1 It is given that \(\mathrm { f } ( x ) = \frac { 19 x - 2 } { ( 5 - x ) ( 1 + 6 x ) }\) can be expressed as \(\frac { A } { 5 - x } + \frac { B } { 1 + 6 x }\), where \(A\) and \(B\) are integers.
- Find the values of \(A\) and \(B\).
- Hence show that \(\int _ { 0 } ^ { 4 } \mathrm { f } ( x ) \mathrm { d } x = k \ln 5\), where \(k\) is a rational number.
[0pt]
[6 marks]