[1/(x^4 - x)]dx
The Attempt at a Solution
I factored the denominator to x(x-1)(x^2 + x +1) and I'm not sure if I can use partial fractions.
You're doing something wrong. Just write the whole polynomial in y and equal it to 1. You should get a system of 4 equations with 4 unknowns which is very easy to solve.
Out of curiosity, why did you switch from x that was used in your integral to y here?So I set
1/[y(y-1)(y^2+y+1)] = A/y + B/(y-1) + (Cy+D)/(y^2+y+1)
1 = (y-1)(y^2+y+1)A + y(y^2+y+1)B + y(y-1)(Cy+D)
y = 0, A = -1
y = 1, B = 1/3
Not sure what to do for C and D