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Question Number 105951 by Study last updated on 01/Aug/20

Answered by Dwaipayan Shikari last updated on 01/Aug/20

$$\sqrt{\frac{x}{\sqrt{\frac{x}{\frac{x}{}...}}}}=p$$$$\sqrt{\frac{x}{p}}=p$$$$p=\sqrt[3]{x}$$$$\int pdx=\int x^{\frac{1}{3}}dx=\frac{3}{4}{x}^{\frac{4}{3}}+C$$

Commented by malwaan last updated on 02/Aug/20

$$\sqrt{x}=\sqrt{\frac{x}{\sqrt{\frac{x}{.}}}}$$$$isthisright?$$

Commented by Her_Majesty last updated on 03/Aug/20

$$yes$$

Answered by Her_Majesty last updated on 01/Aug/20

$$y=\sqrt{\frac{x}{\sqrt{\frac{x}{...}}}}$$$$\Rightarrow$$$$y^2=\frac{x}{y}$$$$\Rightarrow$$$$y=x^{\frac{1}{3}}$$$$\int x^{\frac{1}{3}}dx=\frac{3}{4}{x}^{\frac{4}{3}}+C$$

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