- (a) Express \(\frac { 9 ( 4 + x ) } { 16 - 9 x ^ { 2 } }\) in partial fractions.
Given that
$$\mathrm { f } ( x ) = \frac { 9 ( 4 + x ) } { 16 - 9 x ^ { 2 } } , \quad x \in \mathbb { R } , \quad - \frac { 4 } { 3 } < x < \frac { 4 } { 3 }$$
(b) express \(\int \mathrm { f } ( x ) \mathrm { d } x\) in the form \(\ln ( \mathrm { g } ( x ) )\), where \(\mathrm { g } ( x )\) is a rational function.