Recent advances in artificial intelligence (AI) capabilities have increased the eagerness of companies to integrate AI into software systems. While AI can be used to have a positive impact on several dimensions of sustainability, this is often overshadowed by its potential negative influence. While many studies have explored sustainability factors in isolation, there is insufficient holistic coverage of potential sustainability benefits or costs that practitioners need to consider during decision-making for AI adoption. We therefore aim to synthesize trade-offs related to sustainability in the context of integrating AI into software systems. We want to make the sustainability benefits and costs of integrating AI more transparent and accessible for practitioners. The study was conducted in collaboration with a Dutch financial organization. We first performed a rapid review that led to the inclusion of 151 research papers. Afterward, we conducted six semi-structured interviews to enrich the data with industry perspectives. The combined results showcase the potential sustainability benefits and costs of integrating AI. The labels synthesized from the review regarding potential sustainability benefits were clustered into 16 themes, with “energy management” being the most frequently mentioned one. 11 themes were identified in the interviews, with the top mentioned theme being “employee wellbeing”. Regarding sustainability costs, the review discovered seven themes, with “deployment issues” being the most popular one, followed by “ethics & society”. “Environmental issues” was the top theme from the interviews. Our results provide valuable insights to organizations and practitioners for understanding the potential sustainability implications of adopting AI.