Optimal. Leaf size=11 \[ 2 \sqrt{x+e^x} \]
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Rubi [A] time = 0.0408029, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 23, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.043, Rules used = {2261} \[ 2 \sqrt{x+e^x} \]
Antiderivative was successfully verified.
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Rule 2261
Rubi steps
\begin{align*} \int \left (\frac{1}{\sqrt{e^x+x}}+\frac{e^x}{\sqrt{e^x+x}}\right ) \, dx &=\int \frac{1}{\sqrt{e^x+x}} \, dx+\int \frac{e^x}{\sqrt{e^x+x}} \, dx\\ &=2 \sqrt{e^x+x}\\ \end{align*}
Mathematica [A] time = 0.0047456, size = 11, normalized size = 1. \[ 2 \sqrt{x+e^x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.042, size = 9, normalized size = 0.8 \begin{align*} 2\,\sqrt{{{\rm e}^{x}}+x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.09435, size = 11, normalized size = 1. \begin{align*} 2 \, \sqrt{x + e^{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{x} + 1}{\sqrt{x + e^{x}}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{e^{x}}{\sqrt{x + e^{x}}} + \frac{1}{\sqrt{x + e^{x}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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