Could someone please help me evaluate this integral? The integral is
$$
\int_{0}^{1/\sqrt{\vphantom{\large A}2\,}}
{\arccos\left(x\right) \over \sqrt{\vphantom{\large A}1 -x^2\,}\,}\;{\rm d}x 
$$
I was just wondering if I could use substitution to solve this problem or if I had to solve it a different way.

Integrate direct:
$$u=\arccos x \Rightarrow du=-\frac{dx}{\sqrt{1-x^2}}.$$
Then
$$\int \frac{\arccos x}{\sqrt{1-x^2}}dx=- \int \arccos x\cdot(-\frac{dx}{\sqrt{1-x^2}})=$$
$$=-\frac{1}{2}(\arccos x)^2 +c,$$
so,
$$\int_0^{\frac{1}{\sqrt{2}}} \frac{\arccos x}{\sqrt{1-x^2}}dx =-\frac{1}{2}(\frac{\pi}{4})^2+\frac{1}{2}(\frac{\pi}{2})^2=\cdots=\frac{3\pi^2}{32}.$$
