Integrate the rational functions`x/((x-1)(x-2)(x-3)`

Explanation

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

### Step 1: Set Up Partial Fraction Decomposition
We start by expressing the function \(\frac{x}{(x-1)(x-2)(x-3)}\) as a sum of simpler fractions:
\[ \frac{x}{(x-1)(x-2)(x-3)} = \frac{A}{x-1} + \frac{B}{x-2} + \frac{C}{x-3} \]
where \(A\), \(B\), and \(C\) are constants to be determined.
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