Integration of Gaussian Matrices is common in Physics. A Gaussian matrix integral was suggested on Youtube, done by hand in a slightly different manner, and implemented in code in a different manner all arriving at the same answer. I have been told that these come up in the simplest quantum field theories but alas how would I ever know :P
References
https://en.wikipedia.org/wiki/Common_integrals_in_quantum_field_theory
https://www.youtube.com/watch?v=mUAB1a623cc&t=607s
https://docs.sympy.org/latest/modules/matrices/matrices.html
https://www.geeksforgeeks.org/python-sympy-matrix-diagonalize-method/