Given that m and n are positive integers, show that
int [from 0 to 1] (x^m)(1-x)^n dx = int [from 0 to 1] (x^n)(1-x)^m dx
Using integration by parts:
In fact, using integration by parts t times you get:
Let t = n:
The final integration is simple.
From the symmetry of the answer, it's clear that has the same value.