## Integration by parts.

The so-called integration by parts formula is a direct consequence of Leibniz's formula for derivation of a product (v.s. 5):

In each example, we have to decide who is and who is .

Example 8.2.7   Let .

We choose: Therefore: .

Example 8.2.8   Let .

In this case it is wise to choose , so the logarithm will disappear'':

Therefore:

Thew following example uses the same technique, and its result should be remembered.

Example 8.2.9   Let . Once again, we choose :

Noah Dana-Picard 2007-12-28