In integrating $\dfrac{3t^4+2t^2}{(t-1)^3 (t+1)^3}$ I need to decompose this using partial fraction decomposition.
Using Heaviside cover-up method, I am able to easily get the coefficients of $C = \frac58$ and $F = -\frac58$.
$$\frac{3t^4+2t^2}{ (t-1)^3(t+1)^3 } = \frac{A}{t-1} + \frac{B}{(t-1)^2} + \frac{C}{(t-1)^3} + \frac{D}{t+1} + \frac{E}{(t+1)^2} + \frac{F}{(t+1)^3}.$$
I can also get an equation $0 = A + D$ multiplying by $t$ and sending them to infinity.
What would be the fastest and most efficient way of obtaining the rest, $A$, $B$, $D$ and $E$?
Thanks :)