How do I start this integral problem? – math.stackexchange.com

How do I start this integral problem? – math.stackexchange.com

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How do I prove this? $$\int_0^1 \frac{\ln^3 u}{1-u} du = -\frac{\pi^4}{15} $$ I'm guessing using Riemann zeta function? But then how do I start?

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