Find an anti-derivative of the function $\cos 2x$ using the method of inspection.

$\frac{1}{2}\sin 2x$

The correct answer is Option (2) → $\frac{1}{2}\sin 2x$

We look for a function whose derivative is $\cos 2x$.

$\frac{d}{dx} \sin 2x = 2 \cos 2x$

$\text{or} \quad \cos 2x = \frac{1}{2} \frac{d}{dx} (\sin 2x) = \frac{d}{dx} \left( \frac{1}{2} \sin 2x \right)$

Therefore, an anti derivative of $\cos 2x$ is $\frac{1}{2} \sin 2x$.