Hadamard finite part integral

Okay, so imagine you have a bag of candy with all different kinds of candies inside. Now, you want to know how many blue candies are in the bag, but you can't just count them because the bag is too big and messy. So, you start taking out candies one by one and separating them by color. You soon realize that you don't have enough blue candies to make a full pile, but you still want to figure out how many blue candies you would have if you could keep taking out more candies forever.

This is where the Hadamard finite part integral comes in. It's like taking the same idea of separating candies by color and applying it to really complicated math problems. The finite part of the Hadamard integral means that we only consider the part of the problem that has a finite solution, so we stop when we get to that point.

For example, let's say we had a math problem that went on forever and kept getting bigger and bigger. Using the Hadamard finite part integral, we would figure out the part of the problem that has a finite solution - kind of like finding the blue candies in the bag - and stop there.

Overall, the Hadamard finite part integral is a tool to help us solve big, complicated math problems by breaking them down into smaller, more manageable parts.