Evaluating $\int x\sin^{-1}x dx$ I was integrating $$\int x\sin^{-1}x dx.$$
After applying integration by parts and some rearrangement  I  got stuck at $$\int \sqrt{1-x^2}dx.$$
Now I have two questions:


*

*Please, suggest any further approach from where I have stuck;


*Please, provide an alternative way to solve the original question.

Please help!!!

Alternative way: Let $x=\sin t$ so 
$$\int x\sin^{-1}x dx=\int t\sin t\cos t dt$$
by parts $t=u$ and $\sin t\cos t dt=dv$ and finish it!
