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This is my exercise in Complex Analysis.

$$ \int_0^\infty \left(\frac{\sin x}{x}\right)^2\,dx = ? $$

I tried solving this by $(\sin x)^2=1-\cos(2x)$ but I realized that $\int_0^\infty \frac{dx}{x^2}$ does not converge.

Can someone help me? Thank you so much.

Sangchul Lee
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Ooshi Osoto
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    Welcome to MSE! Have you checked questions that are already answered? https://math.stackexchange.com/questions/646096/calculating-int-0-infty-frac-sin2xx2dx-using-the-residue-theorem?rq=1 – Sangchul Lee Nov 06 '17 at 03:34
  • See also https://math.stackexchange.com/questions/141695/how-to-calculate-the-integral-of-sin2x-x2. – Nosrati Nov 06 '17 at 03:40

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