∫ secx(secx + 2tanx − cosx)dx

Question

Determine the following antiderivative:

∫ secx(secx + 2tanx − cosx)dx

Answer 1

The key here is expanding and rewriting this expression in the form where you can take antiderivatives.

∫sec x (sec x + 2tan x + cos x) = ∫ sec² x + sec x tan x + sec x cos x = ∫ sec² x + sec x tan x + 1

= tan x + sec x + x + c