1. The problem statement, all variables and given/known data [tex]\int[/tex](3x3-4x2-3x+2)/(x4-x2) 2. Relevant equations P(x)/Q(x)=A1/(x-r1)+A2/(x-r2)+... if x-r occurs with multiplicity m, then A/(x-r) must be replaced by a sum of the form: B1/(x-r)+B2/(x-r)2+... I think this second equation is the source of my confusion. 3. The attempt at a solution I began by factoring the denominator: x4-x2 = x2(x+1)(x-1) So, according to my book, we have the following constants: A/x + B/x2 + C/(x+1) + D/(x-1) First question: where did the x come from in the constant A/x? Does this follow from the rule above? That is, because x2 has multiplicity 2, I get A/x and B/x2? Next, according to my book, when you clear the fractions, you should get: Ax(x+1)(x-1) + B(x+1)(x-1) + Cx2(x-1) + Dx2(x+1) I don't understand this. Why isn't it Ax2(x+1)(x-1) + Bx(x+1)(x-1) + Cx3(x-1) + Dx3(x+1)? Can someone explain? Many thanks.