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: 54


$$\int(\csc^2x)e^{\cot x}dx=-e^{\cot x}+C$$

Work Step by Step

$$A=\int(\csc^2x)e^{\cot x}dx$$ We set $a=\cot x$, which means $$da=-\csc^2xdx$$ $$\csc^2xdx=-da$$ Therefore, $$A=-\int e^ada$$ $$A=-e^a+C$$ $$A=-e^{\cot x}+C$$
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