求定積分在區間(正無窮~e)∫1/x(lnx)^p dx

求定積分在區間(正無窮~e)∫1/x(lnx)^p dx

∫[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)