Question

Solve: $\int \frac{1-\cos 2x}{\cos 2x+1}dx$

Answer 1

Now,

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

$=\int \frac{2{\sin }^{2}x}{2{\cos }^{2}x}dx$

$=\int {\tan }^{2}xdx$

$=\int ({\sec }^{2}x-1)dx$

$=\tan x-x+c$ [Where $c$ is integrating constant]