Question Number 219481 by SdC355 last updated on 26/Apr/25
$$\mathrm{pls}\:\mathrm{Help}…. \\ $$$$\mathrm{1}.\:−\frac{\mathrm{1}}{\boldsymbol{{i}}\pi}\:\int_{\:−\infty+\boldsymbol{{i}\zeta}_{\mathrm{0}} } ^{\:\infty+\boldsymbol{{i}\zeta}_{\mathrm{0}} } \:\frac{{e}^{{st}} \left(\mathrm{ln}\left({t}\right)+\boldsymbol{\gamma}\right)}{{t}}\:\mathrm{d}{t}\: \\ $$$$\mathrm{2}.\:\int_{\mathrm{0}} ^{\:\infty} \:\:{t}\centerdot{J}_{\nu} \left({t}\right){J}_{\nu} \left({rt}\right)\:\mathrm{d}{t} \\ $$$$\mathrm{3}.\:\int_{\mathrm{0}} ^{\:\infty} \:{t}\centerdot\mathrm{cos}\left({t}\right){J}_{\nu} \left({rt}\right)\:\mathrm{d}{t} \\ $$