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integral (3x^2-8x+13)/(x^3+x^2-5x+3)

Factor for the denom is (x-1)(x-1)(x+3). So a/(x-1) + b/(x-1)^2 + c/(x+3) = the f(x) in the integral

Factor out and multiply all the polynomials. Comes down to a = -1, b = -2, c = 2

Integral comes to:

2/(x-1)+ln|(x+3)/(x-1)|+k