Integrate the functions`1/(cos^2x(1-tanx)^2)`

1.	Integrate the functions`1/(cos^2x(1-tanx)^2)`
Answer» We can write the given expression as, `sec^2x/(1-tanx)^2` Let `1 - tanx = t` Then, `-sec^2.dx = dt` So, `intsec^2x/(1-tanx)^2dx` becomes `int-1/t^2dt` `=1/t+c` Putting value of `t = 1 - tanx`, our answer becomes,`= 1/(1-tan x) +c`

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