In the case of the classic Geometric Brownian motion $$dS_t = \mu S_t dt + \sigma S_tdW_t$$ we solve it as $$ S_t = S_0 \exp\left[ \left(\mu - \frac{\sigma^2}{2}\right)t + \sigma dW_t\right] $$ and simulate $S_{t_{i+1}} = S(t_i) \exp\left[ \left(\mu - \frac{\sigma^2}{2}\right)(t_{i+1}-t_{i}) + \sigma dW_t\right]$ with $W_t = \sqrt{t_{i+1}-t_i}Z_{i+1}$.
However, I am working with the slightly different version $$dS_t = \mu S_t dt + \sigma S_t^{\beta/2} dW_t$$ When I solve it using the Ito's Lemma, I get $$S_t = S_0 \exp\left[ \left(\mu - \frac{\sigma^2}{2} S_t^{\beta-2}\right)t + \sigma S^{\beta/2 - 1}_t dW_t\right]$$ and have no idea how to simulate it using normal distribution, since $S_t$ is sitting inside. Is it possible to sample from this process?