Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Section 7.3 - Exponential Functions - Exercises 7.3 - Page 390: 30

Answer

$$2{e^x} + \frac{3}{2}{e^{ - 2x}} + C $$

Work Step by Step

$$\eqalign{ & \int {\left( {2{e^x} - 3{e^{ - 2x}}} \right)} dx \cr & {\text{use sum rule for integration}} \cr & = \int {2{e^x}} dx - \int {3{e^{ - 2x}}} dx \cr & {\text{constant multiple rule}} \cr & = 2\int {{e^x}} dx - 3\int {{e^{ - 2x}}} dx \cr & {\text{use the formula }}\int {{e^{ax}}} dx = \frac{{{e^{ax}}}}{a} + C \cr & = 2{e^x} - 3\left( {\frac{{{e^{ - 2x}}}}{{ - 2}}} \right) + C \cr & {\text{simplifying}} \cr & = 2{e^x} + \frac{3}{2}{e^{ - 2x}} + C \cr} $$
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