22 - Integration by Partial Fraction Decomposition

This probably has you really confused, and with valid reason!

The purpose of this lesson is to show how you can sometimes use partial fraction decomposition to break up fractions into much simpler fractions that you can easily integrate.

THIS WILL BE ONE OF THE MOST IMPORTANT INTEGRATION TECHNIQUES YOU WILL EVER USE. PRACTICE AND REMEMBER THIS.

Partial Fraction Decomposition

Notice how we have a product in the denominator:
By elementary algebra we know that this can be the result of, or be broken up into a sum of fractions of form and .

Logically, to combine them back we'd need to do some cross multiplication, which means just literally multiplying in an x-shape. Create an equation based on the final result and the beginning equation.

Done? It should look something like this:
Well, now you have an equation. Solve it!

Now, substitute in the integral, and see how easy it becomes to integrate it.

Did you get it right? I hope so! We'll practice, either way.

22 - Integration by Partial Fraction Decomposition

The purpose of this lesson is to show how you can sometimes use partial fraction decomposition to break up fractions into much simpler fractions that you can easily integrate.

THIS WILL BE ONE OF THE MOST IMPORTANT INTEGRATION TECHNIQUES YOU WILL EVER USE. PRACTICE AND REMEMBER THIS.

Partial Fraction Decomposition

Good job, again!

Let's go. 23 - Practice Integration by Partial Fraction Decomposition