(i) ∫cos/(1 + cos x) dx
Now multiply and divide by (1 - cos x)
On further calculation
= ∫(cot x cosec x – cot2 x) dx
It can be written as
= ∫(cot x cosec x – [cosec2 x – 1]) dx
By integrating w.r.t x
= – cosec x + cot x + x + c
(ii) ∫sin x/(1 - sin x) dx
Now multiply and divide by (1 + sin x)
On further calculation
= ∫(tan x sec x + tan2 x) dx
It can be written as
= ∫(tan x sec x + [sec2 x – 1]) dx
By integrating w.r.t x
= sec x + tan x – x + c
