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: 9

Answer

\[\begin{gathered} \frac{3}{4}\,\left( {2u - 7\ln \left| {2u + 7} \right|} \right)\, + C \hfill \\ \hfill \\ \end{gathered} \]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\frac{{3u}}{{2u + 7}}} \,du \hfill \\ \hfill \\ rewrite \hfill \\ \hfill \\ = 3\int_{}^{} {\frac{u}{{2u + 7}}} \,du \hfill \\ \hfill \\ use\,\,the\,\,formula\,\, \hfill \\ \hfill \\ \int_{}^{} {\frac{u}{{bu + a}}} = \frac{1}{{{b^2}}}\,\left( {bu - a\ln \left| {a + bu} \right|} \right) + C \hfill \\ \hfill \\ with\,\,a = 7\,\,b = 2 \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ 3\int_{}^{} {\frac{u}{{2u + 7}}} \,du = \frac{3}{4}\,\left( {2u - 7\ln \left| {2u + 7} \right|} \right)\, + C \hfill \\ \hfill \\ \end{gathered} \]
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