Given two matrix $A$ and $D$ and a column vector $x$, what is the value of the following integral?
$\int d^nx \; \; e^{x^T A x + \mid x \mid^T D \mid x \mid + B x}$
where $\mid x \mid_i = \mid x_i \mid$
And what are the requirements on $A$ and $D$ to have convergence ?
Thank you!
edit: for simplicity it is possible to assume that $A$ and $D$ are both symmetrical and diagonalizeble by the same orthogonal matrix $M$