0-n-x-x-1-x-2-x-n-dx-x-n-R-

Question Number 3046 by Filup last updated on 03/Dec/15

\int_{0}^{n} x (x + 1) (x + 2) \cdot \cdot \cdot (x + n) d x = ?

(x, n) \in R

Commented by Filup last updated on 04/Dec/15

x (x + 1) (x + 2) \cdot \cdot \cdot (x + n) = \frac{(x + n)!}{(x - 1)!}

= \frac{Γ (x + n + 1)}{Γ (x)}

in Γ form, x and n do not have

to be integers

∴ \int_{0}^{n} \frac{Γ (x + n + 1)}{Γ (x)} d x

Commented by prakash jain last updated on 04/Dec/15

multiplication and integration can be

done since it is a polynomial .