\[\int_{\boldsymbol{\Omega}}\operatorname{etr}\left(-\mathbf{T}\mathbf{X}\right)%
\left|\mathbf{X}\right|^{b-\frac{1}{2}(m+1)}{{}_{1}F_{1}}\left({a\atop b};%
\mathbf{S}\mathbf{X}\right)\,\mathrm{d}{\mathbf{X}}=\Gamma_{m}\left(b\right)%
\left|\mathbf{I}-\mathbf{S}\mathbf{T}^{-1}\right|^{-a}\left|\mathbf{T}\right|^%
{-b},\]