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