15\textit{x}^2 - 35\textit{x} + 25
Let \(f(x) = \frac{15x^2 - 35x + 25}{(x - 1)(x - 2)^2}\). The partial fraction decomposition of \(f(x) = \frac{A}{(x - 1)} + \frac{B}{(x - 2)} + \frac{C}{(x - 2)^2}\), where \(A, B, C \in \mathbb{Z}\).
Work out the values of A, B and C.
A =
B =
C =
Use the partial fraction decomposition of \(f(x)\) to work out \(\int f(x) \, dx\). Write your answer in the form
\(5 \ln|x - 1| + T \ln|x - 2| + U(x - 2)^{-1} + C\) where C is the constant of integration
T =
U =
V =