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:
Usual Change of Variable
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: