Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.2* The Natural Logarithmic Functions - 6.2* Exercises: 74

Answer

$\int \frac{cos(lnt)}{t}dt=sin(lnt)+Constant$

Work Step by Step

Evaluate $\int \frac{cos(lnt)}{t}dt$. Consider $ln t =u$ and $\frac{1}{t} dt = du$ Thus, $\int \frac{cos(lnt)}{t}dt=\int cos (u) du$ $=sin(u)+ Constant$ $=sin(lnt)+Constant$ Hence, $\int \frac{cos(lnt)}{t}dt=sin(lnt)+Constant$
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