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(x)/((x-1)(x-2)(x-3))...

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

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To solve the integral \( I = \int \frac{x}{(x-1)(x-2)(x-3)} \, dx \), we will use the method of partial fractions. Here’s the step-by-step solution: ### Step 1: Set up the Partial Fraction Decomposition We express the integrand as a sum of partial 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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