  In order to generalize the integration rules to general CHY integrands which
include higher order poles, algorithms are proposed in two directions. One is
to conjecture new rules, and the other is to use the cross-ratio identity
method. In this paper,we use the cross-ratio identity approach to re-derive the
conjectured integration rules involving higher order poles for several special
cases: the single double pole, single triple pole and duplex-double pole. The
equivalence between the present formulas and the previously conjectured ones is
discussed for the first two situations.
