Calculus: Early Transcendentals (2nd Edition)

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

Chapter 7 - Integration Techniques - 7.2 Integration by Parts - 7.2 Exercises: 9

Answer

\[ = t\,{e^t}\, - \,{e^t}\, + \,C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {t\,{e^t}\,dt} \hfill \\ \hfill \\ set\,\,\,the\,\,substitution \hfill \\ \hfill \\ u = t\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,then\,\,\,\,\,\,\,\,du = dt \hfill \\ du = {e^t}dt\,\,\,\,\,then\,\,\,\,\,\,\,\,\,v = {e^t} \hfill \\ \hfill \\ use\,\,uv - \int_{}^{} {vdu} \hfill \\ \hfill \\ {\text{replacing the values }}{\text{in the equation}} \hfill \\ \hfill \\ t\,{e^t} - \int_{}^{} {{e^t}dt} \hfill \\ \hfill \\ integrate \hfill \\ \hfill \\ = t\,{e^t}\, - \,{e^t}\, + \,C \hfill \\ \end{gathered} \]
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