Evaluate the integral using integration by parts and substitution. 
Definitions:
Compounded Quarterly
The process where interest on an investment is calculated and added to the principal every three months, contributing to the growth of the investment amount.
Compounded Monthly
Entails the regular addition of interest to the principal balance of a loan or deposit every month, affecting overall returns or costs.
Semi-monthly Payments
Payments that are made twice a month, often on the 1st and 15th, typically in the context of salaries or loans.
Loan to Value Ratio
A financial term used by lenders to express the ratio of a loan to the value of an asset purchased.
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