Can anyone give me some clues about the following integral \begin{equation*} \int_{R^{n}} \cos(\|x\|)\exp(-0.5(x - Ex)'C^{-1}(x - Ex))dx \end{equation*} where $\|x\|$ is the Euclidean norm.
I only know the following special case \begin{equation*} \int_{R^{6}} \cos(x^{T}x) \mathcal{N}(x;0,I)dx = -3\text{Dawson}\left(\frac{1}{\sqrt{2}}\right)/2\sqrt{2} \end{equation*}
