令x＝tant,dx＝(sect)^2dt.x＝0时t＝0,x＝1时,t＝π/4,所以
∫(0,1) dx/√[(1+x^2)^3]
＝∫(0,π/4) cost dt
＝sin(π/4)
＝√2/2