Lec 6 - Integration by Rational Function by Partial Fraction

- Substitution
- Integration by parts
- Trig Integrals
- Trig substitutions
- Partial functions

Sec 7.4

Techniques of Integration

Recall,

We will learn how to do this backwards so that the integrand can be rewritten
as a sum of terms each of which we can be rewritten as a sum of terms each of
which we can integrate.

Definition

We only apply partial fractions on proper rational functions.

If not proper then we long division to reduce it

Example

Evaluate

We can use long division.

Step 1: Use long division to get a proper fraction

Step2: Decompose our proper rational function

In this case we always assume,

The method I present is different from the textbook.

On the LHS, we have

Therefore,

Eg

Evaluate

Step 1: It is proper, no long division.

Step 2: We use partial fractions

Step 3: Evaluate

What if weinstead have

Created by Tim Pei with Microsoft OneNote 2010

One place for all your notes and information