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- “sinc-ing” integral 2 answers

Supposedly the answer is 1 but I have no idea how to evaluate this thing analytically.

$$f(n) = \frac{2}{\pi} \int_{0}^{\infty} 2\cos(x) \cdot \frac{\sin(x)}{x} \cdot \frac{\sin(x/3)}{x/3} \cdot \cdots \cdot \frac{\sin(x/(2n+1))}{x/(2n+1)} dx$$

Any help would be appreciated.