  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. The connection between the integrals
and the maximal rational $H^{d}$-submodule $H^{d rat}$ of $H^{d}$ is found.
That is, $H^{d rat}\cong \int ^l_{H^d} \otimes H$ is proved. The existence and
uniqueness of integrals for braided Hopf algebras in the Yetter-Drinfeld
category $(^B_B{\cal YD},C)$ are given.
