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

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