Optimal. Leaf size=6 \[ \log \left (x+e^x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 6, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.03, size = 6, normalized size = 1.00 \[ \log \left (x+e^x\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.40, size = 5, normalized size = 0.83 \[ \log \left (x + e^{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 5, normalized size = 0.83 \[ \log \left (x + e^{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 6, normalized size = 1.00 \[ \ln \left (x +{\mathrm e}^{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.00, size = 5, normalized size = 0.83 \[ \log \left (x + e^{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 5, normalized size = 0.83 \[ \ln \left (x+{\mathrm {e}}^x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 5, normalized size = 0.83 \[ \log {\left (x + e^{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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