Thread: Polynomial function of nth degree?

If $\displaystyle f(x)$ is a polynomial function of the $\displaystyle n^{th}$ degree, prove that:
$\displaystyle \int e^xf(x)\ dx = e^x[f(x) - f'(x) + f''(x) - f^{(3)}(x) + ... + (-1)^nf^{(n)}(x)]$
where $\displaystyle f^{(n)}(x) = \frac{d^nf}{dx^n}$

It's simply integration by parts until $\displaystyle f^{(n+1)}(x)=0$ because $\displaystyle deg(f)=n$.