Chapter 8 - Techniques of Integration - Chapter Review Exercises - Page 460: 20

$$\frac{1}{2}\sin ^{4} \theta+C$$

\begin{aligned} \int \sin 2 \theta \sin ^{2} \theta d \theta &=\int(2 \sin \theta \cos \theta) \sin ^{2} \theta d \theta \\ &=2 \int \sin ^{3} \theta \cos \theta d \theta\\ &=\frac{1}{2}\sin ^{4} \theta+C \end{aligned}