Integrate $\int \frac{\arccos\frac{x}{2}}{\sqrt{(4-x^2)}}$

Question

I need suggestions on how to integrate this integral:

$$\int \frac{\arccos\frac{x}{2}}{\sqrt{(4-x^2)}}dx$$

I tried putting $\arccos$ or $\sqrt{4-x^2}$ into the differential, but that gave me nothing. Any ideas? Thanks.

Answer 1

HINT:

Let $\arccos\dfrac x2= y\implies dy=-\dfrac1{\sqrt{1-(x/2)^2}}\dfrac{dx}2=-\dfrac{dx}{\sqrt{4-x^2}}$