I would like to know if anyone has an idea what the best way to find the constants A, B, C, D, and E is. Can this be solved/written using a Matrix?
x can be chosen arbitrarily to find the constants A, B, C, D and E.
x4 - 5x3 - 30x2 - 36x = A*(x+1)2(x-2)(x+2)+B(x+1)(x-2)(x+2)+C*(x-2)(x+2)+D(x+1)3(x+2)+E(x+1)3*(x-2)
I know that the most efficient way is to chose x as -1, 2 and -2, so that the maximum amount of summands equal zero. Can this be solved faster, if we somehow write this as a Matrix and apply gaussian elimination?
This is part of solving an integral via partial fractions.