(a)[3]
Determine the quotient when $6x^3 - 5x^2 - 24x - 4$ is divided by $(2x + 1)$, and show that the remainder equals 6.
(b)[5]
Hence evaluate $\displaystyle \int_{2}^{7} \frac{6x^3 - 5x^2 - 24x - 4}{2x + 1}\,dx$, giving your answer in the form $a + b\ln b$, where $a$ and $b$ are integers.