General formula for integral of polynomial expressed as roots product

Question

I’m wondering whether there is a general formula to integrate a polynomial expressed as product of its $n$ roots, in other words

$\int p(x)dx$

With $p(x) = (x-r_1) (x-r_2)...(x-r_n)$

So to have the solution as function of the roots and not of the coefficients of the entire polynomial. Any reference / formula for that?

Thanks!