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: 53


$$\int(\sec^2x)e^{\tan x}dx=e^{\tan x}+C$$

Work Step by Step

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