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## Homework Statement

"Show that [tex]- \int^1_0 x^k\ln{x}\,dx = \frac{1}{(k+1)^2} ; k > -1[/tex].

Hint: rewrite as a gamma function.

## Homework Equations

Well, I know that [tex]\Gamma \left( x \right) = \int\limits_0^\infty {t^{x - 1} e^{ - t} dt}[/tex].

## The Attempt at a Solution

I've tried various substitutions, beginning with u=k*ln(x), but I'm not getting very far. To write it as a gamma function, I'd have to change the limits from (0 to 1) to (0 to infinity) and I can't find a way to do that.

Can someone point me in the right direction?