Solution:

(a) A=2, B=-5, C=0

(b) 2x/(x^{2}+3)

(c) ln(2x-1) – (5/2)ln(x^{2}+3) + C

(a)6 + 5x – 8x^{2} = A(x^{2} + 3) + (Bx + c)(2x – 1)

Sub x = ½

6 + 5/2 – 8(1/2)^{2} = A(1/4 + 3) + 0

13/2 = (13/4)A —— A=2

When x=0, 6 = 2(3) + c(-1) —— C=0

Compare coefficients of x^{2}

-8 = A + 2B

-10 – 2B —— B = -5

(b)d/dx[ln(x^{2}+3)] = 2x/(x^{2}+3)

=2x/(x^{2}+3)

(c)∫ 2/(2x-1) + ∫(-5x)/(x^{2}+3)

=ln(2x-1) – (5/2)ln(x^{2}+3) + C