\(\displaystyle \int1/\sqrt{(1-x^2)*\arcsin(x)}\)

I think I need to use integration by substitution, so have rearranged to give:

\(\displaystyle \int(1-x^2)^{\-1/2} * (sin(x))^{1/2}\)

I am not quite sure what to do next. The formula I have for integration by substitution is:

\(\displaystyle \int{f(g(x))g'(x)dx} = \int{f(u)du}\), where u = g(x)

Would I then get

f(x) = \(\displaystyle (1-x^2)^{\-1/2}\)

and

g(x) = \(\displaystyle (sin(x))^{1/2}\), so u = -cosx

or do I need to integrate both parts first as they are both composite integrals and then use the above formula on the answers I get? (Headbang)

Thanks for any help in advence