Question

Integrate the following:
$\frac{1}{\sqrt{1+\cos 2x}}$

Answer 1

Now,

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

$=\int$ $\frac{1}{\sqrt{2{\cos }^{2}x}}$ [ Since $1+\cos 2x=2{\cos }^{2}x$]

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

$=\frac{1}{\sqrt{2}}\log \left|\tan (\frac{x}{2}+\frac{\pi }{4})\right|+c$ [ Where $c$ is integrating constant]