Optimal. Leaf size=6 \[ \log \left (e^x+1\right ) \]
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Rubi [A] time = 0.014687, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.182, Rules used = {2246, 31} \[ \log \left (e^x+1\right ) \]
Antiderivative was successfully verified.
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Rule 2246
Rule 31
Rubi steps
\begin{align*} \int \frac{e^x}{1+e^x} \, dx &=\operatorname{Subst}\left (\int \frac{1}{1+x} \, dx,x,e^x\right )\\ &=\log \left (1+e^x\right )\\ \end{align*}
Mathematica [A] time = 0.0040945, size = 6, normalized size = 1. \[ \log \left (e^x+1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 6, normalized size = 1. \begin{align*} \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 = 0.922343, size = 7, normalized size = 1.17 \begin{align*} \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 = 1.68215, size = 19, normalized size = 3.17 \begin{align*} \log \left (e^{x} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.084821, size = 5, normalized size = 0.83 \begin{align*} \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 = 1.09375, size = 7, normalized size = 1.17 \begin{align*} \log \left (e^{x} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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