Slide 1

Integration of Rational Functions Slide 2 This presentation is about integrating rational functions such as Slide 3 First lets do some easy ones Slide 4 Find the antiderivative Solution Slide 5 Find the antiderivative Solution Recall the formula: Slide 6 Integrate SolutionNotice top derivative of bottom equals Slide 7 Find Solution This observation allows us to split the difficult integral into two simple integrals. This leaves just one question: how does one find identities like this? The process of breaking a fraction into simpler fractions is called the method of partial fractions. We make an interesting observation: Slide 8 The following discussion is about algebra. Not calculus. Slide 9 Lets consider the problem of splitting apart the following rational function. Now lets split it apart somehow! Simplify: These are equal Conclusion: Slide 10 Lets review what happened. Slide 11 Example: Integrate SolutionUsing partial fractions: (Done on previous slide) Slide 12 Long DivisionThere are situations where partial fractions wont work. Consider Slide 13 Performing long division with Set up long division as in elementary arithmetic. Subtract. We can finally write: Slide 14 Example Integrate: Conclude Now we do partial fractions.