Uncertain load behavior affects the energy system operation scheduling in battery-integrated energy systems (BIES) due to the direct relation between optimal battery scheduling and load demand in the forthcoming time interval. In this paper, the optimal schedule of BIES is investigated with considering load demand uncertainty. The previous works have introduced a cost function and found optimal strategies using evolutionary optimization algorithms, which may fall in local minima. Against the previous works and in order to avoid falling in local minima, a closed-form expression is presented in this paper by analyzing a mathematically-modeled forecast error and considering battery characteristics. In the proposed method, the optimal battery charging/discharging state is analytically obtained based on forecast error and system parameters without the need to use numerical approximation algorithms. The applicability of the proposed scheduling strategy in the real energy system is shown by applying it to online optimal control of the battery in a real system with load demand forecast error, and also by comparing the results with previous methods. The proposed approach leads to the globally-optimal solution for battery scheduling and also shrinks the computational complexity of the BIES scheduling problem.