Optimal. Leaf size=6 \[ \log \left (x+e^x\right ) \]
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Rubi [A] time = 0.0195129, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {6684} \[ \log \left (x+e^x\right ) \]
Antiderivative was successfully verified.
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Rule 6684
Rubi steps
\begin{align*} \int \frac{1+e^x}{e^x+x} \, dx &=\log \left (e^x+x\right )\\ \end{align*}
Mathematica [A] time = 0.0298571, size = 6, normalized size = 1. \[ \log \left (x+e^x\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.017, size = 6, normalized size = 1. \begin{align*} \ln \left ({{\rm e}^{x}}+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.980101, size = 7, normalized size = 1.17 \begin{align*} \log \left (x + e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.89915, size = 19, normalized size = 3.17 \begin{align*} \log \left (x + e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.095375, size = 5, normalized size = 0.83 \begin{align*} \log{\left (x + e^{x} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.2249, size = 7, normalized size = 1.17 \begin{align*} \log \left (x + e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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