Question
Evaluate:$$\int_{2}^{\infty} \frac{d x}{x(x-1)^{2}}$$
Step 1
The integrand can be written as: $$ \frac{1}{x(x-1)^{2}} = \frac{A}{x} + \frac{B}{x-1} + \frac{C}{(x-1)^2} $$ By comparing coefficients, we find that $A = -1$, $B = 1$, and $C = 1$. Show more…
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