integrate integral of dx/(cosx-1).

this is how i tried solving it:

integral dx/(cosx-1)x(cosx+1)/(cosx+1)

=-integral (cosx + 1)/((sinx)^2)

=-integral (cosx)/((sinx)^2) + integral (cscx)^2dx

u=sinx du=cosxdx

=-[integral du/u^2 dx+ integral (1)dx + integral(cotx)^2dx

I don't know how to integrate (cotx)^2.