- (a) Express as partial fractions
$$\frac { 2 x ^ { 2 } + 3 x + 6 } { ( x + 1 ) \left( x ^ { 2 } + 4 \right) }$$
(b) Hence, show that
$$\int _ { 0 } ^ { 2 } \frac { 2 x ^ { 2 } + 3 x + 6 } { ( x + 1 ) \left( x ^ { 2 } + 4 \right) } d x = \ln ( a \sqrt { 2 } ) + b \pi$$
where \(a\) and \(b\) are constants to be determined.