Let $X \sim \mathcal{N}(\mu, \Sigma)$. How to show that $E[X] = \mu$?
Using the definition of the expected value of a continuous random variable: $$ E[X] = \int_{-\infty}^{\infty}x f_X(x) dx $$ I develop the expression by using the multivariate Gaussian density function $f_{X}(x|\mu,\Sigma)=\frac{1}{\sqrt{(2\pi)^d|\Sigma|}}e^{-\frac{1}{2}(x-\mu)^T\Sigma^{-1}(x-\mu)}$: $$ E[X] = \int_{\Bbb R^d}{\frac{x}{\sqrt{(2\pi)^d|\Sigma|}}e^{-\frac{1}{2}(x-\mu)^T\Sigma^{-1}(x-\mu)}}dx $$
I am quite stuck after that. Please kind minds of Mathematics help!