Calculus: Early Transcendentals (2nd Edition)

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

Chapter 7 - Integration Techniques - 7.1 Basic Approaches - 7.1 Exercises: 26

Answer

\[ = - \frac{4}{3}{e^{ - 3x}} - \frac{1}{5}{e^{ - 5x}} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\frac{{4 + {e^{ - 2x}}}}{{{e^{3x}}}}dx} \hfill \\ \hfill \\ {\text{split}}\,\,{\text{the}}\,\,{\text{integrand}} \hfill \\ \hfill \\ = \int_{}^{} {\,\left( {\frac{4}{{{e^{3x}}}} + \frac{{{e^{ - 2x}}}}{{{e^{3x}}}}} \right)dx} \hfill \\ \hfill \\ {\text{Simplify}} \hfill \\ \hfill \\ = \int_{}^{} {\,\left( {4{e^{ - 3x}} + {e^{ - 5x}}} \right)} dx \hfill \\ \hfill \\ \operatorname{int} egrating \hfill \\ \hfill \\ = - \frac{4}{3}{e^{ - 3x}} - \frac{1}{5}{e^{ - 5x}} + C \hfill \\ \end{gathered} \]
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