Step-by-Step Solution
Key Concept: General
$$\int x \cos 2x \, dx = x \int \cos 2x \, dx - \int (1) \left( \int \cos 2x \, dx \right) dx$$ $$= \frac{x \sin 2x}{2} - \int \frac{\sin 2x}{2} \, dx$$ $$= \frac{x \sin 2x}{2} + \frac{\cos 2x}{4} + C$$
Correct Answer: $\frac{x \sin 2x}{2} + \frac{\cos 2x}{4} + C$