(a) Express \(f(x)\) in the form \(\frac{A}{3-x} + \frac{Bx+C}{1+3x^2}\).

Equate coefficients to find \(A = 2\), \(B = 0\), and \(C = 1\).

(b) Integrate to obtain \(-2 \ln(3-x)\) and \(\frac{1}{\sqrt{3}} \arctan(\sqrt{3}x)\).

Substitute limits to find \(2 \ln \frac{3}{2} + \frac{1}{\sqrt{3}} \pi\).