Question Number 131053 by pipin last updated on 01/Feb/21
$$\int\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{x}^{\mathrm{4}} +\mathrm{4}}\mathrm{dx} \\ $$
Answered by Ar Brandon last updated on 01/Feb/21
$$\mathcal{I}=\int\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{x}^{\mathrm{4}} +\mathrm{4}}\mathrm{dx}=\int\frac{\mathrm{1}+\frac{\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }}{\left(\mathrm{x}−\frac{\mathrm{2}}{\mathrm{x}}\right)^{\mathrm{2}} +\mathrm{4}}\mathrm{dx} \\ $$$$\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{2}}{\mathrm{2x}}\right)+\mathcal{C} \\ $$
Commented by pipin last updated on 01/Feb/21
$$\mathrm{wow}\:,\:\mathrm{thank}\:\mathrm{you}\:\mathrm{bro} \\ $$