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Question Number 108738 by mnjuly1970 last updated on 19/Aug/20

$$please:{}^{\ast }{\mathrm{prove}}^{\ast }::::$$$$1{.}^{\mathrm{important}}{\lim }_{\mathrm{z}\to 1}(\zeta \left(\mathrm{z}\right)-\frac{1}{\mathrm{z}-1})=\gamma \left(\mathrm{euler}\mathrm{constant}\right)$$$$2.\stackrel{\mathrm{important}}{}{\int }_0^{\mathrm{\infty }}(\cos \left(\mathrm{x}\right)-\frac{1}{1+{\mathrm{x}}^2})\frac{\mathrm{dx}}{\mathrm{x}}=-\gamma$$$$.....\mathcal{M}.\mathcal{N}.....$$$$$$

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