Question Number 220904 by Nicholas666 last updated on 20/May/25
![∫∫∫_([0,1]^3 ) ((x^4 y^3 z^2 )/((x+y+z)(x^2 +y^2 +z^2 )−(x^3 +y^3 +z^3 ))) dxdydz](https://www.tinkutara.com/question/Q220904.png)
$$ \\ $$$$\:\:\int\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{3}} } \frac{{x}^{\mathrm{4}} {y}^{\mathrm{3}} {z}^{\mathrm{2}} }{\left({x}+{y}+{z}\right)\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)−\left({x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} \right)}\:{dxdydz}\:\:\:\:\:\:\: \\ $$$$\: \\ $$