求x趋向于无穷时的极限，怎么求？

Question

如题所述

Answer 1

∫ln[x+√(x^2+1)] dx
=x*ln[x+√(x^2+1)]-∫x dln[x+√(x^2+1)],分部积分法
=xln[x+√(x^2+1)]-∫x/√(x^2+1) dx
=xln[x+√(x^2+1)]-(1/2)∫1/√(x^2+1) d(x^2+1)
=xln[x+√(x^2+1)]-(1/2)*2√(x^2+1)+C
=xln[x+√(x^2+1)]-√(x^2+1)+C