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 Q10  Integrate the functions  \frac{1}{x - \sqrt x } 

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Given function  \frac{1}{x - \sqrt x },

\int \frac{1}{x - \sqrt x } dx

Can be written in the form:

\frac{1}{x - \sqrt x } = \frac{1}{\sqrt {x}(\sqrt{x}-1)}

Assume the (\sqrt{x}-1) =t

\therefore \frac{1}{2\sqrt{x}}dx =dt

\Rightarrow \int \frac{1}{\sqrt{x}(\sqrt{x}-1)}dx = \int \frac{2}{t}dt

= 2\log|t| +C

= 2\log|\sqrt{x}-1| +C, where C is any constant value.

Posted by

Divya Prakash Singh

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