Optimal. Leaf size=24 \[ 2 e^{\sqrt {x}} \sqrt {x}-2 e^{\sqrt {x}} \]
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Rubi [A] time = 0.01, antiderivative size = 24, normalized size of antiderivative = 1.00, 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 2176
Rule 2194
Rule 2207
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*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 0.67 \[ 2 e^{\sqrt {x}} \left (\sqrt {x}-1\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 11, normalized size = 0.46 \[ 2 \, {\left (\sqrt {x} - 1\right )} e^{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.85, size = 11, normalized size = 0.46 \[ 2 \, {\left (\sqrt {x} - 1\right )} e^{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 17, normalized size = 0.71 \[ 2 \sqrt {x}\, {\mathrm e}^{\sqrt {x}}-2 \,{\mathrm e}^{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 11, normalized size = 0.46 \[ 2 \, {\left (\sqrt {x} - 1\right )} e^{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 11, normalized size = 0.46 \[ 2\,{\mathrm {e}}^{\sqrt {x}}\,\left (\sqrt {x}-1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 20, normalized size = 0.83 \[ 2 \sqrt {x} e^{\sqrt {x}} - 2 e^{\sqrt {x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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