For quantum symmetric pairs (U, U ı ) of Kac-Moody type, we construct ıcanonical bases for the highest weight integrable U-modules and their tensor products regarded as U ı -modules, as well as an ıcanonical basis for the modified form of the ıquantum group U ı . A key new ingredient is a family of explicit elements called ıdivided powers, which are shown to generate the integral form ofU ı . We prove a conjecture of Balagovic-Kolb, removing a major technical assumption in the theory of quantum symmetric pairs. Even for quantum symmetric pairs of finite type, our new approach simplifies and strengthens the integrality of quasi-K-matrix and the constructions of ıcanonical bases, by avoiding a case-by-case rank one analysis and removing the strong constraints on the parameters in a previous work.