Optimal. Leaf size=23 \[ -\frac {1}{2} \sqrt [4]{e} \sqrt {\pi } \text {erf}\left (\frac {1}{2}-\log (x)\right ) \]
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Rubi [F]
time = 0.01, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int x^{-\log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\int x^{-\log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 25, normalized size = 1.09 \begin {gather*} \frac {1}{2} \sqrt [4]{e} \sqrt {\pi } \text {erf}\left (\frac {1}{2} (-1+2 \log (x))\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.00, size = 0, normalized size = 0.00 \[\int x^{-\ln \left (x \right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.59, size = 12, normalized size = 0.52 \begin {gather*} \frac {1}{2} \, \sqrt {\pi } \operatorname {erf}\left (\log \left (x\right ) - \frac {1}{2}\right ) e^{\frac {1}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int x^{- \log {\left (x \right )}}\, dx \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.44, size = 12, normalized size = 0.52 \begin {gather*} \frac {1}{2} \, \sqrt {\pi } \operatorname {erf}\left (\log \left (x\right ) - \frac {1}{2}\right ) e^{\frac {1}{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int {\mathrm {e}}^{-{\ln \left (x\right )}^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 9, normalized size = 0.39 \begin {gather*} \frac {\expIntegral \left (-\ln \left (x \right )^{2}\right )}{2} \end {gather*}
Warning: Unable to verify antiderivative.
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