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x-x-x-x-dx-




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

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