3.677 \(\int x^{-2-\frac{1}{x}} (1-\log (x)) \, dx\)

Optimal. Leaf size=9 \[ -x^{-1/x} \]

[Out]

-x^(-x^(-1))

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Rubi [F]  time = 0.102966, 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. \[ \text{Int}\left (x^{-2-\frac{1}{x}} (1-\log (x)),x\right ) \]

Verification is Not applicable to the result.

[In]  Int[x^(-2 - x^(-1))*(1 - Log[x]),x]

[Out]

Defer[Int][x^(-2 - x^(-1)), x] - Log[x]*Defer[Int][x^(-2 - x^(-1)), x] + Defer[I
nt][Defer[Int][x^(-2 - x^(-1)), x]/x, x]

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \int x^{-2 - \frac{1}{x}} \left (- \log{\left (x \right )} + 1\right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(x**(-2-1/x)*(1-ln(x)),x)

[Out]

Integral(x**(-2 - 1/x)*(-log(x) + 1), x)

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Mathematica [A]  time = 0.0115296, size = 9, normalized size = 1. \[ -x^{-1/x} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(-2 - x^(-1))*(1 - Log[x]),x]

[Out]

-x^(-x^(-1))

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Maple [A]  time = 0.025, size = 18, normalized size = 2. \[ -{x}^{2}{x}^{-{\frac{2\,x+1}{x}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(x^(-2-1/x)*(1-ln(x)),x)

[Out]

-x^2*x^(-(2*x+1)/x)

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Maxima [A]  time = 0.86336, size = 12, normalized size = 1.33 \[ -\frac{1}{x^{\left (\frac{1}{x}\right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-x^(-1/x - 2)*(log(x) - 1),x, algorithm="maxima")

[Out]

-1/x^(1/x)

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Fricas [A]  time = 0.236697, size = 24, normalized size = 2.67 \[ -\frac{x^{2}}{x^{\frac{2 \, x + 1}{x}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-x^(-1/x - 2)*(log(x) - 1),x, algorithm="fricas")

[Out]

-x^2/x^((2*x + 1)/x)

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Sympy [A]  time = 0.560478, size = 12, normalized size = 1.33 \[ - x^{2} x^{-2 - \frac{1}{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x**(-2-1/x)*(1-ln(x)),x)

[Out]

-x**2*x**(-2 - 1/x)

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \mathit{undef} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-x^(-1/x - 2)*(log(x) - 1),x, algorithm="giac")

[Out]

undef