Understanding how functions behave is really important when you're picking the right way to integrate them. Here’s why this matters:

1. Knowing the Type of Function: Not all functions are the same. For example, when I worked on the function $f(x) = x \sin(x)$, I saw that I needed to use integration by parts because it's made up of two different functions. If I hadn’t noticed this, I would have had a hard time finding the integral.

2. Looking for Patterns: With some functions, especially simple ones or rational functions, using substitution can make things easier. For instance, when I had $f(x) = \frac{1}{x^2 + 1}$, I figured out that if I let $u = x$, it became a much simpler problem to solve.

3. Thinking About Function Behavior: It helps to know if a function is going up, going down, or repeating itself. This can give you clues about how to integrate it. For example, functions that keep changing might need special techniques, while polynomials that grow in a predictable way are usually easier with substitution.

4. Trying Different Methods: Sometimes I changed my approach while calculating. But knowing how the function behaves often helped me find the quickest way to solve it.

In the end, understanding how functions act can save you time and help you avoid frustration, making the integration process go much smoother!