Question Number 31543 by Cheyboy last updated on 09/Mar/18
$$\int\frac{{x}^{\mathrm{3}} +{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx} \\ $$$$ \\ $$$$ \\ $$
Commented by prof Abdo imad last updated on 10/Mar/18
$${I}=\int\:\frac{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)\:+\mathrm{1}}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx}=\:\int\:{xdx}\:+\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$$=\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:+{arctanx}\:+\lambda\:\:. \\ $$
Commented by Cheyboy last updated on 10/Mar/18
$${Thank}\:{you}\:{sir} \\ $$