Let $$ X \sim \mathcal{W}_{q} (n, \Sigma) \; \; n > q$$

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 $$E_{X}\left\{\left(I+XA\right)^{-1}\right\}$$ where $A$ is a given matrix. Thanks for your help!

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!