Optimal. Leaf size=11 \[ e^x \log (x)-\text{ExpIntegralEi}(x) \]
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Rubi [A] time = 0.0159023, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 3, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.5, Rules used = {2194, 2554, 2178} \[ e^x \log (x)-\text{ExpIntegralEi}(x) \]
Antiderivative was successfully verified.
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Rule 2194
Rule 2554
Rule 2178
Rubi steps
\begin{align*} \int e^x \log (x) \, dx &=e^x \log (x)-\int \frac{e^x}{x} \, dx\\ &=-\text{Ei}(x)+e^x \log (x)\\ \end{align*}
Mathematica [A] time = 0.0055287, size = 11, normalized size = 1. \[ e^x \log (x)-\text{ExpIntegralEi}(x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.01, size = 12, normalized size = 1.1 \begin{align*}{{\rm e}^{x}}\ln \left ( x \right ) +{\it Ei} \left ( 1,-x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.0295, size = 14, normalized size = 1.27 \begin{align*} e^{x} \log \left (x\right ) -{\rm Ei}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.7651, size = 27, normalized size = 2.45 \begin{align*} e^{x} \log \left (x\right ) -{\rm Ei}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.98923, size = 8, normalized size = 0.73 \begin{align*} e^{x} \log{\left (x \right )} - \operatorname{Ei}{\left (x \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07051, size = 14, normalized size = 1.27 \begin{align*} e^{x} \log \left (x\right ) -{\rm Ei}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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