Answer
$$
\int(x+25)^{-2} d x=-\frac{1}{x+25}+c.
$$
Work Step by Step
Since $ u=x+25 $, then $ du=dx $ and hence, $$
\int(x+25)^{-2} d x=\int u^{-2} d u=- u^{-1}+c\\
=-(x+25)^{-1}+c=-\frac{1}{x+25}+c.
$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 275: 8
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