Optimal. Leaf size=26 \[ -x+x \left (1-\frac {e^{-e^2} \left (x+\log \left (\frac {1}{x}\right )\right )}{x}\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 21, normalized size of antiderivative = 0.81, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 43} \begin {gather*} e^{-e^2} \log (x)-e^{-e^2} x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 43
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{-e^2} \int \frac {1-x}{x} \, dx\\ &=e^{-e^2} \int \left (-1+\frac {1}{x}\right ) \, dx\\ &=-e^{-e^2} x+e^{-e^2} \log (x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 0.58 \begin {gather*} -e^{-e^2} (x-\log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 13, normalized size = 0.50 \begin {gather*} -{\left (x - \log \relax (x)\right )} e^{\left (-e^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 14, normalized size = 0.54 \begin {gather*} -{\left (x - \log \left ({\left | x \right |}\right )\right )} e^{\left (-e^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 13, normalized size = 0.50
method | result | size |
default | \({\mathrm e}^{-{\mathrm e}^{2}} \left (\ln \relax (x )-x \right )\) | \(13\) |
norman | \(-x \,{\mathrm e}^{-{\mathrm e}^{2}}+{\mathrm e}^{-{\mathrm e}^{2}} \ln \relax (x )\) | \(18\) |
risch | \(-x \,{\mathrm e}^{-{\mathrm e}^{2}}+{\mathrm e}^{-{\mathrm e}^{2}} \ln \relax (x )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 13, normalized size = 0.50 \begin {gather*} -{\left (x - \log \relax (x)\right )} e^{\left (-e^{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 13, normalized size = 0.50 \begin {gather*} -{\mathrm {e}}^{-{\mathrm {e}}^2}\,\left (x-\ln \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 8, normalized size = 0.31 \begin {gather*} \frac {- x + \log {\relax (x )}}{e^{e^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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