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: 10

Answer

\[ = \frac{1}{9}\ln \left| {\frac{y}{{2y + 9}}} \right| + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\frac{{dy}}{{y\,\left( {2y + 9} \right)}}} \hfill \\ \hfill \\ use\,\, \hfill \\ \hfill \\ \int_{}^{} {\frac{{du}}{{u\,\left( {bu + a} \right)}}} = \frac{1}{a}\ln \left| {\frac{u}{{bu + a}}} \right| + C \hfill \\ \hfill \\ b = 2,{\text{ }}a = 3 \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ = \frac{1}{9}\ln \left| {\frac{y}{{2y + 9}}} \right| + C \hfill \\ \end{gathered} \]
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