Question

Show that\[\large \int\limits_0^1 x^{2014}(1-x)^{2015}\, dx = \dfrac{(2015!)^2}{2015[((2(2015))!]}\]

Answer 1

i smell beta

Answer 2

BINGO!

Answer 3

it is trivial if you're able to smell beta function ;)
else finding a recurrence relation is bit interesting too !