Let \(f(x) = \frac{3 - 3x^2}{(2x + 1)(x + 2)^2}\).

(a) Express \(f(x)\) in partial fractions.

(b) Hence find the exact value of \(\int_0^4 f(x) \, dx\), giving your answer in the form \(a + b \ln c\), where \(a, b,\) and \(c\) are integers.