Solving the integral $\int \frac{2dx}{(x-2)(x-1)x}$

Question

$\int \frac{2dx}{(x-2)(x-1)x}$

Any help with how to solve this will be appreciated.

Answer 1

Partial fraction expansion

$$\frac{2}{(x-2)(x-1)x}=\frac{1}{x}-\frac{2}{x-1}+\frac{1}{x-2}$$

The rest is easy.