Question

Integrate : ∫dx/(1 + sin x)

Answer 1

= ∫(sec² x - tan x sec x) dx

= ∫sec² x dx - ∫tan x sec x dx

= tan x - sec x + c 

Answer 2

\(\int \frac {dx}{1 + \sin x} = \int \frac{(1 - \sin x)dx}{\cos^2x}\)

\(= \int \sec^2 xdx - \int \sec x \tan x dx\)

\(= \tan x - \sec x + C\)