Calculus: Early Transcendentals (2nd Edition)

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

Chapter 7 - Integration Techniques - 7.1 Basic Approaches - 7.1 Exercises: 8

Answer

\[ = - \frac{1}{{18\,{{\left( {9x - 2} \right)}^2}}} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\,{{\left( {9x - 2} \right)}^{ - 3}}dx} \hfill \\ \hfill \\ substituting\,\,\,\left( {9x - 2} \right) = u\,\,\,\,and\,\,\,\,dx = \frac{{du}}{9} \hfill \\ \hfill \\ = \frac{1}{9}\int_{}^{} {{u^{ - 3}}\,du} \hfill \\ \hfill \\ {\text{use }}\int {{x^n}dx = \frac{{{x^{n + 1}}}}{{n + 1}} + C} \hfill \\ \hfill \\ = \frac{1}{9}\,\left( {\frac{{ - 1}}{{2{u^2}}}} \right) + C = - \frac{1}{{18{u^2}}} + C \hfill \\ \hfill \\ substituting\,\,back\,\,u = \,\left( {9x - 2} \right) \hfill \\ \hfill \\ = - \frac{1}{{18\,{{\left( {9x - 2} \right)}^2}}} + C \hfill \\ \end{gathered} \]
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.