Find the following integral: $\int \sec x(\sec x+\tan x) \, dx$

(N/A) We are given the integral: $\int \sec x(\sec x+\tan x) \, dx$
First,distribute $\sec x$ inside the parentheses:
$= \int (\sec^2 x + \sec x \tan x) \, dx$
Using the linearity property of integration,we can split this into two separate integrals:
$= \int \sec^2 x \, dx + \int \sec x \tan x \, dx$
We know the standard integrals:
$\int \sec^2 x \, dx = \tan x + C_1$
$\int \sec x \tan x \, dx = \sec x + C_2$
Combining these results,we get:
$= \tan x + \sec x + C$,where $C$ is an arbitrary constant.