6.
$$f ( x ) = \frac { 1 + 3 x } { ( 1 - x ) ( 1 - 3 x ) } , \quad | x | < \frac { 1 } { 3 }$$
- Find the values of the constants \(A\) and \(B\) such that
$$\mathrm { f } ( x ) = \frac { A } { 1 - x } + \frac { B } { 1 - 3 x }$$
- Evaluate
$$\int _ { 0 } ^ { \frac { 1 } { 4 } } f ( x ) d x$$
giving your answer as a single logarithm.
- Find the series expansion of \(\mathrm { f } ( x )\) in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\), simplifying each coefficient.