- In this question you must show all stages of your working.
\section*{Solutions relying on calculator technology are not acceptable.}
- Use the substitution \(x = 2 \sin u\) to show that
$$\int _ { 0 } ^ { 1 } \frac { 3 x + 2 } { \left( 4 - x ^ { 2 } \right) ^ { \frac { 3 } { 2 } } } d x = \int _ { 0 } ^ { p } \left( \frac { 3 } { 2 } \operatorname { secutanu } + \frac { 1 } { 2 } \sec ^ { 2 } u \right) d u$$
where \(p\) is a constant to be found.
- Hence find the exact value of
$$\int _ { 0 } ^ { 1 } \frac { 3 x + 2 } { \left( 4 - x ^ { 2 } \right) ^ { \frac { 3 } { 2 } } } d x$$