∫(arcsin√x)/√(x-x^2)dxt=√x x=t^2=∫(arcsint)/(t^2-t^4)^0.5dt^2=2∫(arcsint)/(1-t^2)^0.5dtt=sinuu=arcsint=2∫u/(1-sin^2u)^0.5dsinu=2∫ucosu/cosudu=2∫udu=u^2+C=arcsin^2t+C=arcsin^2(√x)+C...