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Integrate the rational functions(3x-1)/...

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

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To solve the integral of the rational function \(\frac{3x-1}{(x-1)(x-2)(x-3)}\), we will use the method of partial fractions. Here’s the step-by-step solution: ### Step 1: Set up the partial fraction decomposition We can express the integrand as: \[ \frac{3x-1}{(x-1)(x-2)(x-3)} = \frac{A}{x-1} + \frac{B}{x-2} + \frac{C}{x-3} \] where \(A\), \(B\), and \(C\) are constants to be determined. ...
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