I don't remember what this method is named in English, but I want to write the fraction in the form I multiply A with (s-3)(s+2), B with (s^2 + 1)(s+2) and C with (s^2 + 1)(s-3), to get and the equations (1) B + C = 0 (2) A + 2B - 3C = 0 (3) -A + B + C = 0 (4) -6A + 2B - 3C = 1 (1) and (3) gives A = 0 (2) then gives B = C = 0 This is obviously wrong. The correct answer is A = 2s - 4 B = 2 C = -4 according to my book. There must be something I don't understand here...
The general is partial fractions, I think this is called partial fractions with repeated and quadratic roots.