How do you use integration by parts?

Problem Statement

How do you use integration by parts?

Step-by-Step Explanation

Integration by parts reverses the product rule and is useful for products of functions.

1. Identify what the question is asking. In Calculus 2, this usually means naming the known quantities, the unknown quantity, and the concept that connects them.
2. Write the relevant definition, rule, or relationship before substituting numbers or manipulating symbols.
3. Work one step at a time and keep units, signs, and restrictions visible.
4. Check whether the answer makes sense in the original context.

Key Formula

Final Answer

Integration by parts reverses the product rule and is useful for products of functions. The reliable strategy is to start from the definition, apply the correct rule carefully, and then interpret the result in plain language.