Optimal. Leaf size=11 \[ -\text {Ei}(x)+e^x \log (x) \]
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Rubi [A]
time = 0.01, 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 = {2225, 2634,
2209} \begin {gather*} e^x \log (x)-\text {ExpIntegralEi}(x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2209
Rule 2225
Rule 2634
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 \begin {gather*} -\text {Ei}(x)+e^x \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 12, normalized size = 1.09
method | result | size |
risch | \({\mathrm e}^{x} \ln \left (x \right )+\expIntegral \left (1, -x \right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.80, size = 10, normalized size = 0.91 \begin {gather*} e^{x} \log \left (x\right ) - {\rm Ei}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.50, size = 10, normalized size = 0.91 \begin {gather*} e^{x} \log \left (x\right ) - {\rm Ei}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.98, size = 8, normalized size = 0.73 \begin {gather*} e^{x} \log {\left (x \right )} - \operatorname {Ei}{\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.72, size = 10, normalized size = 0.91 \begin {gather*} e^{x} \log \left (x\right ) - {\rm Ei}\left (x\right ) \end {gather*}
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 \begin {gather*} {\mathrm {e}}^x\,\ln \left (x\right )-\mathrm {ei}\left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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