Evaluate-
$$\int_0^\infty\frac{\sin^2(ax)}{(ax)^2\sqrt{x^2+bi}} dx$$
where $a>0$ and $b>0$ are two given constants and $i$ is an imaginary unit. I have no clue how to solve this problem. I tried to use the Residue theorem to imitate the method of calculating the Dirichlet integral, but it didn't work.