https://youtu.be/79lWkqMEzUU

In this video I go over another example on integrating rational functions by the method of partial fractions and this time go over an example that requires both polynomial long division and partial fraction decomposition to simplify and integrate. The example is solving the integral of (x<sup>4</sup>-2x<sup>2</sup>+4x+1)/(x<sup>3</sup>-x<sup>2</sup>-x+1).

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# Integration of Rational Functions by Partial Fractions: Example 4

![Integration by Partial Fractions Example 4.jpeg](https://cdn.steemitimages.com/DQmc46tPFkqrKq6C9S4jz16HB2YkbZfQ7Kna4V3wSWtfBhb/Integration%20by%20Partial%20Fractions%20Example%204.jpeg)

**Example:**

![](https://cdn.steemitimages.com/DQmen8vvzNKY4orrU6f7NNLfSqExY1w1cCcWzd7rjNTQBoh/image.png)

**Solution:**

![](https://cdn.steemitimages.com/DQmfWToE3aEaQmW4kU9KZnq3mP3HqNtnRcqb72A5FRFH4ZQ/image.png)

![](https://cdn.steemitimages.com/DQmQFQxYaHnQyyaPDvWAsNTpi3TTpUT9S2QZGnDboEMnVJE/image.png)

![](https://cdn.steemitimages.com/DQmdxbnP5FeRNJrKKsLwSsZpgu6oprZ3XN2UzR86fa5cFi7/image.png)