I am new to the field of Gaussian integration, could anyone help me to solve this integration and give me a detailed explanation of each step? The equation is as follow where $\mu$ and $\sigma$ refers to the mean and s.d and z has a dimensional of J:
$ \int N(z; \mu, \sigma)\log(N(z; 0, I))dz$
Many thanks in advance!!!
Edited to to include a bit more details, I could personally solve $ \int N(z; 0, I)dz$, but don't know how to deal with this complex integral, and I am not sure about the multi-dimensional case.