Optimal. Leaf size=6 \[ \text{ExpIntegralEi}\left (x+e^x\right ) \]
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Rubi [A] time = 0.105787, antiderivative size = 6, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {6707, 2178} \[ \text{ExpIntegralEi}\left (x+e^x\right ) \]
Antiderivative was successfully verified.
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Rule 6707
Rule 2178
Rubi steps
\begin{align*} \int \frac{e^{e^x+x} \left (1+e^x\right )}{e^x+x} \, dx &=\operatorname{Subst}\left (\int \frac{e^x}{x} \, dx,x,e^x+x\right )\\ &=\text{Ei}\left (e^x+x\right )\\ \end{align*}
Mathematica [A] time = 0.0357706, size = 6, normalized size = 1. \[ \text{ExpIntegralEi}\left (x+e^x\right ) \]
Antiderivative was successfully verified.
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Maple [B] time = 0.004, size = 13, normalized size = 2.2 \begin{align*} -{\it Ei} \left ( 1,-{{\rm e}^{x}}-x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \frac{{\left (e^{x} + 1\right )} e^{\left (e^{x}\right )}}{x + e^{x}} - \int \frac{{\left ({\left (x - 2\right )} e^{x} - 1\right )} e^{\left (e^{x}\right )}}{x^{2} + 2 \, x e^{x} + e^{\left (2 \, x\right )}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.4728, size = 18, normalized size = 3. \begin{align*}{\rm Ei}\left (x + e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.00931, size = 5, normalized size = 0.83 \begin{align*} \operatorname{Ei}{\left (x + e^{x} \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07683, size = 7, normalized size = 1.17 \begin{align*}{\rm Ei}\left (x + e^{x}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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