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Question Number 186195 by normans last updated on 02/Feb/23

      ∫_1 ^2    ((1/2 ∙(x^2 ) )/(x (√(x^2  +  2))))  dx

$$ \\ $$$$\:\:\:\:\underset{\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\:\:\frac{\mathrm{1}/\mathrm{2}\:\centerdot\left(\boldsymbol{{x}}^{\mathrm{2}} \right)\:}{\boldsymbol{{x}}\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} \:+\:\:\mathrm{2}}}\:\:\boldsymbol{{dx}}\:\:\:\: \\ $$

Answered by MJS_new last updated on 02/Feb/23

you are not really into mathematics?  ((1/2.(x^2 ))/(x(√(x^2 +2))))=(x/(2(√(x^2 +2))))  ∫(x/(2(√(x^2 +2))))dx=((√(x^2 +2))/2)+C  answer is (((√6)−(√3))/2)

$$\mathrm{you}\:\mathrm{are}\:\mathrm{not}\:\mathrm{really}\:\mathrm{into}\:\mathrm{mathematics}? \\ $$$$\frac{\mathrm{1}/\mathrm{2}.\left({x}^{\mathrm{2}} \right)}{{x}\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}=\frac{{x}}{\mathrm{2}\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}} \\ $$$$\int\frac{{x}}{\mathrm{2}\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}{dx}=\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}{\mathrm{2}}+{C} \\ $$$$\mathrm{answer}\:\mathrm{is}\:\frac{\sqrt{\mathrm{6}}−\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$

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