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: 10

Answer

\[ = - \frac{1}{4}{e^{\,\left( {3 - 4x} \right)}} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {{e^{\,\left( {3 - 4x} \right)}}\,dx} \hfill \\ \hfill \\ substituting\,\,\,\left( {3 - 4x} \right) = u\,\,and\,\,dx = - \frac{{du}}{4} \hfill \\ \hfill \\ = - \frac{1}{4}\int_{}^{} {{e^u}du} \hfill \\ \hfill \\ integrate\,\,\,{\text{using }}\int {{e^u}du = {e^u} + C} \hfill \\ \hfill \\ = - \frac{1}{4}{e^u} + C \hfill \\ \hfill \\ substituting\,back\,\,\,u = 3 - 4x \hfill \\ \hfill \\ = - \frac{1}{4}{e^{\,\left( {3 - 4x} \right)}} + C \hfill \\ \end{gathered} \]
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