Question

The integral ∫ (sec² x/(sec x + tan x)^9/2) dx equals

Answer 1

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