Question

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

Answer 1

$$\begin{gathered} \mathrm{Let}I=\int \left(\left[\frac{\cos 2x+2{\sin }^{2}x}{{\cos }^{2}x}\right]\right)dx \\ =\int \left(\frac{1-2{\sin }^{2}x+2{\sin }^{2}x}{{\cos }^{2}x}\right)dx \\ =\int {\sec }^{2}xdx \\ =\tan x+C \end{gathered}$$