The rational function 89 x (4 x + 9) (9x -2) can be decomposed into partial fractions: 89 x A B + (4 x + 9) (9x-2) 4x + 9 9x - 2 Hence 89 x = A(9: - 2) + B(4x + 9). We can find A and B from this equation. One way is to expand this equation and equate coefficients of a - and a to get two linear equations. Another way is to observe that: . when c = we see that A = . when = we see that B = This partial fraction decomposition allows us to integrate the original function as 89 x 1 1 I = da = A dx + B dx. (4x +9) (9x-2) 4x + 9 9x - 2 So I = OF +C