1. The problem statement, all variables and given/known data Q. Solve ∫ (5x^2 - 42x + 24)/(x^3 - 10x^2 + 12x + 72) dx 2. Relevant equations ∫ x^n dx = ∫ (1/n+1)x^(n+1) + C ∫ 1/x dx = ln x + C 3. The attempt at a solution Hi everyone, Here's what I've done so far: (i) I factored the bottom equation into (x + 2)(x - 6)^2 and then separated the fraction 1/[(x + 2)(x - 6)^2] into a sum of three fractions of the form: A/(x + 2) + B/(x - 6) + C/[ (x-6)^2 ] and found that A = 1/64, B = -1/64, C = 1/8 (ii) The only way I can see to go from here is to split the top integral into three integrals: (1/64) ∫ (5x^2 - 42x + 24)/(x + 2) dx + (-1/64) ∫ (5x^2 - 42x + 24)/(x - 6) dx + (1/8) ∫ (5x^2 - 42x + 24)/(x-6)^2 dx and solve them all individually using substitution, letting u = x+2, x-6 and x-6 respectively. The answer I get in this way is: (5/8)x - 21/4 +2ln(x+2) + 3ln(x-6) + 6/(x-6) + C, C = constant of integration, which is incorrect, according to the WebWork site, but I can't find any algebraic errors. So, I'm thinking perhaps what I do in step (ii) is not the best way to do it. Has anyone any suggestions? Thanks for any help!