上限是e,下限是1的lnx/x的三次方的定积分

Question

求过程，急啊
用分部积分法求

Answer 1

∫(1,e)lnx/x^3*dx
=(-1/2)∫(1,e)lnxd(1/x^2)
=(-1/2)lnx/x^2|(1,e)+(1/2)∫(1,e)(1/x^2)dlnx
=-1/(2e^2)+(1/2)∫(1,e)(1/x^3)dx
=-1/(2e^2)+(-1/4)(1/x^2)|(1,e)
=-3/(4e^2)+1/4