Question

What is the integral of sec x (sec x + tan x ) dx

Answer 1

$\sec x(\sec x+\tan x)=\sec^2x+\sec x\tan x$

Recall that $(\tan x)'=\sec^2x$, and $(\sec x)'=\sec x\tan x$.

So,

$\displaystyle\int \sec x(\sec x+\tan x)\,\mathrm dx=\tan x+\sec x+C$