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Category: Integration

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-

Question Number 220904 by Nicholas666 last updated on 20/May/25 $$ \\ $$$$\:\:\int\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{3}} } \frac{{x}^{\mathrm{4}} {y}^{\mathrm{3}} {z}^{\mathrm{2}} }{\left({x}+{y}+{z}\right)\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \right)−\left({x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} \right)}\:{dxdydz}\:\:\:\:\:\:\: \\ $$$$\:…

0-1-3-1-1-x-1-y-1-z-1-xyz-dxdydz-

Question Number 220898 by Nicholas666 last updated on 20/May/25 $$ \\ $$$$\:\:\:\int\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\:\mathrm{3}} \:\:} \frac{\mathrm{1}}{\:\sqrt{\left(\mathrm{1}\:−{x}\right)\left(\mathrm{1}\:−\:{y}\right)\left(\mathrm{1}\:−{z}\right)\left(\mathrm{1}\:−\:{xyz}\right)}}\:{dxdydz}\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

x-2-y-2-z-2-1-1-1-x-2-y-2-z-2-2-dxdydz-

Question Number 220892 by Nicholas666 last updated on 20/May/25 $$ \\ $$$$\:\:\:\:\int\int\int_{\boldsymbol{{x}}^{\mathrm{2}} \:+\:\boldsymbol{{y}}^{\mathrm{2}} \:+\:\boldsymbol{{z}}^{\mathrm{2}} \:\:\leqslant\:\mathrm{1}} \:\frac{\mathrm{1}}{\left(\mathrm{1}\:+\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+\:{z}^{\mathrm{2}} \right)^{\mathrm{2}} }\:{dxdydz}\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Answered…

0-1-3-ln-1-xyz-1-x-1-y-1-z-dxdydz-

Question Number 220895 by Nicholas666 last updated on 20/May/25 $$ \\ $$$$\:\:\:\int\int\int_{\left[\mathrm{0},\mathrm{1}\right]^{\mathrm{3}} } \frac{{ln}\:\left(\mathrm{1}\:+\:{xyz}\right)}{\left(\mathrm{1}\:+\:{x}\right)\left(\mathrm{1}\:+\:{y}\right)\left(\mathrm{1}\:+\:{z}\right)}\:{dxdydz}\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com