`int dx/(cos(x) - 1)` Evaluate the integral

`intdx/(cosx-1)=`

``Multiply by the conjugate of the denominator.

`int1/(cosx-1)*(cosx+1)/(cosx+1)dx=`

`int(cosx+1)/(cos^2x-1)dx=`

``Simplify, then integrate.

`int(cosx+1)/(-sin^2x)dx=` 

`intcosx/(-sin^2x)dx+int1/(-sin^2x)dx=`

`intcosx/(-sinxsinx)dx+int(-csc^2x)dx=`

`int(-cotxcscx-csc^2x)dx=`

`cscx+cotx+C`