∫√（8-x²）dx=2√2×∫√（1-(x/√2)²）dx
令x/√2=sint(-∏/2≦t≦∏/2),则cost=x/√2 ,t=arcsin(x/√2) 则dx/√2=costdt,dx=√2costdt
2√2×∫√（1-(x/√2)²）dx=2√2×∫√（1-sin²t）√2costdt=4∫cos²tdt=4∫(cos2t+1)dt/2=2∫cos2tdt+4∫dt=sin2t+4t=2sint×cost+4t=x+4arcsin(x/√2)