Integration by Substitution
Tutorials with examples and detailed solutions and exercises with answers on how to use the powerful technique of integration by substitution to find integrals.
Review
The method of integration by substitution may be used to easily compute complex integrals. Let us examine an integral of the form
With the above substitution, the given integral is given by
In what follows C is a constant of integration which is added in the final result.
Example 1: Evaluate the integral
Solution to Example 1:
Example 2: Evaluate the integral
Solution to Example 2:
Example 3: Evaluate the integral
Solution to Example 3:
Example 4: Evaluate the integral
Solution to Example 4:
Example 5: Evaluate the integral
Solution to Example 5:
Example 6: Evaluate the integral
Solution to Example 6:
Example 7: Evaluate the integral
Solution to Example 7:
Example 8: Evaluate the integral
Solution to Example 8:
Example 9: Evaluate the integral
Solution to Example 9:
Example 10: Evaluate the integral
Solution to Example 10:
Example 11: Evaluate the integral
Solution to Example 11:
Exercises: Use the table of integrals and the method of integration by parts to find the integrals below. [Note that you may need to use the method of integration by parts more than once].
