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How to Find $$\zeta(4)=\sum_ {k=1}^{\infty}{\frac{1}{k^4}}$$ the most basic way possible?

I know it's $\pi^4/90$ but to arrive at this figure? Curious, because I need it to solve the integral $\int_{0}^{\infty}x^3\cdot(e^x-1)^{-1}\;dx$.


marked as duplicate by MathOverview, TMM, Potato, Andrew, Michael Albanese Jan 7 '14 at 12:25

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