As an example, consider the following six-dimensional integral $$ \begin{equation*} \int_{-\infty}^{\infty}\mathbf{dxdy}g(\mathbf{x, y}), \end{equation*} $$ where $$ \begin{equation*} g(\mathbf{x, y})=\exp{(-\mathbf{x}^2-\mathbf{y}^2)}(\mathbf{x}-\mathbf{y})^2 \end{equation*} $$ with \( d=6 \).