Question Number 35290 by Fiko Jean last updated on 17/May/18
$$\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{3}} }{dx} \\ $$
Commented by abdo mathsup 649 cc last updated on 17/May/18
$$\int\:\frac{{x}+\mathrm{1}}{{x}^{\mathrm{3}} }{dx}\:=\:\int\:\frac{{dx}}{{x}^{\mathrm{2}} }\:\:+\:\int\:\:\:\frac{{dx}}{{x}^{\mathrm{3}} }\:=\:−\frac{\mathrm{1}}{{x}}\:\:+\:\frac{\mathrm{1}}{−\mathrm{3}+\mathrm{1}}{x}^{−\mathrm{3}+\mathrm{1}} \:+{c} \\ $$$$=−\frac{\mathrm{1}}{{x}}\:−\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} }\:\:+{c}\:. \\ $$