Ok, so the problem is take the indefinite integral of $\displaystyle x^4 / (x-1)^3$. The section the homework problem is in taught the Partial Fraction Decomposition method to rewrite an integral in a way that it can be integrated.

When I do it, I have $\displaystyle x^4 = A(x-1)^2 + B(x-1) + C$ so the only convenient x value is 1, so I was able to solve for c, because $\displaystyle c=1$, but if I use any X value per the rules to find the other two, well, I can't isolate one. For instance, I tried using $\displaystyle x=2$ which gave me $\displaystyle A + B = 15$ which doesn't help me much.

Any ideas on how to use PCD (or a more efficient method if there is one) to solve this integral? Thanks!