Find the following indefinite integral, identifying any rules of calculus that you use:

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

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?

Thanks for any help in advence