∫ secx(secx + 2tanx − cosx)dx

Question

Determine the following antiderivative:

∫ secx(secx + 2tanx − cosx)dx

Answer 1

First convert the integrand to all sines and cosines to get:

(1+ 2 sin x -cos²x)/cos²x which becomes tan²x + 2 sec x tan x

This integrates to x-tan x + 2 sec x