Optimal. Leaf size=9 \[ -x^{-1/x} \]
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Rubi [F] time = 0.07, 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 = {} \[ \int x^{-2-\frac {1}{x}} (1-\log (x)) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int x^{-2-\frac {1}{x}} (1-\log (x)) \, dx &=\int \left (x^{-2-\frac {1}{x}}-x^{-2-\frac {1}{x}} \log (x)\right ) \, dx\\ &=\int x^{-2-\frac {1}{x}} \, dx-\int x^{-2-\frac {1}{x}} \log (x) \, dx\\ &=-\left (\log (x) \int x^{-2-\frac {1}{x}} \, dx\right )+\int x^{-2-\frac {1}{x}} \, dx+\int \frac {\int x^{-2-\frac {1}{x}} \, dx}{x} \, dx\\ \end {align*}
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Mathematica [A] time = 0.02, size = 9, normalized size = 1.00 \[ -x^{-1/x} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 18, normalized size = 2.00 \[ -\frac {x^{2}}{x^{\frac {2 \, x + 1}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.47, size = 16, normalized size = 1.78 \[ -x e^{\left (-\frac {x \log \relax (x) + \log \relax (x)}{x}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 18, normalized size = 2.00 \[ -x^{2} x^{-\frac {2 x +1}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.38, size = 9, normalized size = 1.00 \[ -\frac {1}{x^{\left (\frac {1}{x}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.58, size = 9, normalized size = 1.00 \[ -\frac {1}{x^{1/x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.27, size = 12, normalized size = 1.33 \[ - x^{2} x^{-2 - \frac {1}{x}} \]
Verification of antiderivative is not currently implemented for this CAS.
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