Hints on choosing u and v'

The integration by parts formula may be written as

You are going to
• differentiate the u part, and
• integrate the v' part .

We suggest you follow this order to find which part for u:

1. If one part is  ln x  or a similar logarithm, choose that as the u.
   

   Explanation There is no direct way to integrate ln x (except by parts!) so this should be that part you choose to differentiate.

2. Otherwise, if one part is a power of x, choose that as the u.
   

   Explanation When this is differentiated you will have a lower power of x and consequently a simpler integral.

3. Otherwise, if one part is an exponential, choose that as the u.
   

   Explanation When this is differentiated you will have a similar exponential no more complicated than the original. You should be able to obtain an integral similar to the original, and use an algebraic method to solve the problem. Click to see an example of repeated integration by parts.

Return to Question or Go back to Contents List