**Integration by Parts**

A formula used to integrate the product of two functions.

Formula: | |||||||||

Example 1: | Evaluate . | ||||||||

It follows that
| |||||||||

Example 2: | Evaluate . | ||||||||

Use the following:
Thus
| |||||||||

Example 3: | Evaluate . | ||||||||

Let
Thus Now use integration by parts on the remaining integral . Use the following assignments:
Thus Note that appears on both sides of this equation. Replace it with We finally obtain |

**See also**

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