Alright, let's break this down into something that an 11-year-old can understand!

Calculus is a type of math that helps us understand how things change over time. Integration is a part of calculus that helps us find the total amount of something when we know how fast it's changing.

Integration by parts is a special trick we can use when we want to find the integral of a product of two functions. We can use this trick to make it easier to solve the problem.

Here's how it works:

First, we pick one function to be "u" and the other function to be "dv". Then we find the derivative of "u" and the antiderivative of "dv".

We use these values to plug into a formula: ∫u dv = uv - ∫v du

We solve the formula to find the answer!

To help you remember this, I made a rap:

Integration by parts, it's a special trick
To solve the integral of a product quick
Pick "u" and "dv" with precision
Find their derivatives, that's the mission

The formula is ∫u dv = uv - ∫v du
Use it right, and you'll know what to do
Plug in the values and solve with care
And the answer will be waiting there!

So, that's integration by parts in a nutshell! Remember the rap, and you'll be able to solve calculus problems like a pro!
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