Question Number 36420 by abdo.msup.com last updated on 01/Jun/18
$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\:{arctan}\left({xt}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{4}} }{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({x}\right). \\ $$