Question Number 164231 by Zaynal last updated on 15/Jan/22
![∫_(−∞) ^∞ −(1/3) ∫_0 ^1 ((((^4 log 3.^4 log 6)/( ^4 log 9.^8 log 2+^4 log 9.^8 log 3))/((^9 log 4.^2 log27+^3 log 81)/(^2 log 64−^2 log 8))))dxdy {z.}](https://www.tinkutara.com/question/Q164231.png)
$$\int_{−\infty} ^{\infty} \:−\frac{\mathrm{1}}{\mathrm{3}}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\left(\frac{\frac{\:^{\mathrm{4}} \boldsymbol{\mathrm{log}}\:\mathrm{3}.^{\mathrm{4}} \boldsymbol{\mathrm{log}}\:\mathrm{6}}{\:\:^{\mathrm{4}} \boldsymbol{\mathrm{log}}\:\mathrm{9}.^{\mathrm{8}} \boldsymbol{\mathrm{log}}\:\mathrm{2}+\:^{\mathrm{4}} \boldsymbol{\mathrm{log}}\:\mathrm{9}.^{\mathrm{8}} \boldsymbol{\mathrm{log}}\:\mathrm{3}}}{\frac{\:^{\mathrm{9}} \boldsymbol{\mathrm{log}}\:\mathrm{4}.^{\mathrm{2}} \boldsymbol{\mathrm{log}}\mathrm{27}+^{\mathrm{3}} \boldsymbol{\mathrm{log}}\:\mathrm{81}}{\:^{\mathrm{2}} \boldsymbol{\mathrm{log}}\:\mathrm{64}−^{\mathrm{2}} \boldsymbol{\mathrm{log}}\:\mathrm{8}}}\right)\boldsymbol{\mathrm{dxdy}} \\ $$$$\left\{\boldsymbol{\mathrm{z}}.\right\} \\ $$