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: 77


$$-\frac{1}{\ln 7}7^{-x} +c.$$

Work Step by Step

Let $u=7^{-x}$, then $du=-7^{-x} \ln 7 dx$. We have $$\int 7^{-x} dx=-\frac{1}{\ln 7}\int du=-\frac{1}{\ln 7}u+c\\ =-\frac{1}{\ln 7}u+c=-\frac{1}{\ln 7}7^{-x} +c. $$
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