(3) (a) The form of the partial fraction decomposition of a rational function is given below. 5x - 5x2 - 65 A Bx + C (z - 4)(x2 +9) x-4 x2 + 9 A =B=0c=0 Now evaluate the indefinite integral. 5x - 5x2 - 65 (2 - 4) (202 + 9) da = (b) Consider the following indefinite integral. 6x3 + 3x2 - 45x - 24 x2 - 9 The integrand decomposes into the form: C ax + b+ - x - 3 x+ 3 Compute the coefficients: a = b = C = d = Now integrate term by term to evaluate the integral. Answer: + C