Integrability of the logarithm-weighted sawtooth integrand $(\lfloor x \rfloor + \tfrac12 - x)\, x^{-(s+1)}\, (-\log x)$ on $(N, \infty)$

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Integrability of the logarithm-weighted sawtooth integrand $(\lfloor x \rfloor + \tfrac12 - x)\, x^{-(s+1)}\, (-\log x)$ on $(N, \infty)$ · Prove2Me