Calculus (3rd Edition)

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


$$ \int(x+25)^{-2} d x=-\frac{1}{x+25}+c. $$

Work Step by Step

Since $ u=x+25 $, then $ du=dx $ and hence, $$ \int(x+25)^{-2} d x=\int u^{-2} d u=- u^{-1}+c\\ =-(x+25)^{-1}+c=-\frac{1}{x+25}+c. $$
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