Let $$ X \sim \mathcal{W}_{n} (n, \Sigma) \; \;$$
Where $\mathcal{W}$ denotes the Wishart distribution and $\Sigma \in \mathbb{R}^{q \times q}$ is the corresponding scale matrix (symmetric, positive definite).
How to calculate the expectation of $$E_{X}\left\{\left(I+X\right)^{-1}\right\}$$ Thanks for your help!
