Bernoulli formula for integrals

[eljose]

let be the Bernoulli formula for calculating an integral in the form:

$$\int{f(x)dx}=C+\sum_{n=1}^{\infty}(-1)^{n}x^{n}\frac{d^{n}f}{dx^{n}}\frac{1}{\Gamma(n)}$$

my question is..could we calculate the integral from this series?..thanks.

 

[dextercioby]

It's actually a series for the antiderivative. I don't see why not...

Daniel.

P.S. It's kinda mysterious that this formula involves Euler's gamma function and not Bernoulli's numbers.