Question

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

Answer 1

$\frac{\cos 2x+2{\sin }^{2}x}{{\cos }^{2}x}$
$=\frac{\cos 2x+(1-\cos 2x)}{{\cos }^{2}x}$
$=\frac{1}{{\cos }^{2}x}={\sec }^{2}x$
$\therefore \int \frac{\cos 2x+2{\sin }^{2}x}{{\cos }^{2}x}dx=\int {\sec }^{2}xdx=\tan x+C$