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.
2026-05-14 22:51:34.1778799094
How can I evaluate $\int_0^\infty \frac{\sin x}{x} \,dx$? [may be duplicated]
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It's a famous Dirichlet integral. http://en.wikipedia.org/wiki/Dirichlet_integral