Continuous Kelly for Normal Returns

Each round you allocate a fraction $f$ of wealth to a position whose one-period return $R$ is approximately normal with small mean $\mu>0$ and variance $\sigma^2$ (with $\mu^2\ll\sigma^2$), so post-round wealth is multiplied by $1+fR$. Using a second-order expansion of the log, derive the growth-optimal fraction $f^*$.