Calculus: Early Transcendentals (2nd Edition)

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

Chapter 7 - Integration Techniques - 7.3 Trigonometric Integrals - 7.3 Exercises: 26

Answer

\[ = 6\tan x + 2{\tan ^3}x + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {6\,{{\sec }^4}xdx} \hfill \\ \hfill \\ write\,{\text{ }}{\sec ^4}x{\text{ as }}\,{\sec ^2}x{\sec ^2}x \hfill \\ \hfill \\ = 6\int_{}^{} {{{\sec }^2}x{{\sec }^2}xdx} \hfill \\ \hfill \\ use\,\,\,{\sec ^2}x = 1 + {\tan ^2}x \hfill \\ \hfill \\ then \hfill \\ \hfill \\ = 6\int_{}^{} {\,\left( {1 + {{\tan }^2}x} \right){{\sec }^2}xdx} \hfill \\ \hfill \\ = 6\int_{}^{} {{{\sec }^2}xdx + 6\int_{}^{} {{{\tan }^2}x{{\sec }^2}xdx} } \hfill \\ \hfill \\ integrate \hfill \\ \hfill \\ = 6\tan x + 2{\tan ^3}x + C \hfill \\ \end{gathered} \]
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.