Suppose we have two integers $a$ and $b$, and a polynomial in $x$, $p(x)$.
What's the fastest way to get an exact value for $\int_a^b{(p(x))^n dx}$, with $n$ large?
This is a more complicated version of this questionthis question, but an easier version of "What's the fastest way to get an exact value for a product of (powers of polynomials)?""What's the fastest way to get an exact value for a product of (powers of polynomials)?".