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Evaluate: int1/(1-2sinx)\ dx...

Evaluate: `int1/(1-2sinx)\ dx`

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`sinx=frac{2tan x/2}{1+tan^2x/2}`
`=int frac{1+tan^2 x/2}{1(1+tan^2x/2)-2(2tan x/2)}dx`
On replacing `(1 + tan^2x)/2` in numerator by `sec^2x/2`
`=int frac{sec^2 x/2}{1+tan^2 x2-4tan x/2}dx`
On putting `tan (x/2) = t` and `sec^2(x/2) dx = 2dt`
`=2 int frac{1}{(t-2)^2-(sqrt 3)^2}dt `
`=1/sqrt3 log abs(frac{tan x/2-2-sqrt 3}{tan x/2-2+sqrt 3})+C`
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