8 An appropriate form for expressing \(\frac { 3 x } { ( x + 1 ) ( x - 2 ) }\) in partial fractions is
$$\frac { A } { x + 1 } + \frac { B } { x - 2 }$$
where \(A\) and \(B\) are constants.
- Without evaluating any constants, state appropriate forms for expressing the following in partial fractions:
- \(\frac { 4 x } { ( x + 4 ) \left( x ^ { 2 } + 3 \right) }\),
- \(\frac { 2 x + 1 } { ( x - 2 ) ( x + 2 ) ^ { 2 } }\).
- Show that \(\int _ { 3 } ^ { 4 } \frac { 3 x } { ( x + 1 ) ( x - 2 ) } \mathrm { d } x = \ln 5\).