∫(0,ln2) xe^(-x)dx
=∫(0,ln2)(-x)e^(-x)d(-x)
=∫(0,ln2)(-x)d(e^(-x))
=(-x)e^(-x)|(0,ln2)-∫(0,ln2)e^(-x)d(-x)
=-(1/2)*ln2-e^(-x)|(0,ln2)
=-(1/2)*ln2-(1/2-1)
=-(1/2)*ln2+(1/2)
=(1-ln2)/2
用到分部积分法
有不懂欢迎追问