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Question Number 197384 by Erico last updated on 15/Sep/23

If f (x) = {\int_{\frac{1}{x}}}^{x} \frac{l n t}{t^{2} - 1} a r c t a n (t) d t

Prove that :

∙ \forall x > 0 f (x) = \frac{π}{8} {\int_{0}}^{π} \arctan [\frac{1}{2} (x - \frac{1}{x}) sint] dt

∙ \lim_{x \to + \infty} f (x) = \frac{π^{3}}{16}