Answer
$$ du = \frac{dt}{(t+1)^2} .$$
Work Step by Step
Recall the quotient rule: $(\dfrac{u}{v})'=\dfrac{vu'-uv'}{v^2}$
$$ u= \frac{t}{t+1}\Longrightarrow du = \frac{(t+1)(1)-t(1)}{(t+1)^2} d t=\frac{dt}{(t+1)^2} .$$
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: 6
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