Answer
$$\int(\csc^2x)e^{\cot x}dx=-e^{\cot x}+C$$
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, $$A=-\int e^ada$$ $$A=-e^a+C$$ $$A=-e^{\cot x}+C$$
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: 54
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