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## Homework Statement

I'm trying to prove the following definite integral of [tex]sinc(x)[/tex]

[tex]\int_{-\infty}^{\infty}\frac{\sin(x)}{x}dx=\pi[/tex]

## Homework Equations

## The Attempt at a Solution

I've tried power series expansions as well as trigonometric identities like

[tex]\frac{\cos 2x}{x}=\frac{\cos^2 x}{x}-\frac{\sin^2 x}{x}[/tex]

I also looked at techniques used to integrate the definite integral

[tex] \int_{-\infty}^{\infty}e^{-x^2}dx [/tex]

which I know is solved by double integration and changing to polar coordinates. However, this does not help me integrate [tex]sinc(x)[/tex].