Home >> PURE MATHS, Integration, integration 'by parts'

Integration 'By Parts' - from the Product Rule

The integration of expressions where there are two separate functions multiplied together, is essentially by an amended version of Leibnitz's Product Rule.

To integrate an expression of the type:

make       and   

the expression becomes:      

using the Product Rule:       

                       rearranging         

integrating with respect to x

back to top

Example #1

integrate      

make      

then     

    so        

make     

         so    

    hence     

now using the formula   

back to top

Example #2

integrate    

make      

then   

  make    

           then       

     integrating                    

now using the formula   

back to top

Example #3

integrate    

make    

then         

 make  

      then   

  integrating           

now using the formula   

back to top

[ About ] [ FAQ ] [ Links ] [ Terms & Conditions ] [ Privacy ] [ Site Map ] [ Contact ]