Is there a simple solution for $ \frac{d}{dy} \log\big( \int_{0}^{y} \exp(-a \frac{x^{3/2}}{y}+ b x)\, dx \big) $

Question

What is the solution of $$ \frac{d}{dy} \log\left( \int_0^y \exp\left(-a \frac{x^{3/2}}{y}+ b x\right)\, dx \right) $$

Where a and b are constants. Even if the solution is an approximate solution. The solution without log was explained here.