How can I integrate the following:
$$\frac{1}{b^2}\int_0^\infty z^{-2}\exp(-a z)\sin^2(b z)\, \mathrm dz$$
for $a,b>0$? Maple gives a compact result:
$$\frac{1}{b} \tan^{-1}(c) - \frac{1}{ac^2} \ln(1 + c^2)$$
where $c=2b/a$. I can solve it when the powers of $z$ and $\sin$ are $-1$ and $1$ respectively, but not for 2.