设t=√x,x=t^2,dx=2tdt,
原式=∫ arcsint *2tdt/t
=2∫ arcsint dt
=2[ tarcsint-∫ td(arcsint)]
=2[tarcsint-∫tdt/√(1-t^2)
=2[tarcsint+(1/2)∫ d(1-t^2)/√(1-t^2)]
=2[tarcsint+√(1-t^2)+C1]
=2√x arcsin√x+2√(1-x)+C.