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\end{equation}  Where $B_0=C$ and $B_i=[x^if^{(i-1)}]_a^b$, for $i=1\dots n$. So for example we have \begin{equation}  \int_0^\infty x^n\frac{d^n}{dx^n}\bigg(\frac{x^s-1}{e^x-1}\bigg)\;dx=(-1)^nn!\zeta(s)\Gamma(s)+\sum_{k=1}^n\frac{(-1)^{k+n}n!}{k!}\bigg[x^k\frac{d^{k-1}}{dx^{k-1}}\bigg(\frac{x^{s-1}}{e^x-1}\bigg)\bigg]_0^\infty  \end{equation}