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: 31

Answer

\[ = {\left( {\tan x} \right)^{10}}\, + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {10{{\tan }^9}x{{\sec }^2}x\,dx} \hfill \\ \hfill \\ set\,\,\,\tan \,\,x = t\,\,\,\,\,then\,\,\,\,\,{\sec ^2}xdx = dt \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ \int_{}^{} {10{{\tan }^9}x{{\sec }^2}x\,dx} = \int_{}^{} {10\,\,{t^9}dt} \hfill \\ \hfill \\ integrate \hfill \\ \hfill \\ = 10\frac{{{t^{10}}}}{{10}}\, + C \hfill \\ \hfill \\ = {t^{10}}\, + C \hfill \\ substitute\,\,back \hfill \\ \hfill \\ = {\left( {\tan x} \right)^{10}}\, + C \hfill \\ \end{gathered} \]
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