How to plot $\int\frac{\mathrm{d}y}{W(-e^{-y^2/2-1})+1}=x$ in Matlab?

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I would like to plot in Matlab the following implicit equation: $$\int\frac{\mathrm{d}y}{W(-e^{-y^2/2-1})+1}=x,$$ where $W(\cdot)$ is the Lambert $W$ function. I am trying to plot it symbolically with ezplot but Matlab's lambertw function does not allow symbolic inputs. How would you plot it?

Thanks!