How Do You Integrate 1/(cos(x)-1)?

[montana111]

Homework Statement

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)

Homework Equations

integral of 1/(cosx-1)

 

[Mark44]

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.

 

[vela]

What function has as its derivative -cot x csc x?