Integrate x^3 + 4x^2 + 9x + 14
.................x^2 + 4x + 3
The function can be decomposed in partial fractions as follows...
$\displaystyle f(x)= \frac{x^{3}+ 4\cdot x^{2} + 9\cdot x + 14}{x^{2} + 4\cdot x + 3}= x + \frac {6\cdot x + 14}{x^{2} + 4\cdot x + 3}= x + \frac{a}{x+3} + \frac{b}{x+1}$
The constants a and b are easily found, after that f(*) can be integrated in 'standard fashion'...
Kind regards
$\displaystyle \chi$ $\displaystyle \sigma$