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

Optimal. Leaf size=17 \[ -\text{ExpIntegralEi}(-\log (x))-\frac{1}{x \log (x)} \]

[Out]

-ExpIntegralEi[-Log[x]] - 1/(x*Log[x])

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Rubi [A]  time = 0.0486889, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.375 \[ -\text{ExpIntegralEi}(-\log (x))-\frac{1}{x \log (x)} \]

Antiderivative was successfully verified.

[In]  Int[1/(x^2*Log[x]^2),x]

[Out]

-ExpIntegralEi[-Log[x]] - 1/(x*Log[x])

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Rubi in Sympy [A]  time = 2.3296, size = 14, normalized size = 0.82 \[ - \operatorname{Ei}{\left (- \log{\left (x \right )} \right )} - \frac{1}{x \log{\left (x \right )}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-Ei(-log(x)) - 1/(x*log(x))

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Mathematica [A]  time = 0.00988236, size = 17, normalized size = 1. \[ -\text{ExpIntegralEi}(-\log (x))-\frac{1}{x \log (x)} \]

Antiderivative was successfully verified.

[In]  Integrate[1/(x^2*Log[x]^2),x]

[Out]

-ExpIntegralEi[-Log[x]] - 1/(x*Log[x])

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Maple [A]  time = 0.006, size = 15, normalized size = 0.9 \[ -{\frac{1}{x\ln \left ( x \right ) }}+{\it Ei} \left ( 1,\ln \left ( x \right ) \right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x^2/ln(x)^2,x)

[Out]

-1/x/ln(x)+Ei(1,ln(x))

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Maxima [A]  time = 1.48322, size = 8, normalized size = 0.47 \[ -\Gamma \left (-1, \log \left (x\right )\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-gamma(-1, log(x))

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Fricas [F]  time = 0., size = 0, normalized size = 0. \[ -\frac{x \log \left (x\right ) log_integral\left (\frac{1}{x}\right ) + 1}{x \log \left (x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-(x*log(x)*log_integral(1/x) + 1)/(x*log(x))

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x**2/ln(x)**2,x)

[Out]

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

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{x^{2} \log \left (x\right )^{2}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate(1/(x^2*log(x)^2), x)