Expected value of the gradient of logistic loss function to a normal distribution

Question

Given a vector $\beta\in\mathbb{R}^d$, and a random vector $x\sim\mathbf{N}(0_d,I_{d\times d})$, that is $\{x_j\}_{j=1}^d$ are i.i.d generated from gaussian $\mathbf{N}(0,1)$, can we compute or approximate $\mathbf{E}_{x\sim\mathbf{N}(0_d,I_{d\times d})}[\frac{x}{1+\exp(x^\top \beta)}]$, that is, for all $j$, $$ \int_{\mathbb{R}^d} \frac{x_j}{1 + \exp(x^\top \beta)} \frac{1}{(2\pi)^{d/2}} \exp\left(-\frac{1}{2} x^\top x\right) \, dx. $$