I've been trying to calculating the following integral$\displaystyle \int xsin^{-1}(x)\, dx$

Here's my solution as far as I've been able to calculate. Let$\displaystyle U=sin^{-1}x \Rightarrow dU=\frac{1}{\sqrt{1-x^2}}dx$

$\displaystyle dV = x \cdot dx \Rightarrow V = \frac{x^2}{2}$

Then

$\displaystyle I=VU-\int V\cdot du=sin^{-1}x \cdot \frac{x^2}{2} -\int \frac{x^2}{2}\cdot \frac{1}{\sqrt{1-x^2}}dx$

I get stuck here, using U and V for new functions and using the relationship again doesn't lead me anywhere.