Question Number 89311 by nimnim last updated on 16/Apr/20
$$\:\:{Show}\:{that} \\ $$$$\underset{\:\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\mathrm{1}} {\int}}\left\{\underset{\:\:\:\:\mathrm{0}} {\overset{\:\:\:\mathrm{1}} {\int}}\frac{{x}−{y}}{\left({x}+{y}\right)^{\mathrm{2}} }{dy}\right\}{dx}=\underset{\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\mathrm{1}} {\int}}\left\{\underset{\:\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\mathrm{1}} {\int}}\frac{{x}−{y}}{\left({x}+{y}\right)^{\mathrm{2}} }{dx}\right\}{dy} \\ $$$$ \\ $$