令x=tany,则siny=x/√(x²+1),dx=sec²ydy
∫dx/[x²√(x²+1)]=∫sec²ydy/(tan²y*secy)
=∫cosydy/sin²y
=∫d(siny)/sin²y
=C-1/siny (C是积分常数)
=C-1/[x/√(x²+1)]
=C-√(x²+1)/x.