Question Number 86254 by sakeefhasan05@gmail.com last updated on 27/Mar/20
$$\int\:\sqrt{\mathrm{x}\sqrt{\mathrm{x}\sqrt{\mathrm{x}\sqrt{\mathrm{x}…….}}}}\:\:\:\mathrm{dx} \\ $$
Answered by TANMAY PANACEA. last updated on 27/Mar/20
$${y}=\sqrt{{x}\sqrt{{x}\sqrt{{x}\sqrt{{x}…\infty}\:\:\:}}} \\ $$$${y}=\sqrt{{xy}}\: \\ $$$${y}^{\mathrm{2}} ={xy} \\ $$$${y}={x} \\ $$$${so} \\ $$$$\int{xdx}=\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+{c} \\ $$
Commented by sakeefhasan05@gmail.com last updated on 27/Mar/20
$$\mathrm{thank}\:\mathrm{u}\:\mathrm{very}\:\mathrm{much} \\ $$
Commented by peter frank last updated on 29/Mar/20
$${thank}\:{you} \\ $$