Question

Evaluate :

$\int \frac{1}{\sqrt{1+\cos 2x}}dx$

Answer 1

$I=\int \frac{1}{\sqrt{1+\cos 2x}}dx$

$I=\int \frac{1}{\sqrt{2{\cos }^{2}x}}dx$

$I=\frac{1}{\sqrt{2}}\int \sec xdx$

$I=\frac{1}{\sqrt{2}}\log |\sec x+\tan x|+C$