Answer
$$\int e^y\csc(e^y+1)\cot(e^y+1)dy=-\csc(e^y+1)+C$$
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, $$A=\int \csc a\cot ada$$ $$A=-\csc a+C$$ $$A=-\csc(e^y+1)+C$$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 5 - Practice Exercises - Page 343: 52
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