finding an estimate for $y(x)$ accurate to the 10 decimal places

Question

the solution to the IVP

$\frac{dy}{dx}=1-Ax^{A-1}y$ where $y(0) = 0$ is

$y(x) = e^{-x^A} \int_{0}^{x}e^{t^A}dt$. How can I find an estimate for $y(x)$ accurate to the 10 decimal places?