The integral ∫ (sec2x/(sec x + tan x)9/2) dx equals
Put sec x + tan x = t
sec x (sec x + tan x) dx = dt
sec x dx = dt/t
Also
sec x – tan x = 1/(sec x + tan x) = (1/t)
Thus, sec x = (1/2) (t + (1/t)) dt
The given intergral (i) reduces to