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Question
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Solution
Let `I = int 1/(cos^2 x . (1 - tan x)^2)` dx
or `= int (sec^2)/(1 - tan)^2` dx `(because 1/(cos^2 x) = sec^2 x)`
1 - tan x = t
- sec2 x dx = dt
∴ `I = - int dt/t^2 = (t^(-2+1))/(-2 + 1) + C`
`= 1/t + C = 1/ (1 - tanx) + C`
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