Question Number 186195 by normans last updated on 02/Feb/23
$$ \\ $$$$\:\:\:\:\underset{\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\:\:\frac{\mathrm{1}/\mathrm{2}\:\centerdot\left(\boldsymbol{{x}}^{\mathrm{2}} \right)\:}{\boldsymbol{{x}}\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} \:+\:\:\mathrm{2}}}\:\:\boldsymbol{{dx}}\:\:\:\: \\ $$
Answered by MJS_new last updated on 02/Feb/23
$$\mathrm{you}\:\mathrm{are}\:\mathrm{not}\:\mathrm{really}\:\mathrm{into}\:\mathrm{mathematics}? \\ $$$$\frac{\mathrm{1}/\mathrm{2}.\left({x}^{\mathrm{2}} \right)}{{x}\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}=\frac{{x}}{\mathrm{2}\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}} \\ $$$$\int\frac{{x}}{\mathrm{2}\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}{dx}=\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}{\mathrm{2}}+{C} \\ $$$$\mathrm{answer}\:\mathrm{is}\:\frac{\sqrt{\mathrm{6}}−\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$