Calculus: Early Transcendentals (2nd Edition)

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

Chapter 7 - Integration Techniques - 7.6 Other Integration Strategies - 7.6 Exercises: 12

Answer

\[ = - \frac{1}{9}\ln \left| {\frac{{9 + \sqrt {81 - {x^2}} }}{x}} \right| + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\frac{{dx}}{{x\sqrt {81 - {x^2}} }}} \hfill \\ \hfill \\ use\,\,\int_{}^{} {\frac{{du}}{{u\sqrt {{a^2} - {u^2}} }}} = \frac{1}{a}\ln \left| {\frac{{a + \sqrt {{a^2} - {u^2}} }}{u}} \right| + C \hfill \\ \hfill \\ with\,\,a = 9 \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ = - \frac{1}{9}\ln \left| {\frac{{9 + \sqrt {81 - {x^2}} }}{x}} \right| + C \hfill \\ \end{gathered} \]
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