What $\int_0^a x^ne^xdx$ looks like? Given the integral $$\int_0^ax^ne^xdx$$
I wanted to know what it looks like for an integer $n$ and a positive $a$. After evaluating some values with mathematica, I believe it looks like $e^ap_n(a)+c_n$, where $p_n(a)$ is a polynomial with degree $n$ in $a$, and $c_n$ is an integer. Is this correct?

Another approach would be to expand the exponential as an infinite sum...
$$\int_{0}^{a}{x^n}{e^x}dx=\sum_{k=0}^{\infty}{1\over k!}\int_{0}^{a}x^{(n+k)}dx$$
$$=\sum_{k=0}^{\infty}{{a^{(n+k+1)}}\over{(n+k+1)\cdot k!}}$$
