University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 5 - Practice Exercises - Page 343: 52


$$\int e^y\csc(e^y+1)\cot(e^y+1)dy=-\csc(e^y+1)+C$$

Work Step by Step

$$A=\int e^y\csc(e^y+1)\cot(e^y+1)dy$$ We set $a=e^y+1$, which means $$da=e^ydy$$ Therefore, $$A=\int \csc a\cot ada$$ $$A=-\csc a+C$$ $$A=-\csc(e^y+1)+C$$
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