Question

$\int \frac{\sec x}{\sec 2x}dx$

Answer 1

$$\begin{gathered} \int \frac{\sec x}{\sec 2x}dx \\ =\int \frac{\cos 2x}{\cos x}dx \\ =\int \frac{2{\cos }^{2}x-1}{\cos x}dx \\ =\int \left(2\cos x-\sec x\right)dx \\ =2\sin x-\ln \left|\sec x+\tan x\right|+\mathrm{C} \end{gathered}$$