Calculus (3rd Edition)

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


$2 \sin \sqrt t +C$

Work Step by Step

Substitute $u=\sqrt t$. This implies $t=u^{2}$. $⇒\frac{dt}{du}=2u$ or $dt= 2udu$ Then, $\int \frac{\cos \sqrt t}{\sqrt t}dt=\int \frac{\cos u}{u}2udu$ $=2\int \cos u du= 2\sin u+C$ $=2\sin \sqrt t+C$
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