Find \int \frac{7x^2+31x+54}{(x+1)(x^2+6x+11)}dx using partial fractions decomposition. Hint: one of the factors of the denominator is an irreducible quadratic and this we put use a linear expression (one degree less) as its numerator. In other words:

\frac{7x^2+31x+54}{(x+1)(x^2+6x+11)} = \frac{A}{x+1}+\frac{Bx+C}{x^2+6x+11}

Your job, should you choose to do it is to find A, B and C and then find the integral.