Question Number 158333 by amin96 last updated on 02/Nov/21
$$\int_{\left(\mathrm{1};\pi\right)} ^{\left(\mathrm{2};\pi\right)} \left(\mathrm{1}−\frac{\boldsymbol{\mathrm{y}}^{\mathrm{2}} }{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\boldsymbol{\mathrm{cos}}\left(\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}}\right)\right)\boldsymbol{\mathrm{dx}}+\left(\boldsymbol{\mathrm{sin}}\left(\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}}\right)+\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{cos}}\left(\frac{\boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{x}}}\right)\right)\boldsymbol{\mathrm{dy}}=? \\ $$$$\boldsymbol{\mathrm{OY}}\:\:\boldsymbol{\mathrm{on}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{road}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{doesn}}'\boldsymbol{\mathrm{t}}\:\boldsymbol{\mathrm{cut}}\:\boldsymbol{\mathrm{your}}\:\boldsymbol{\mathrm{arrow}} \\ $$