The faithful quasi-dual H^d and strict quasi-dual H^d＇ of an infinite braided Hopf algebra H are introduced and it is proved that every strict quasi-dual H^d＇ is an H-Hopf module. A connection between the integrals and the maximal rational H^d-submodule Hdrat of Hd is found. That is, H^drat ≌∫Hdl ×H is proved. The existence and uniqueness of integrals for braided Hopf algebras in the Yetter-Drinfeld category （BBYD, C） are given.
