Optimal. Leaf size=10 \[ x e^{x+\frac {1}{\log (x)}} \]
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Rubi [F] time = 0.19, 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 = {} \[ \int \frac {e^{x+\frac {1}{\log (x)}} \left (-1+(1+x) \log ^2(x)\right )}{\log ^2(x)} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {e^{x+\frac {1}{\log (x)}} \left (-1+(1+x) \log ^2(x)\right )}{\log ^2(x)} \, dx &=\int \left (e^{x+\frac {1}{\log (x)}}+e^{x+\frac {1}{\log (x)}} x-\frac {e^{x+\frac {1}{\log (x)}}}{\log ^2(x)}\right ) \, dx\\ &=\int e^{x+\frac {1}{\log (x)}} \, dx+\int e^{x+\frac {1}{\log (x)}} x \, dx-\int \frac {e^{x+\frac {1}{\log (x)}}}{\log ^2(x)} \, dx\\ \end {align*}
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Mathematica [A] time = 0.08, size = 10, normalized size = 1.00 \[ x e^{x+\frac {1}{\log (x)}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.42, size = 14, normalized size = 1.40 \[ x e^{\left (\frac {x \log \relax (x) + 1}{\log \relax (x)}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.05, size = 14, normalized size = 1.40 \[ x e^{\left (\frac {x \log \relax (x) + 1}{\log \relax (x)}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 10, normalized size = 1.00 \[ x \,{\mathrm e}^{x +\frac {1}{\ln \relax (x )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.90, size = 9, normalized size = 0.90 \[ x e^{\left (x + \frac {1}{\log \relax (x)}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.31, size = 9, normalized size = 0.90 \[ x\,{\mathrm {e}}^{\frac {1}{\ln \relax (x)}}\,{\mathrm {e}}^x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.34, size = 8, normalized size = 0.80 \[ x e^{x + \frac {1}{\log {\relax (x )}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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