Find the following integral (using partial fraction method)
`int (3x)/((x-1)(x-2)) dx`

Explanation

To solve the integral \(\int \frac{3x}{(x-1)(x-2)} \, dx\) using the method of partial fractions, we will follow these steps:

### Step 1: Set up the partial fraction decomposition
We want to express the integrand \(\frac{3x}{(x-1)(x-2)}\) in the form:
\[ \frac{A}{x-1} + \frac{B}{x-2} \]
where \(A\) and \(B\) are constants to be determined.
...