How could I integrate $\int_0^\infty \sin(k|x|)/k^2\,dk$?

62 Views Asked by At

Does anybody know how to evaluate this integral?

I have $\int_0^\infty \frac{\sin(k|x|)}{k^2}\,dk$ and I tried several contour integration in the complex plane like the key-hole.

I think I'm doing something wrong when I try to calculate the limit on the little circle surrounding $z=0$, but I can't figure out what and how to solve the integral.

Thanks for answering!