Evaluate: `int1/(1-sinx+cosx)\ dx`

Explanation

`int1/(1-sinx+cosx)\ dx`

`sinx=frac{2tan x/2}{1+tan^2x/2}` and `cos x=frac{1-tan^2x/2}{1+tan^2x/2}`

`=int frac{1+tan^2 x/2}{1+tan^2x/2-2tan x/2+1-tan^2x/2}dx`

Replacing `1 + tan^2x/2` in numerator by `sec^2x/2` and putting `tan x/2 = t` and `sec^2 x/2 dx = 2dt`

`=int 1/(1-t)dt`

`=-log abs(1-tan x/2)+C`