>>555
∫[x=0,∞] (x^3/(e^x−1)) dx
= Σ[k=1,∞] ∫[x=0,∞] x^3 e^(-kx) dx
= Σ[k=1,∞] 6/k^4
= 6ζ(4)
= 6π^4/90 = π^4/15