Final answer:
The question appears to pertain to integration by parts, a technique in calculus used for finding the integral of the product of two functions. However, the provided information is incomplete and contains typos, making it difficult to solve without further clarification.
Step-by-step explanation:
The integration question provided refers to a mathematical method used to find the area under a curve or to sum continuous data. However, the question as it was provided appears to be incomplete and contains several typographical errors, which makes it challenging to address directly. Nonetheless, integration by parts is a technique often used when the integrand is a product of two functions, and it is based on the product rule for differentiation. The general formula for integration by parts is ∫ u dv = uv - ∫ v du, where u and v are functions of x. The provided snippets seem to indicate steps from different integration problems, including setting up expressions and substituting variables.
It's worth noting that in situations where standard integration techniques do not apply or are difficult to use, one may need to expand expressions, use trigonometric substitutions, or apply special integrals that have been established for particular functions.