Polynomial function of nth degree?

**fardeen_gen** · May 4th 2009, 01:16 AM

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

**Infophile** · May 4th 2009, 01:23 AM

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

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