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### Proving $\int\limits _0^\infty\frac {\sin^{2n+1}x}{x}dx=\frac 1 {4^n}\binom{2n}{n}\int_0^\infty \frac {\sin{x}}{x}dx$

The question is Prove that for any $n\in\mathbb N$, $\int\limits _0^\infty\frac {\sin^{2n+1}x}{x}dx=\frac 1 {4^n}\binom{2n}{n}\int_0^\infty \frac {\sin{x}}{x}dx$ I don't have any ideas how to ...
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### Parameterizing divots in contour integrals

I have recently attempted to pick up complex analysis and have been stuck on this problem for a few days: $$\int_{-\infty}^\infty \frac{\sin^2x}{x^2}\mathrm{d}x$$ Fortunately, it would seem that ...