Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.1 Exercises - Page 512: 38

$cscx+cotx+C$

$ \int \frac {cosx+1}{(cosx-1)(cosx+1)}dx$ $ \int \frac {cosx+1}{(cosx-1)(cosx+1)}dx \times \frac {cosx+1}{cosx+1}$ $\int \frac {cosx+1}{cos^2x-1}dx$ $-\int \frac {cosx+1}{1-cos^2x}dx$ $-\int \frac {cosx+1}{sin^2x}dx$ $-\int \frac {cosx}{sin^2x}dx+ \int \frac{1}{sin^2x}dx$ $-\int cscxcotxdx +\int csc^2xdx$ $-(-cscx-cotx+C)$ $cscx+cotx+C$