\[\Pi\Big(\frac{s}{2}-1\Big) \pi^{-\frac{s}{2}} \zeta(s) = \int_1^{+\infty} \psi(x) \big( x^{\frac{s}{2}} + x^{\frac{1-s}{2}} \big) \frac{dx}{x} - \frac{1}{s(1-s)}.\]

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