How can these integrals be solved:
$${1\over \pi} \int_{0}^{\infty}\left({{\sqrt{x}(a-bx)}\over {x^{3}+(a-bx)^{2}}}\right)\cos(\sqrt{\alpha x}) \exp(-xt)\,\mathrm{d} x, $$
and
$${1\over \pi} \int_{0}^{\infty}\left({{x^2}\over {x^{3}+(a-bx)^{2}}}\right)\sin(\sqrt{\alpha x}) \exp(-xt)\,\mathrm{d} x. $$