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1-calculate-F-a-0-pi-4-arctan-1-a-cosx-dx-2-find-the-valeur-of-0-pi-4-arctan-1-2-cosx-dx-




Question Number 71813 by mathmax by abdo last updated on 20/Oct/19
1)calculate F(a)=∫_0 ^(π/4) arctan(1+a cosx)dx  2)find the valeur of  ∫_0 ^(π/4)  arctan(1+(√2)cosx)dx
$$\left.\mathrm{1}\right){calculate}\:{F}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {arctan}\left(\mathrm{1}+{a}\:{cosx}\right){dx} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{valeur}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{arctan}\left(\mathrm{1}+\sqrt{\mathrm{2}}{cosx}\right){dx} \\ $$

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