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(1)/(x(x-1))...

`(1)/(x(x-1))`

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To solve the integral \(\int \frac{1}{x(x-1)} \, dx\), we will use the method of partial fractions. Here’s a step-by-step solution: ### Step 1: Set up the partial fraction decomposition We want to express \(\frac{1}{x(x-1)}\) as a sum of simpler fractions: \[ \frac{1}{x(x-1)} = \frac{A}{x} + \frac{B}{x-1} \] where \(A\) and \(B\) are constants to be determined. ...
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