You didn't multiply by did you?.
Cancel appropriately, expand out, and we get:
Solve the system and we get:
So, we get:
I'm not certain why but I can't seem to get the right answer no matter how many times I run through this
Integrate (x^2) / ((x - 3)(x + 2)^2)
(A / x - 3) + (B / x + 2) + (C / (x + 2)^2)
My values for A and C seem correct from the method I was taught by the professor
A = 9 / 25 C = - 4 / 5
Now to get B, I equated for cubics.
x^2 = ((9/25)(x + 2)^3) + B(x - 3)(x + 2)^2 - (4/5)(x - 3)(x + 2)
Now the B I got was - 9 / 25.
Can someone tell me if I've done this right so far? Thanks