Integrate[Exp[I x]/x/(1-I x)^2,x]

(%/.x->w)-(%/.x->w/Dr)+Exp[I w](1/(1-I w/Dr)-1/(1-I w))//FullSimplify

F[w_,Dr_]=%;

ContourPlot[Evaluate[{Re[F[w,Dr]]==0,Im[F[w,Dr]]==0}],{w,0,20},{Dr,1.5,100},Contours->{0}]

FindRoot[Evaluate[{Re[F[w,Dr]],Im[F[w,Dr]]}==0],{{w,4.5},{Dr,20}}]