Question Number 197338 by yusufkhabibulloh last updated on 13/Sep/23
$$\int\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$
Answered by TheHoneyCat last updated on 13/Sep/23
$$=\int\frac{{x}^{\mathrm{2}} +\mathrm{1}−\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{d}{x} \\ $$$$=\int\mathrm{d}{x}\:−\int\frac{\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{d}{x} \\ $$$$={x}−\mathrm{arctan}\left({x}\right)+{c}\:\:\:\:\:\:\left({c}\in\mathbb{R}\right) \\ $$