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Math Help - Polynomial function of nth degree?

  1. #1
    Super Member fardeen_gen's Avatar
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    Polynomial function of nth degree?

    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}
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  2. #2
    Junior Member Infophile's Avatar
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    It's simply integration by parts until f^{(n+1)}(x)=0 because deg(f)=n.

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