Question

my question is: Integral ( 1 / (1 - sec x) )

Answer 1

There are a few ways to do this. Here's one. Multiply top and bottom first by 1 + sec x and obtain

-(1 + sec x)/tan^2 x = -cos^2 x / sin^2 x + cos x / sin^2 x
= -cosec^2 x + 1 - cos x / sin^2 x

Now integrate that.