} \left (-1+\sqrt {x}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67
method | result | size |
meijerg | \(2-\left (-2 \sqrt {x}+2\right ) {\mathrm e}^{\sqrt {x}}\) | \(16\) |
derivativedivides | \(-2 \,{\mathrm e}^{\sqrt {x}}+2 \,{\mathrm e}^{\sqrt {x}} \sqrt {x}\) | \(17\) |
default | \(-2 \,{\mathrm e}^{\sqrt {x}}+2 \,{\mathrm e}^{\sqrt {x}} \sqrt {x}\) | \(17\) |
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none
Time = 0.24 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.46 \[ \int e^{\sqrt {x}} \, dx=2 \, {\left (\sqrt {x} - 1\right )} e^{\sqrt {x}} \]
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Time = 0.08 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int e^{\sqrt {x}} \, dx=2 \sqrt {x} e^{\sqrt {x}} - 2 e^{\sqrt {x}} \]
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none
Time = 0.19 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.46 \[ \int e^{\sqrt {x}} \, dx=2 \, {\left (\sqrt {x} - 1\right )} e^{\sqrt {x}} \]
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none
Time = 0.27 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.46 \[ \int e^{\sqrt {x}} \, dx=2 \, {\left (\sqrt {x} - 1\right )} e^{\sqrt {x}} \]
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Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.46 \[ \int e^{\sqrt {x}} \, dx=2\,{\mathrm {e}}^{\sqrt {x}}\,\left (\sqrt {x}-1\right ) \]
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