Partial Fraction Decomposition with Integration

1. The problem statement, all variables and given/known data



∫(2x³-4x-8)/(x²-x)(x²+4) dx





2. Relevant equations







3. The attempt at a solution



∫(2x³-4x-8)/x(x-1)(x²+4) dx

Next I left off the integral sign so I could do the partial fractions:



2x³-4x-8=(A/x)+(B/(x-1))+((Cx+D)/(x²+4))



2x³-4x-8=A(x³-x²+4x-4)+B(x³+4x)+(Cx+D)(x²-x)



2x³-4x-8=x³(A+B+C)-x²(A+C-D)+x(4A+4B-D)-4A



2=A+B+C



0=A+C-D



-4=4A+4B-D



-8=-A(4)

A=2



Did I set this up correctly? I'm not entirely sure how to solve for these variables.