Simplifying Integral Expression w/ Antiderivative
I'm trying to simplify this formula here. For the most part, evaluating this expression is straightforward. However I am very confused about how to approach this last term in the expression. I want to simplify this part of the formula and break it down further if possible by coming up with an antiderivative formulation or something similar to make it more understandable, and to be able to evaluate it in terms of its unknowns. It's clearly related to the normal distribution but I'm unsure of how to simplify it in terms of the normal as well. How should I approach this? What would be the best way to evaluate this term?