Optimal. Leaf size=9 \[ -x^{-1/x} \]
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Rubi [F]
time = 0.05, 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^{-2-\frac {1}{x}} (1-\log (x)) \, dx \end {gather*}
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 = 0.01, size = 9, normalized size = 1.00 \begin {gather*} -x^{-1/x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 18, normalized size = 2.00
method | result | size |
risch | \(-x^{2} x^{-\frac {2 x +1}{x}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 9, normalized size = 1.00 \begin {gather*} -\frac {1}{x^{\left (\frac {1}{x}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 18, normalized size = 2.00 \begin {gather*} -\frac {x^{2}}{x^{\frac {2 \, x + 1}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 12, normalized size = 1.33 \begin {gather*} - x^{2} x^{-2 - \frac {1}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.70, size = 16, normalized size = 1.78 \begin {gather*} -x e^{\left (-\frac {x \log \left (x\right ) + \log \left (x\right )}{x}\right )} \end {gather*}
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 \begin {gather*} -\frac {1}{x^{1/x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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