Answer
$$2\tan \theta + C$$
Work Step by Step
$$\eqalign{
& \int {2{{\sec }^2}\theta } d\theta \cr
& {\text{take out the constant}} \cr
& = 2\int {{{\sec }^2}\theta } d\theta \cr
& {\text{by the basic formula of the integration }}\int {{{\sec }^2}x} dx = \tan x + C \cr
& 2\int {{{\sec }^2}\theta } d\theta = 2\left( {\tan \theta } \right) + C \cr
& {\text{simplify}} \cr
& = 2\tan \theta + C \cr} $$
