Question Number 185455 by cortano1 last updated on 22/Jan/23
$$\:\int\:\frac{{x}^{\mathrm{3}} .{e}^{{x}^{\mathrm{2}} } }{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }\:{dx}\:=? \\ $$
Answered by SEKRET last updated on 22/Jan/23
$$\left.\:\:\mathrm{1}\right)\:\:\:\:\:\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} =\boldsymbol{\mathrm{t}} \\ $$$$\left.\:\:\:\mathrm{2}\right)\:\:\:\:\int\:\boldsymbol{\mathrm{udv}}=\:\boldsymbol{\mathrm{uv}}\:−\:\int\boldsymbol{\mathrm{vdu}} \\ $$$$\:\:\:\:\boldsymbol{\mathrm{aswer}}\:\:\:\frac{\boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{x}}^{\mathrm{2}} } }{\mathrm{2}\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{1}\right)}+\boldsymbol{\mathrm{C}} \\ $$$$ \\ $$