Evaluate the definite integral by using the method of integration by parts. 
Definitions:
Primary Caregiver
The main individual, often a family member or professional, responsible for providing direct care and support to a person with health or personal needs.
Unexpectedly Hospitalized
The unforeseen admission of a person to a hospital for medical care.
Cognitive Restructuring
A psychological technique aimed at identifying and challenging negative and irrational thoughts and replacing them with more balanced and constructive ones.
Coping Abilities
The skills and strategies individuals use to manage stress, challenges, or adversity.
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