Evaluate: ∫10 xsin⁻¹x√1-x²dx

I = ∫ xsin⁻¹x√1-x²dx
Let t = sin⁻¹x ⇒ dt = dx/√1-x² ⇒ I = ∫ tsin t dt = t∫ sin t dt − ∫ (dt/dt)(∫ sin t dt)dt = −tcos t + ∫ cos t dt = −tcos t + sin t + c
∴I = −tcos t + sin t + c
I = −sin⁻¹xcos(sin⁻¹x) + sin(sin⁻¹x) + c