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1-1-1-x-2-1-x-2-1-1-x-2-y-2-1-1-y-2-x-2-y-2-z-2-5-2-dx-dy-dz-is-




Question Number 199369 by universe last updated on 02/Nov/23
∫_(−1) ^1  ∫_(−(√(1−x^2  ))) ^(√(1−x^2 ))  ∫_(1−(√(1−x^2 −y^2 ))) ^(1+(√(1−y^2 ))) (x^2 +y^2 +z^2 )^(5/2) dx dy dz  is
$$\int_{−\mathrm{1}} ^{\mathrm{1}} \:\int_{−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} \:}} ^{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }} \:\int_{\mathrm{1}−\sqrt{\mathrm{1}−{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }} ^{\mathrm{1}+\sqrt{\mathrm{1}−{y}^{\mathrm{2}} }} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)^{\mathrm{5}/\mathrm{2}} {dx}\:{dy}\:{dz}\:\:{is} \\ $$

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