i need to find the integral of: sin^-1 (x^1/2) what substituion should i use and what identity do i need to use to do this?
There are always various ways to tackle these, but you could try parts.
$\displaystyle \int{sin^{-1}(\sqrt{x})}dx$
Let $\displaystyle u=sin^{-1}(\sqrt{x})dx, \;\ dv=dx, \;\ du=\frac{1}{2\sqrt{x(1-x)}}dx, \;\ v=x$
This leads to:
$\displaystyle xsin^{-1}(\sqrt{x})+\int\sqrt{1-u^{2}}du$
Now, continue?.