求积分∫xe^x/(x+1)^2dx解题步骤

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求积分∫xe^x/(x+1)^2dx解题步骤求积分∫xe^x/(x+1)^2dx解题步骤求积分∫xe^x/(x+1)^2dx解题步骤∫xe^x/(x+1)^2dx=∫xe^xd[-1/(x+1)]=x

求积分∫xe^x/(x+1)^2dx解题步骤
求积分∫xe^x/(x+1)^2dx解题步骤

求积分∫xe^x/(x+1)^2dx解题步骤
∫xe^x/(x+1)^2dx
=∫xe^xd[-1/(x+1)]
=xe^x·[-1/(x+1)] -∫-1/(x+1)d(xe^x)
=-xe^x/(x+1)+∫1/(x+1) ·(1+x)e^xdx
=-xe^x/(x+1)+e^x +C
=e^x/(x+1) +C
注:∫UdV+∫VdU=UV