Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

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

Answer

$cscx+cotx+C$

Work Step by Step

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