Answer
$2 \sin \sqrt t +C$
Work Step by Step
Substitute $u=\sqrt t$. This implies $t=u^{2}$.
$⇒\frac{dt}{du}=2u$ or $dt= 2udu$
Then, $\int \frac{\cos \sqrt t}{\sqrt t}dt=\int \frac{\cos u}{u}2udu$
$=2\int \cos u du= 2\sin u+C$
$=2\sin \sqrt t+C$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 276: 49
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