Answer
$$ \displaystyle\int \dfrac{1}{{x}^{3}{\cdot}\sqrt{{x}^{2}-4}}\, \mathrm d x = -{{x^2\,\arcsin \left({{2}\over{\left| x\right| }}\right)-2\,\sqrt{ x^2-4}}\over{16\,x^2}} $$
Explanation
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