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Question Number 89362 by cindiaulia last updated on 17/Apr/20

$$\int \frac{1}{\sqrt{\mathrm{x}}{(\sqrt{\mathrm{x}}+1)}^3}$$

Commented by jagoll last updated on 17/Apr/20

$$u=1+\sqrt{x}\Rightarrow du=\frac{dx}{2\sqrt{x}}$$$$\int \frac{2du}{u^3}=\int 2u^{-3}du=-u^{-2}+c$$$$=-\frac{1}{{(\sqrt{x}+1)}^2}+c$$

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