Tutorials with examples and detailed solutions and exercises with answers on how to use the powerful technique of integration by substitution to find integrals.

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.

## Examples
## Example 1Evaluate the integral
## Example 2Evaluate the integral^{3x - 2} dx
## Example 3Evaluate the integral^{2} + 5)^{4} dx
## Example 4Evaluate the integral
## Example 5Evaluate the integral^{-4} dx
## Example 6Evaluate the integral^{x2 + 2} dx
## Example 7Evaluate the integral^{4}(x) dx
## Example 8Evaluate the integral
## Example 9Evaluate the integral
## Example 10Evaluate the integral^{3}(x + 4)^{2} dx
## Example 11Evaluate the integral^{2} + 3x + 1) ) dx
## ExercisesUse 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].1. cos(3x - 2) dx 2. e ^{4x - 7} dx
3. x(4x ^{2} + 5)^{4} dx
4. 1 / (x + 3) ^{3} dx
## Answers to Above Exercises1. (1/3) sin(3x - 2) 2. (1/4) e ^{4x - 7} + C
3. (1/40) (4x ^{2} + 5)^{5} + C
4. (-1/2) 1 / (x + 3) ^{2} + C
## More References and linksintegrals and their applications in calculus. |