Question

Integrate the function $\frac{1}{x-\sqrt{x}}$

Answer 1

$\frac{1}{x-\sqrt{x}}=\frac{1}{\sqrt{x}(\sqrt{x}-1)}$
Put $(\sqrt{x}-1)=t$
$\Rightarrow \frac{1}{2\sqrt{x}}dx=dt$
$=\int \frac{1}{\sqrt{x}(\sqrt{x}-1)}dx=\int \frac{2}{t}dt$
$=2\log |t|+C=2\log |\sqrt{x}-1|+C$