Given the rational function $f(x) = \frac{8x^2 - 5x - 27}{x^3 - 2x^2 - 5x + 6}$
a) Find the roots a, b and c of the denominator (write them in increasing order)
a =
b =
c =
b) Find the coefficients A, B and C in the decomposition in partial fractions:
$f(x) = \frac{A}{x - a} + \frac{B}{x - b} + \frac{C}{x - c}$
A =
B =
C =
b) Evaluate $\int \frac{8x^2 - 5x - 27}{x^3 - 2x^2 - 5x + 6} dx$
+ C