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 $\displaystyle f^{(n)}(x) = \frac{d^nf}{dx^n}$