Answer
$$-\frac{1}{\ln 7}7^{-x} +c.$$
Work Step by Step
Let $u=7^{-x}$, then $du=-7^{-x} \ln 7 dx$. We have
$$\int 7^{-x} dx=-\frac{1}{\ln 7}\int du=-\frac{1}{\ln 7}u+c\\
=-\frac{1}{\ln 7}u+c=-\frac{1}{\ln 7}7^{-x} +c.
$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
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
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