Question

Evaluate: $\int \frac{\cos 2x+2{\sin }^{2}x}{{\cos }^{2}x}dx$

Answer 1

Now,

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

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

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

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

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