Evaluate $\int \sin^{2} x\cos^{2} x\,dx$.

Explanation

1. 01

   $\sin^{2} x\cos^{2} x = \frac{\sin^{2} 2x}{4} = \frac{1 - \cos 4x}{8}$.

2. 02

   $\int \frac{1 - \cos 4x}{8}\,dx = \frac{x}{8} - \frac{\sin 4x}{32} + C$.