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 « Integration by Substitution
Integration Techniques: (lesson 2 of 4)

## Integration by Parts

Theorem:

The formula for the method of integration by parts is given by: Four steps to use this formula:

Step 1: Identify u and dv. Priorities for Choosing u are: 1. u = lnx 2. u = xn 3. u = eax

Step 2: Compute du and v

Step 3: Use the formula for the integration by parts

Example 1: Evaluate the following integral Solution:

Step 1: In this example we choose u = x and dv will be everything else that remains. Step 2: Compute du and v Step 3: Use the formula. Therefore: Example 2: Evaluate the following integral Solution:

Step 1: In this example we choose u = ln x (first priority) and dv = x dx. Step 2: Compute du and v Step 3: Use the formula. The solution is: Exercise 1: Evaluate the following integrals

Level 1     Level 2     ### Integration by parts twice

Example 3: Evaluate the following integral Solution:

Let: So that Therefore: We need to perform integration by parts again: Try yourself     