How to integrate $\cos2\pi\left(x+\frac{n}{x}\right)$

Question

This is a follow up question of Integrate $\cos^2(\pi x)\cos^2(\frac{n\pi}{x})$. By using product to sum formula, this could be converted to question to integrate $$\int\cos2\pi\left(x+\frac{n}{x}\right)\text{d}x, \text{ where } 2 \le x \le n$$ But this seems hard to integrate too. Very appreciate if you can help to make any progress.