4. (a) Given that \(y = \cot ^ { - 1 } x\), show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { - 1 } { x ^ { 2 } + 1 }\).
(b) Express \(\frac { 6 x ^ { 2 } - 10 x - 9 } { ( 2 x + 3 ) \left( x ^ { 2 } + 1 \right) }\) in terms of partial fractions.
(c) Hence find \(\int \frac { 6 x ^ { 2 } - 8 x - 6 } { ( 2 x + 3 ) \left( x ^ { 2 } + 1 \right) } \mathrm { d } x\).
(d) Explain why \(\int _ { - 2 } ^ { 5 } \frac { 6 x ^ { 2 } - 8 x - 6 } { ( 2 x + 3 ) \left( x ^ { 2 } + 1 \right) } \mathrm { d } x\) cannot be evaluated.