Answer
$\sin(e^x) +c $
Work Step by Step
Recall that $(e^x)'=e^x$
Recall that $(\sin x)'=\cos x$.
Let $ u=e^x $, then $ du=e^x dx $ and hence 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 - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 328: 82
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