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`