I'm trying to follow along with my textbook on Auction Theory, but don't understand one of the steps. I don't see how they got $E[x^N] = 1/(N+1)$ in the final step. Please see the linked image below. Any help is greatly appreciated, thanks so much! Image here
2026-03-25 06:04:49.1774418689
Expectation of $x^n$ when $x$~$U[0,1]$
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Note:
$$E(X^n)=\int_0^1 t^n \ dt$$