The integrand is a rational function and can be expressed as the sum of simpler fractions. We have:
$$
\frac{1}{x(x-1)} = \frac{A}{x} + \frac{B}{x-1}
$$
Multiplying through by the common denominator $x(x-1)$ gives:
$$
1 = A(x-1) + Bx
$$
Setting $x = 1$ gives
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