Answer
$$8\tan x + C$$
Work Step by Step
$$\eqalign{
& \int {8{{\sec }^2}} xdx \cr
& {\text{use multiple constant rule }} \cr
& = 8\int {{{\sec }^2}} xdx \cr
& {\text{integrate by using the Basic Trigonometric integral }}\int {{{\sec }^2}x} dx = \tan x + C \cr
& then \cr
& = 8\tan x + C \cr} $$