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. 
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
