∫ dx/[x^2√(1+x^2)]换元,x=tant=∫ d(tant)/[tan^2t√(1+tan^2)]=∫ (dt/cos^2t) / [tan^2t/cost]=∫ dt / cost*tan^2t=∫ cost/sin^2t dt=∫ 1/sin^2t d(sint)=-1/sint + C因为x=tant即：1/x^2=cot^2t再即：1+1/x...