Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.3 Exercises: 6

Answer

$3sin\frac x 3 -sin^3 \frac x 3 +C$

Work Step by Step

$\int cos^3\frac x 3 dx$ $\int (cos^2 \frac x 3)(cos\frac x 3)dx$ $\int (cos\frac x 3-sin^2\frac x 3cos\frac x 3)dx$ $3\int cos \frac x 3 (\frac 1 3)dx-3\int sin^2\frac x 3(cos \frac x 3)(\frac 1 3)dx$ $u=\frac x 3, du=\frac 1 3 dx$ $3\int cosdu=3sinu+C=3sin\frac x 3 +C$ $u=sin\frac x 3, du=(cos\frac x 3)(\frac 1 3)dx$ $3\int u^2du=u^3+C=sin^3\frac x 3+C$ $3sin\frac x 3 -sin^3 \frac x 3 +C$
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