Question:
$\frac{1}{x-\sqrt{x}}$
Solution:
$\frac{1}{x-\sqrt{x}}=\frac{1}{\sqrt{x}(\sqrt{x}-1)}$
Let $(\sqrt{x}-1)=t$
$\therefore \frac{1}{2 \sqrt{x}} d x=d t$
$\Rightarrow \int \frac{1}{\sqrt{x}(\sqrt{x}-1)} d x=\int \frac{2}{t} d t$
$=2 \log |t|+\mathrm{C}$
$=2 \log |\sqrt{x}-1|+\mathrm{C}$
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