Question

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

Answer 1

$\begin{array}{c}\int \frac{\cos 2x+2{\sin }^{2}x}{{\cos }^{2}x}dx\\ =\int \frac{\left({\cos }^{2}x-{\sin }^{2}x+2{\sin }^{2}x\right)dx}{{\cos }^{2}x}\\ =\int {\sec }^{2}xdx\\ =\tan x+C\end{array}$