Answer
$$\sin e^x+c$$
Work Step by Step
Let $u=e^x$, then $du=e^xdx$. Now, we have
$$\int e^x \cos e^x dx= \int \cos u du=\sin u +c\\
=\sin e^x+c.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - 7.8 Inverse Trigonometric Functions - Exercises - Page 375: 93
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