Optimal. Leaf size=11 \[ 2 \sqrt {x+e^x} \]
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Rubi [A] time = 0.03, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {6686} \[ 2 \sqrt {x+e^x} \]
Antiderivative was successfully verified.
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Rule 6686
Rubi steps
\begin {align*} \int \frac {1+e^x}{\sqrt {e^x+x}} \, dx &=2 \sqrt {e^x+x}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 1.00 \[ 2 \sqrt {x+e^x} \]
Antiderivative was successfully verified.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 8, normalized size = 0.73 \[ 2 \, \sqrt {x + e^{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 9, normalized size = 0.82 \[ 2 \sqrt {x +{\mathrm e}^{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.95, size = 8, normalized size = 0.73 \[ 2 \, \sqrt {x + e^{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.50, size = 8, normalized size = 0.73 \[ 2\,\sqrt {x+{\mathrm {e}}^x} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 8, normalized size = 0.73 \[ 2 \sqrt {x + e^{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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