Question Number 129867 by Bird last updated on 20/Jan/21
$${calculate}\:\int\:\:\:\frac{\mathrm{2}{x}−\mathrm{1}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} }{dx} \\ $$
Answered by Olaf last updated on 20/Jan/21
$$\Omega\:=\:\int\frac{\mathrm{2}{x}−\mathrm{1}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}} }{dx}\:=\:\int\frac{{du}}{{u}^{\mathrm{3}} } \\ $$$$\left({u}\:=\:{x}^{\mathrm{2}} −{x}+\mathrm{1}\right) \\ $$$$\Omega\:=\:−\frac{\mathrm{1}}{\mathrm{2}{u}^{\mathrm{2}} }+\mathrm{C}\:=\:−\frac{\mathrm{1}}{\mathrm{2}\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{2}} }+\mathrm{C} \\ $$