junk

${{d^3\,q\,e^{-{{L^2\,q^2}\over{4}}}}\over{\left(w-w\left(q\right)\right)^2+{{T^2}\over{4}}}}$

$I(\omega)=\int\frac{e^{\frac{-q^{2}L^{2}}{4}}}{\left[\omega-\omega(q)\right]^{2}+\left[\Gamma/2\right]^{2}}\:d^{3}q$

$I(\omega)=\int\frac{4\pi q^{2}e^{\frac{-q^{2}L^{2}}{4}}}{\left[\omega-\omega(q)\right]^{2}+\left[\Gamma/2\right]^{2}}\:dq$