## Calculus (3rd Edition)

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