Computational models of soft tissue growth and remodeling (G&R) have been developed in the last decades to increase understanding of tissue G&R, identify patients at risk of maladaptive G&R, and improve personalized therapy options. Meanwhile, constrained mixture models are widely adopted in this field. However, even two decades after the initial proposal, these models are still rare on the 3D organ-scale, mainly due to the computational cost (evaluation time and memory consumption). We developed and implemented novel approaches to adaptively integrate the history variables in constrained mixture models by exploiting the typically decreasing influence of prior deposited mass on the current stress response of the mixture through tissue degradation. The goal of the adaptive integration strategy is to control integration error over the G&R history and thereby reduce the computational cost of the model. After presenting the novel approaches, we apply the strategies to a patient-specific model of two ventricles using a finite element mesh with 300.000 degrees of freedom. Starting from a healthy baseline (homeostasis), we simulate two distinct hypertension conditions resulting in mechanobiologically stable and unstable G&R. Adaptive integration of the history variables reduces the model evaluation time of constrained mixture models to a level comparable to homogenized constrained mixture models and kinematic growth models. The memory consumption of the model is also reduced to a level that allows large 3D organ-scale simulations of G&R on modern computer hardware. Adaptive integration of G&R history allows the simulation of microstructure-motivated constrained mixture models on larger scales, helping to improve computational models of cardiac, vascular, and other soft tissue G&R.