# How do you integrate #int (x-5) / (x^2(x+1))# using partial fractions?

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To integrate (\int \frac{x-5}{x^2(x+1)} , dx) using partial fractions, first, express the integrand as the sum of two fractions with unknown constants:

[\frac{x-5}{x^2(x+1)} = \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x+1}]

Then, clear the fractions by multiplying both sides by the common denominator (x^2(x+1)). Afterward, equate coefficients of like terms to find the values of (A), (B), and (C). Finally, integrate each term separately.

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