Sure thing! Here's an explanation of integration by parts for an 11-year-old, followed by a rap to help you remember the basics of calculus:

Integration by parts is a way to find the answer to a tricky math problem called an integral. Sometimes, we can't solve an integral using normal methods, so we use integration by parts instead. It's like breaking the problem down into two parts and putting them back together.

Let's say we have an integral that looks like this: ∫x cos(x) dx. We can use integration by parts to solve it. First, we pick one part of the problem to be u and the other part to be dv. Then, we find the derivative of u and the integral of dv. We plug these values into the integration by parts formula and we get our answer!

Here's a rap to help you remember the basics of calculus:

Verse 1:
Calculus is all about rates of change,
How things move, grow, or rearrange.
Derivatives show the slope of a line,
Integrals find the area, oh so fine.

Chorus:
Calculus, calculus, it's so cool,
Helps us understand things, that's the rule.
With derivatives and integrals in your hand,
You can solve problems all across the land.

Verse 2:
Integration by parts is a slick trick,
Splits a problem in two, it's no lick.
Find the derivative and integral too,
Plug them in and you're good as new.

Chorus:
Calculus, calculus, it's so cool,
Helps us understand things, that's the rule.
With derivatives and integrals in your hand,
You can solve problems all across the land.

Outro:
So when you're stuck on a tough math quest,
Just remember calculus is the best.
With integration by parts and more,
You'll be a calculus pro, that's for sure!
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