Chapter 7 - Principles Of Integral Evaluation - 7.5 Integrating Rational Functions By Partial Fractions - Exercises Set 7.5 - Page 521: 6

$$\frac{A}{{x - 1}} + \frac{{Bx + C}}{{{x^2} + 6}}$$

$$\eqalign{ & \frac{{3x}}{{\left( {x - 1} \right)\left( {{x^2} + 6} \right)}} \cr & x - 1{\text{ is a linear factor}}{\text{, so its decomposition is }}\frac{A}{{x - 1}} \cr & {x^2} {\text{ is a quadratic factor, so the numerator for its decomposition is }} \cr & {\text{a linear factor}}{\text{. Then}}{\text{,}} \cr & \frac{{3x}}{{\left( {x - 1} \right)\left( {{x^2} + 6} \right)}} = \frac{A}{{x - 1}} + \frac{{Bx + C}}{{{x^2} + 6}} \cr} $$