# Strange integral

Calculus Level 5

$\def\sinc{sinc\,} \large \int_{0}^{\infty} \prod\limits_{k=0}^{n}\sinc\left(\frac{x}{2k+1}\right)dx=\, \frac{\pi}{2}$

Find the largest value of $n$ which satisfies the above equation.

$n$ is a natural number.

$\def\sinc{sinc\,} \sinc (x)=\frac{\sin x}{x}.$

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