Question

Integrate: 1/ (1 - 2sinx)

Answer 1

see attachment ,

after putting z = tan(x/2)
then ,
answer will be
$\frac{1}{2 \sqrt{3} } ln | \frac{tan \frac{x}{2} - 2 - \sqrt{3} }{tan \frac{x}{2} - 2 + \sqrt{3} } | + c$