Question

求定积分在区间（正无穷~e）∫1/x(lnx)^p dx

Answer 1

∫[e,+∞]1/[x(lnx)^p] dx

= ∫[e,+∞](lnx)^(-p) dlnx

= 1/(lnx)^(p-1) * 1 / (-p+1)

= 0 - 1/(lne)^(p-1) * 1/(1-p)

= -1/(1-p)

= 1/(p-1)