Is there a general form for calculating the mean values $E[X^TAX]$ and $E[[X-\mu]^TA[X-\mu]]$ where $X$ is a vector of dependent normal random variables with the distribution $X\sim N(\mu,\Sigma)$. I found very nice results for the independent case in the Matrices Cook Book (Equations 378 and 380). But I want some results for the dependent case when the covariance matrix is in the equicorreated form as $\Sigma=[c_{ij}]_{M\times M}$ with $c_{ij}=\sigma^2,\forall i=j$ and $c_{ij}=\rho\sigma^2,\forall i \neq j$.
Thank you very much.