Chapter 8: Techniques of Integration - Section 8.1 - Using Basic Integration Formulas - Exercises 8.1 - Page 448: 6

$2 \ln|\sqrt {x}-1|+C$

$\int \frac{dx}{x-\sqrt x}=\int\frac{dx}{\sqrt x(\sqrt x-1)}$ Put $t= \sqrt {x}-1$ Then $dx= 2\sqrt x dt$ Therefore, $\int \frac{dx}{x-\sqrt x}= 2\int \frac{1}{t}dt$ $= 2\times\ln|t|+C= 2 \ln|\sqrt {x}-1|+C$