原式=∫(sect)^2dt/((tant)^4sect) (令x=tant,则sint=x/√(x^2+1))=∫(1-(sint)^2)d(sint)/(sint)^4=1/sint-(1/3)/(sint)^3+C (C是积分常数)=√(x^2+1))/x-(1/3)(√(x^2+1))/x)^3+C.