# Integration by Change of Varibale

The **change of varibale** or **substitution** method is essentially applying the chain rule in reverse:

To change the variable, identify the part of the function that is going to integrate with a new variable, **t**, in order to obtain a simpler integral.

### Integrate by Substitution Steps

1.Perform the **change of variable** method and differentiate the two terms:

2.Determine the value of **u** and **dx** by substituting these values into the integral.

3. If the resulting integral is simpler, integrate:

4. Return to the initial variable:

#### Example

## Usual Change of Variable

1.

2.

3.

4.

5. In the **rational functions of radicals with different indices** and the same linear radicand, ax + b, the **change of variable** is **t** raised to the least common multiple of the indices.

6. If is even:

7. If is not even:

### Examples

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