Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.8 Inverse Trigonometric Functions - Exercises - Page 375: 82


$$\frac{2^xe^{4x}}{4+\ln 2}+c.$$

Work Step by Step

Since $2^x=e^{x\ln 2}$, then we have $$\int 2^xe^{4x}dx =\int e^{(4+\ln 2)x}dx=\frac{e^{(4+\ln 2)x}}{4+\ln 2}+c\\ =\frac{2^xe^{4x}}{4+\ln 2}+c.$$
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