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How can I evaluate $\displaystyle\int_0^\infty \frac{\sin x}{x} \, dx$? (Let $\displaystyle \frac{\sin0}{0}=1$.)

I proved that this integral exists by Cauchy's sequence.

However I can't evaluate what is the exact value of this integral.

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marked as duplicate by Lord_Farin, user1729, Elias, O.L., Martin Jun 6 '13 at 11:08

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up vote 2 down vote accepted

It's a famous Dirichlet integral. http://en.wikipedia.org/wiki/Dirichlet_integral

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