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Exercise

$\int_{\sqrt{2}}^2\left(\frac{1}{x^3\sqrt{\left(x^2-1\right)}}\right)dx$

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Final answer to the exercise

$-\frac{1}{4}-\frac{1}{2}\mathrm{arcsec}\left(\sqrt{2}\right)+\frac{\sqrt{3}}{8}+\frac{1}{2}\mathrm{arcsec}\left(2\right)$

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