Optimal. Leaf size=9 \[ -x^{-1/x} \]
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Rubi [F] time = 0.0726652, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., 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*}
Mathematica [A] time = 0.0199442, size = 9, normalized size = 1. \[ -x^{-1/x} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.032, size = 18, normalized size = 2. \begin{align*} -{x}^{2}{x}^{-{\frac{1+2\,x}{x}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.16794, size = 12, normalized size = 1.33 \begin{align*} -\frac{1}{x^{\left (\frac{1}{x}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.815074, size = 30, normalized size = 3.33 \begin{align*} -\frac{x^{2}}{x^{\frac{2 \, x + 1}{x}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.338044, size = 12, normalized size = 1.33 \begin{align*} - x^{2} x^{-2 - \frac{1}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.29806, size = 22, normalized size = 2.44 \begin{align*} -x e^{\left (-\frac{x \log \left (x\right ) + \log \left (x\right )}{x}\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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