Question Number 71813 by mathmax by abdo last updated on 20/Oct/19
$$\left.\mathrm{1}\right){calculate}\:{F}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {arctan}\left(\mathrm{1}+{a}\:{cosx}\right){dx} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{valeur}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{arctan}\left(\mathrm{1}+\sqrt{\mathrm{2}}{cosx}\right){dx} \\ $$