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Question Number 122823 by bemath last updated on 19/Nov/20

Answered by liberty last updated on 19/Nov/20

$$L\left(x\right)=\int \frac{1}{\sqrt{x(1+\sqrt{x})}}dx=\int \frac{1}{\sqrt{x}\sqrt{1+\sqrt{x}}}dx$$$$letu=1+\sqrt{x}\Rightarrow du=\frac{dx}{2\sqrt{x}}$$$$L\left(x\right)=2\int \frac{1}{\sqrt{u}}du=4\sqrt{u}+c$$$$L\left(x\right)=4\sqrt{1+\sqrt{x}}+c$$

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