Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 5 - Integration - 5.5 Substitution Rule - 5.5 Exercises: 62

Answer

\[ = \frac{1}{4}\,\sec \,\,4w\,\, + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\sec \,4w\tan 4w\,dw} \hfill \\ \hfill \\ set\,\,u = 4w\,\,\,\,\,\,\,\,then\,\,\,\,\,du = 4dw \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ = \frac{1}{4}\int_{}^{} {\sec \,\,u\,\,\tan u\,\,du} \hfill \\ \hfill \\ integrate\,\, \hfill \\ \hfill \\ = \frac{1}{4}\sec \,\,u\,\, + C \hfill \\ \hfill \\ replace\,\,u\,\,with\,\,\,u = 4w \hfill \\ \hfill \\ = \frac{1}{4}\,\sec \,\,4w\,\, + C \hfill \\ \end{gathered} \]
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