Optimal. Leaf size=11 \[ e^x \log (x)-\text {Ei}(x) \]
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Rubi [A] time = 0.02, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 3, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.500, Rules used = {2194, 2554, 2178} \[ e^x \log (x)-\text {ExpIntegralEi}(x) \]
Antiderivative was successfully verified.
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Rule 2178
Rule 2194
Rule 2554
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*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 1.00 \[ e^x \log (x)-\text {Ei}(x) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 10, normalized size = 0.91 \[ e^{x} \log \relax (x) - {\rm Ei}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.19, size = 10, normalized size = 0.91 \[ e^{x} \log \relax (x) - {\rm Ei}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 12, normalized size = 1.09 \[ {\mathrm e}^{x} \ln \relax (x )+\Ei \left (1, -x \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 10, normalized size = 0.91 \[ e^{x} \log \relax (x) - {\rm Ei}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 10, normalized size = 0.91 \[ {\mathrm {e}}^x\,\ln \relax (x)-\mathrm {ei}\relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.95, size = 8, normalized size = 0.73 \[ e^{x} \log {\relax (x )} - \operatorname {Ei}{\relax (x )} \]
Verification of antiderivative is not currently implemented for this CAS.
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