SATech-01 is an experimental satellite for space science exploration and on-orbit demonstration of advanced technologies. The satellite is equipped with 16 experimental payloads and supports multiple working modes to meet the observation requirements of various payloads. Due to the limitation of platform power supply and data storage systems, proposing reasonable mission planning schemes to improve scientific revenue of the payloads becomes a critical issue. In this article, we formulate the integrated task scheduling of SATech-01 as a multi-objective optimization problem and propose a novel Fair Integrated Scheduling with Proximal Policy Optimization (FIS-PPO) algorithm to solve it. We use multiple decision heads to generate decisions for each task and design the action mask to ensure the schedule meeting the platform constraints. Experimental results show that FIS-PPO could push the capability of the platform to the limit and improve the overall observation efficiency by 31.5% compared to rule-based plans currently used. Moreover, fairness is considered in the reward design and our method achieves much better performance in terms of equal task opportunities. Because of its low computational complexity, our task scheduling algorithm has the potential to be directly deployed on board for real-time task scheduling in future space projects.