I was asked this $$\int_0^\infty \frac{\sin(x^2)}{x^2}\ \,dx$$
I have a solution by letting $$I(b) = \int_0^\infty \frac{\sin(x^2)}{x^2}e^{-bx} \,dx$$
However, I was told that the question can also be solved via contour integration. Can anyone demonstrate that? You can take a picture of the steps if you are too lazy to deal with mathjax symbols.
Thanks!