(a)[3]
Determine the quotient when $9x^3 - 6x^2 - 20x + 1$ is divided by $(3x + 2)$, and show that the remainder is $9$.
(b)[5]
Hence calculate $\int_1^6 \frac{9x^3 - 6x^2 - 20x + 1}{3x + 2} \, dx$, expressing the answer in the form $a + b \ln b$ where $a$ and $b$ are integers.
(c)[4]
Determine the exact root of the equation $9e^{9y} - 6e^{6y} - 20e^{3y} - 8 = 0$.