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: 6


$$ du = \frac{dt}{(t+1)^2} .$$

Work Step by Step

Recall the quotient rule: $(\dfrac{u}{v})'=\dfrac{vu'-uv'}{v^2}$ $$ u= \frac{t}{t+1}\Longrightarrow du = \frac{(t+1)(1)-t(1)}{(t+1)^2} d t=\frac{dt}{(t+1)^2} .$$
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