Optimal. Leaf size=24 \[ 2 e^{\sqrt{x}} \sqrt{x}-2 e^{\sqrt{x}} \]
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Rubi [A] time = 0.0077433, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.429, Rules used = {2207, 2176, 2194} \[ 2 e^{\sqrt{x}} \sqrt{x}-2 e^{\sqrt{x}} \]
Antiderivative was successfully verified.
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Rule 2207
Rule 2176
Rule 2194
Rubi steps
\begin{align*} \int e^{\sqrt{x}} \, dx &=2 \operatorname{Subst}\left (\int e^x x \, dx,x,\sqrt{x}\right )\\ &=2 e^{\sqrt{x}} \sqrt{x}-2 \operatorname{Subst}\left (\int e^x \, dx,x,\sqrt{x}\right )\\ &=-2 e^{\sqrt{x}}+2 e^{\sqrt{x}} \sqrt{x}\\ \end{align*}
Mathematica [A] time = 0.005531, size = 16, normalized size = 0.67 \[ 2 e^{\sqrt{x}} \left (\sqrt{x}-1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 17, normalized size = 0.7 \begin{align*} -2\,{{\rm e}^{\sqrt{x}}}+2\,{{\rm e}^{\sqrt{x}}}\sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.946347, size = 15, normalized size = 0.62 \begin{align*} 2 \,{\left (\sqrt{x} - 1\right )} e^{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.21775, size = 36, normalized size = 1.5 \begin{align*} 2 \,{\left (\sqrt{x} - 1\right )} e^{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.177795, size = 20, normalized size = 0.83 \begin{align*} 2 \sqrt{x} e^{\sqrt{x}} - 2 e^{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.06747, size = 15, normalized size = 0.62 \begin{align*} 2 \,{\left (\sqrt{x} - 1\right )} e^{\sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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