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Question
Find the integrals of the function:
`cos x/(1 + cos x)`
Solution
Let `I = int cos x/(1 + cos x) dx`
`= int ((1 + cos x) - 1)/(1 + cos x) dx`
`= int 1 dx - int 1/ (1 + cos x) dx`
`= int dx - int 1/ (2 cos^2 x/2) dx`
`= int dx - 1/2 int sec^2 x/2 dx`
`= x = 1/2* (tan x/2)/(1/2) + C`
`= x - tan x/2 + C`
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