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 - Page 366: 42

Answer

$$\frac{{{3^{2x}}}}{{2\left( {\ln 3} \right)}} + C$$

Work Step by Step

$$\eqalign{ & \int {{3^{2x}}} dx \cr & {\text{use the integration formula }}\int {{a^{kx}}} dx = \frac{{{a^{kx}}}}{{k\left( {\ln a} \right)}} + C{\text{ with }}k \ne 0.{\text{ see page 361 }} \cr & {\text{for this exercise we can set }}a = 10{\text{ and }}k = 2.{\text{ then}} \cr & \int {{3^{2x}}} dx = \frac{{{3^{2x}}}}{{2\left( {\ln 3} \right)}} + C \cr} $$
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