Question

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

Answer 1

$\begin{array}{c}=\int \frac{dx}{\cos 2x+{\sin }^{2}x}\\ =\int \frac{dx}{{\cos }^{2}x-{\sin }^{2}x+{\sin }^{2}x}\left(\cos 2x=2{\cos }^{2}x-1\right)\\ =\int {\sec }^{2}xdx\\ =\tan x+C\end{array}$

Hence, solved.