Is it possible to evaluate the following integral $$ \int_{-1}^1 \dots \int_{-1}^1 e^{- (\mathbf x- \mathbf y)^T A (\mathbf x-\mathbf y)} dx_1 \dots dx_n $$ where $\mathbf x, \mathbf y \in \mathbb{R^n}$ and $A$ is positive definite matrix.
I have no idea how to do it for general matrix $A$. Is it even possible to write down the answer with nice formula?