`int(3x-1)/((x-1)(x-2)(x-3))dx`

Explanation

To solve the integral \( \int \frac{3x - 1}{(x - 1)(x - 2)(x - 3)} \, dx \), we will use the method of partial fractions. Here’s a step-by-step solution:

### Step 1: Set up the partial fraction decomposition
We start by expressing the integrand as a sum of partial fractions:
\[ \frac{3x - 1}{(x - 1)(x - 2)(x - 3)} = \frac{A}{x - 1} + \frac{B}{x - 2} + \frac{C}{x - 3} \]
where \( A \), \( B \), and \( C \) are constants to be determined.
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