Question

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

Answer 1

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

Let ($\sqrt x$-1) = t

∴ $\frac{1}{2\sqrt x}$ dx = dt

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

=2log|t|+C

= 2log|$\sqrt x$-1|+C