Question Number 136267 by Algoritm last updated on 20/Mar/21
Commented by liberty last updated on 20/Mar/21
$$\int_{{e}} ^{\:{e}^{\mathrm{2}} } \sqrt{{x}+\frac{\mathrm{1}}{\mathrm{2}}\sqrt{{x}+\frac{\mathrm{1}}{\mathrm{4}}\sqrt{{x}+\frac{\mathrm{1}}{\mathrm{8}}\sqrt{…}}}}\:−\sqrt{{x}−\frac{\mathrm{1}}{\mathrm{2}}\sqrt{{x}−\frac{\mathrm{1}}{\mathrm{4}}\sqrt{{x}−\frac{\mathrm{1}}{\mathrm{8}}\sqrt{…}}}}\:{dx} \\ $$