(i) ∫sec x(sec x + tan x) dx
It can be written as
= ∫sec2 x + sec x tan x dx
By integrating w.r.t x
= tan x + sec x + c
(ii) ∫cosec x(cosec x – cot x) dx
It can be written as
= ∫cosec2 x – cosec x cot x dx
By integrating w.r.t x
= – cot x + cosec x + c