Problem

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

$$\int_0^1\frac{3x+2}{(4-x^2)^{\frac32}}\,dx=\int_0^p\left(\frac32\sec u\tan u+\frac12\sec^2u\right)\,du$$

where $p$ is a constant to be found.

(b) Hence find the exact value of

$$\int_0^1\frac{3x+2}{(4-x^2)^{\frac32}}\,dx$$