Question

In carl jung's view, the task of integrating unconscious archetypal aspects of the self is part of ________ in the second half of life.

Answer 1

I believe the answer is:  the self-realization process

According to carl jung,  the self-realization process refers to the efforts that individuals make in order to achieve a sense of fulfillment in their life based on their desires and unique personalities. 
In  the self-realization process, the first thing that people tend to do would be integrating unconscious archetypal aspects of the self in order to findout their characters/personalities and what they truly want in their life