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: 63

Answer

\[ = \frac{1}{{10}}\tan \,\left( {10x} \right) + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {{{\sec }^2}10xdx} \hfill \\ \hfill \\ find\,\,du \hfill \\ \hfill \\ u = 10x\,\,\,then\,\,\,du = 10dx\, \hfill \\ \hfill \\ apply\,\,the\,\,\,substitution \hfill \\ \hfill \\ = \frac{1}{{10}}\int_{}^{} {{{\sec }^2}udu} \hfill \\ \hfill \\ integrate\,\, \hfill \\ \hfill \\ = \frac{1}{{10}}\tan u + C \hfill \\ \hfill \\ replace\,\,u\,\,with\,\,\,u = 10x \hfill \\ \hfill \\ = \frac{1}{{10}}\tan \,\left( {10x} \right) + C \hfill \\ \hfill \\ \end{gathered} \]
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