Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 7 - Integration - 7.1 Antiderivatives - 7.1 Exercises: 24

Answer

\[\frac{{{u^{3/2}}}}{{3/2}} + \frac{{{u^{ - 1}}}}{{ - 1}} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\,\left( {\sqrt u + \frac{1}{{{u^2}}}} \right)du} \hfill \\ Write\,\,\sqrt u \,as\,\,{u^{1/2}}\,\,and\,\,\frac{1}{{{u^2}}} = {u^{ - 2}} \hfill \\ Use\,\,the\,\,power\,\,rule\,\,\int_{}^{} {{u^n}du} = \frac{{{u^{n + 1}}}}{{n + 1}} + C \hfill \\ Then \hfill \\ \frac{{{u^{1/2}}}}{{1/2 + 1}} + \frac{{{u^{ - 2 + 1}}}}{{ - 2 + 1}} + C \hfill \\ Simplifying \hfill \\ \frac{{{u^{3/2}}}}{{3/2}} + \frac{{{u^{ - 1}}}}{{ - 1}} + C \hfill \\ \end{gathered} \]
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