$$ \int_0^1 \frac{\sin ^{-1} \sqrt{x}}{x^2-x+1} $$
What I have done is to substitute
$$ x=\sin ^2 \theta $$ After that:
$$ d x=2 \sin \theta \cos \theta d \theta $$
$$ \int \frac{2 \cdot \theta \cdot \sin \theta \cdot \cos \theta}{\sin ^4 \theta-\sin ^2 \theta+1} d\theta $$
But I think that the process is bit lengthy.
Is there any other way to integrate the expression or proceed with the above integral ?
Thanks in advance.
