Integration In multidimensional domain

How to resolve?:

$\displaystyle \int_{X} \exp{ \left( -\frac{X^{T}QX}{2} \right)}\left( -\frac{X^{T}QX}{2} \right)dX$

where $\displaystyle X$ is a vector $\displaystyle [x_{1},...,x_{n}]^T$ and $\displaystyle Q$ a n*n matrix. The integral should be calculated over $\displaystyle \mathbb{R}^n$..

In analogy with the 1dimensional case, I supposed to consider the argument as a sort of $\displaystyle Qx^2$, and resolve the integral by parts , dividing the last term and trying to obtain the derivate of the term $\displaystyle \left( -\frac{X^{T}QX}{2} \right)$.

But I am not shure how to proceed in the multidimensional domain. Is my thought valid? Someone can help me?

Thanks

Pollo