I have the following question that I'm having issues solving

$\displaystyle \int\limits_0^1{(1+\sqrt{x})^8}dx$

I tried using uv substitution with u being $\displaystyle {(1+\sqrt{x})^8}$ and v being just dx. However, it quickly devolved into uv substitution after uv substition that spiralled into a massively negative number, so I must be doing something wrong. My plan was just to uv until I got that exponent down to something I could easily multiply out.

Any tips, tricks, or something I may have missed?