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If f(x) is polynomaial function of degre...

If `f(x)` is polynomaial function of degree n, prove that `int e^x f(x) dx=e^x[f(x)-f '(x)+f''(x)-f'''(x)+......+(-1)^n f^n (x)]` where `f^n(x)=(d^nf)/(dx^n)`

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`I=int e^(x)f(x)dx`
`=f(x)e^(x)-int e^(x)f'(x)dx`
`=f(x)e^(x)-f'(x)e^(x)+int e^(x)f''(x)dx`
`=f(x)e^(x)-f'(x)e^(x)+f''(x)e^(x)-inte^(x)f'''(x)dx`
`=f(x)e^(x)-f'(x)e^(x)+f''(x)e^(x)-f'''(x)e^(x)+int e^(x)f'^(v)(x)dx`
continuing this way, we get
`I=e^(x)[f(x)-f'(x)+f''(x)-f'''(x) ...+(-1)^(n)f^((n))(x)]`
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