7.1 Integration of Parts

You should remember that the product rule is :

By rearranging this equation you see that:

By using the substitution rule and replacing u for f(x), v for g(x), du for f'(x)dx, and dv for g'(x)dx, you will see that the formula for integreation of parts becomes:

Let's look at a couple of examples!

1)
Choose your simplest component for u. In this case that would be x. Make a table of your u, du, v, and dv.

Now plug it into the equation
You get


Don't forget the C!

2)
You can use the tabular method here.

Now try a problem!

Here, you must use integration by parts again

Now plug this equation back into the end of the first integration of parts:

Here is a good site for Integration of Parts:
http://www.sosmath.com/calculus/integration/byparts/byparts.html

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