Question

Find the integral of the function: $\frac{\cos 2x+2{\sin }^{2}x}{{\cos }^{2}x}$

Answer 1

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

$=\int \frac{(1-2{\sin }^{2}x+2{\sin }^{2}x)}{{\cos }^{2}x}.dx$

$[\because 1-\cos 2x=2{\sin }^{2}x]$

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

$=\int {\sec }^{2}x.dx$

$=\tan x+C$

Where $C$ is constant of integration.