Optimal. Leaf size=8 \[ e \log \left (e^x+1\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 8, normalized size of antiderivative = 1.00, 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 31
Rule 2246
Rule 2247
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*}
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Mathematica [A] time = 0.01, size = 8, normalized size = 1.00 \[ e \log \left (e^x+1\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 11, normalized size = 1.38 \[ e \log \left (e + e^{\left (x + 1\right )}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.10, size = 8, normalized size = 1.00 \[ e \log \left (e^{x} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 9, normalized size = 1.12 \[ {\mathrm e} \ln \left ({\mathrm e}^{x}+1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.56, size = 8, normalized size = 1.00 \[ e \log \left (e^{x} + 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.18, size = 8, normalized size = 1.00 \[ \mathrm {e}\,\ln \left ({\mathrm {e}}^x+1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 8, normalized size = 1.00 \[ e \log {\left (e^{x} + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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