# Integration by Substitution

The method of **integration by substitution** or **change of variable** is based on the derivative of the composite function or **chain rule**.

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.

### Steps to Integrate by Substitution

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

Work out the value of **u** and **dx** by substituting these values into the integral.

2. If the resulting integral is simpler, integrate:

3. Return to the initial variable:

#### Example

## Usual Change of Variable

1.

2.

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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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