Calculus (3rd Edition)

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


$\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 $$ \int e^x \cos (e^x) dx=\int \cos (u) du= \sin(u) +c=\sin(e^x) +c . $$
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