Calculus: Early Transcendentals (2nd Edition)

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

Chapter 6 - Applications of Integration - 6.8 Logarithmic and Exponential - 6.8 Exercises: 58

Answer

$$\frac{{{7^{2x}}}}{{2\ln 7}} + C$$

Work Step by Step

$$\eqalign{ & \int {{7^{2x}}} dx \cr & {\text{substitute }}u = 2x,{\text{ }}du = 2dx \cr & = \frac{1}{2}\int {{7^u}} du \cr & {\text{find the antiderivative by the formula }}\int {{a^x}} dx = \frac{{{a^x}}}{{\ln a}} + C \cr & {\text{letting }}a = 10 \cr & = \frac{1}{2}\left( {\frac{{{7^u}}}{{\ln 7}}} \right) + C \cr & {\text{with }}u = 2x \cr & = \frac{1}{2}\left( {\frac{{{7^{2x}}}}{{\ln 7}}} \right) + C \cr & = \frac{{{7^{2x}}}}{{2\ln 7}} + C \cr} $$
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