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Integration by Parts

The purpose here is to convert a tough integral into
an easier one. 

The following rule is  used:

1

The rule comes from reversing the product rule for
differentiation.

Steps

  1. Identify u and dv/dx
  2. Find du/dx   and v
  3. Plug into formula.

 

Go again if necessary !

Tip : Pick u as the function which is easier to differentiate

Example

Find the  integral 

   2  

3

4

 

Example

Find the  integral 

5

6

7

8

9

 

Example

Find the  integral 

10

11

12

 

© Alexander Forrest