Question

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

Answer 1

Consider the given function,

$\int \frac{cos2x+2si{n}^{2}x}{co{s}^{2}x}$

Then,

$\int \frac{co{x}^{2}x-{\sin }^{2}x+2si{n}^{2}x}{co{s}^{2}x}dx$

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

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

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

$=\tan x+C$

Hence this is the answer.