# Integral of 1/(cosx-1)

1. ### montana111

12
1. The problem statement, all variables and given/known data

help me out. I want to find the integral of 1/(cosx-1). I first multiplied the function by cosx+1/cosx+1. then i ended up with the integral of (cosx+1)/(-sinx)^2 leading to integral of cosx/(-sinx)^2 plus integral of 1/(-sinx)^2.

the integral of 1/(-sinx)^2 i believe is just cotx.

the integral of cosx/(-sinx)^2 i think is -(integral of cotx*cscx)

2. Relevant equations

integral of 1/(cosx-1)

### Staff: Mentor

What's your question? I don't see anything wrong in what you've described. You can check any antiderivative you get by taking its derivative. If you get back to the integrand, you're good.

3. ### vela

12,972
Staff Emeritus
What function has as its derivative -cot x csc x?