1.
$$\mathrm { f } ( x ) = \frac { 1 } { x ( 3 x - 1 ) ^ { 2 } } = \frac { A } { x } + \frac { B } { ( 3 x - 1 ) } + \frac { C } { ( 3 x - 1 ) ^ { 2 } }$$
- Find the values of the constants \(A , B\) and \(C\).
- Hence find \(\int \mathrm { f } ( x ) \mathrm { d } x\).
- Find \(\int _ { 1 } ^ { 2 } \mathrm { f } ( x ) \mathrm { d } x\), leaving your answer in the form \(a + \ln b\), where \(a\) and \(b\) are constants.
1
\(f ( x ) = \frac { 1 } { x ( 3 x - 1 ) ^ { 2 } } = \frac { A } { x } + \frac { } { ( 3 x }\)
- Find the values of the constants \(A , B\) and \(C\).