# Using Tables to Find Antiderivatives

## Using "Recursive" Formulas

A recursive formula in the table is one that gives one antiderivative in terms of another antiderivative. Usually the new antiderivative is simpler than the original one. For example, table entry #19 gives the pattern for the antiderivative of in terms of the antiderivative of . If we start with the integral of , then we can use the table to get an answer in terms of the integral of . Using the recursion formula again, we can get the integral of in terms of the integral of , which is easy to integrate.

**Example 5:** Use the given recursive formula to evaluate .

Solution: In this example and . Then

**Practice 5: **Use the recursion formula in the table to evaluate .