Integrating Functions Using Long Division and Completing the Square
Abigail Young
6 min read
Study Guide Overview
This study guide covers integration techniques using long division and completing the square. It explains how to simplify rational functions and quadratic expressions within integrals to make them solvable. The guide includes walkthrough examples and practice problems for both methods, focusing on applying these algebraic techniques to integration problems. It also highlights common scenarios where these methods are applicable.
#6.10 Integrating Functions Using Long Division and Completing the Square
Ever find yourself dealing with a tricky integral that doesn't seem possible with techniques you’re familiar with? This is when your knowledge of Algebra and Precalculus comes in handy. As you’ll learn today, it is possible to use techniques such as polynomial long division and completing the square to rearrange integral expressions into simpler, more approachable problems to solve. 🙌
#➗ Integrating Using Long Division
If you can recall from Precalculus, a rational function has a polynomial in the numerator and the denominator of the function. A good rule of thumb is if the numerator of the rational function is an equal degree or higher than the denominator, long division might be the way to go.
#✏️ Integrating Using Long Division Walkthrough
Solve the integral expression:
First things first, we can see that we have a rational function, where the degree in the numerator is higher than that of the denominator. Let’s go ahead and solve it with long division!
Since we can see a quadratic function in the numerator and a linear function in the denomi...
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