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: 35

Answer

\[\frac{{{e^{2u}}}}{2} + 2{u^2} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\,\left( {{e^{2u}} + 4u} \right)} du \hfill \\ By\,\,the\,\,sum\,\,and\,\,difference\,\,rule \hfill \\ \int_{}^{} {{e^{2u}}du + \int_{}^{} {4udu} } \hfill \\ Use\,\,indefinite\,\,integrals \hfill \\ \int_{}^{} {{e^{kx}}dx = \frac{{{e^{kx}}}}{k} + C\,\,,\,\,\int_{}^{} {{u^n}du = \frac{{{u^{n + 1}}}}{{n + 1}} + C} } \hfill \\ Then \hfill \\ \frac{{{e^{2u}}}}{2} + 4\,\left( {\frac{{{u^2}}}{2}} \right) + C \hfill \\ Simplifying \hfill \\ \frac{{{e^{2u}}}}{2} + 2{u^2} + C \hfill \\ \end{gathered} \]
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