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: 25

Answer

\[ = \frac{1}{3}\arcsin \,\left( {3x} \right) + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\frac{{dx}}{{\sqrt {1 - 9{x^2}} }}} \hfill \\ \hfill \\ rewrite \hfill \\ \hfill \\ = \frac{1}{3}\int_{}^{} {\frac{{3dx}}{{\sqrt {1 - \,{{\left( {3x} \right)}^2}} }}} \hfill \\ \hfill \\ integrate\,\, \hfill \\ \hfill \\ = \frac{1}{3}\arcsin \,\left( {3x} \right) + C \hfill \\ \end{gathered} \]
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