Optimal. Leaf size=8 \[ e \log \left (e^x+1\right ) \]
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Rubi [A] time = 0.0340458, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.231, Rules used = {2247, 2246, 31} \[ e \log \left (e^x+1\right ) \]
Antiderivative was successfully verified.
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Rule 2247
Rule 2246
Rule 31
Rubi steps
\begin{align*} \int \frac{e^{1+x}}{1+e^x} \, dx &=e \int \frac{e^x}{1+e^x} \, dx\\ &=e \operatorname{Subst}\left (\int \frac{1}{1+x} \, dx,x,e^x\right )\\ &=e \log \left (1+e^x\right )\\ \end{align*}
Mathematica [A] time = 0.0052211, size = 8, normalized size = 1. \[ e \log \left (e^x+1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 9, normalized size = 1.1 \begin{align*}{\rm e}\ln \left ( 1+{{\rm e}^{x}} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.931826, size = 11, normalized size = 1.38 \begin{align*} e \log \left (e^{x} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.94737, size = 30, normalized size = 3.75 \begin{align*} e \log \left (e + e^{\left (x + 1\right )}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.096068, size = 7, normalized size = 0.88 \begin{align*} e \log{\left (e^{x} + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.0825, size = 11, normalized size = 1.38 \begin{align*} e \log \left (e^{x} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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