(a)[3]
Find the quotient and remainder after dividing $18x^3 - 6x^2 - 30x + 4$ by $(3x - 1)$.
(b)[5]
Hence, find $\displaystyle \int_{1}^{5} \frac{18x^3 - 6x^2 - 30x + 4}{3x - 1}\,dx$ and express your answer as $a - \ln b$, where $a$ and $b$ are integers.