1. Chapter7 TECHNIQUES OF INTEGRATION
In this chapter we develop techniques for using these basic integration formulas to obtain indefinite integrals of more complicated functions.

2. Find Find Sec 7.1: INTEGRATION BY PARTS
formula for integration by parts.
Example
Example
Find
Find

3. Find Sec 7.1: INTEGRATION BY PARTS formula for integration by parts.
REMARK1: aim in using integration by parts is to obtain a simpler integral than the one we started with.
Example
Find

4. Find Sec 7.1: INTEGRATION BY PARTS
Example
REMARK2: in some integral, we may need to apply integration by parts many times.
Find

5. Find Find Find Sec 7.1: INTEGRATION BY PARTS
Example
REMARK2: in some integral, we may need to apply integration by parts many times.
Find
Example
Find
Example
Find

6. Find Sec 7.1: INTEGRATION BY PARTS
formula for integration by parts.
Example
Find
REMARK3: sometimes a repeated application of integration by parts leads back to an integral similar to our original one. If so, this expression can be combined with original integral.

7. Sec 7.1: INTEGRATION BY PARTS
Exam2
Term082
Exam2
Term102

8. Exam2
Term092

12. Reduction Formula Sec 7.1: INTEGRATION BY PARTS
Observe:
Reduction Formula
REMARK3: sometimes The reduction formula is useful because by using it repeatedly we could eventually express our integral.

13. Sec 7.1: INTEGRATION BY PARTS
Reduction Formula
Example
Example

14. Reduction Formula Reduction Formula Sec 7.1: INTEGRATION BY PARTS
Example
Example
Reduction Formula

15. Reduction Formula

17. Sec 7.1: INTEGRATION BY PARTS