Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.4 Derivatives of Logarithmic Functions - 6.4 Exercises: 78

Answer

$\int\frac{cosx}{2+sinx}dx=ln(2+sinx)+constant$

Work Step by Step

Evaluate the integral $\int\frac{cosx}{2+sinx}dx$ Consider $2+sinx= t$ and $cosx.dx=dt$ Thus, $\int\frac{cosx}{2+sinx}dx=\int\frac{dt}{t}$ $=ln(t)+constant$ Hence, $\int\frac{cosx}{2+sinx}dx=ln(2+sinx)+constant$
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