Evaluate the integral. 
Definitions:
Optimal Choice
The most efficient, advantageous selection or decision based on available information and constraints.
Substitution Effect
The change in consumption patterns due to a change in relative prices, leading consumers to substitute the consumption of one good for another.
Interest Rate
The remuneration, depicted as a fraction of the principal, that a lender exacts from a borrower for asset utilization.
Income Effect
A change in the consumption patterns of individuals or economies due to a change in real income or purchasing power.
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