Intergration by parts

[markraz]

Hi I'm confused with the first half of the integration by parts formula

= uv -


The u I'm ok with but the v is confusing me. Why does the v represent the derivative?

When they came up with this, why didn't they write it as = u dv-

Seems inconsitent? and convoluted. Is there some rational behind this?

thanks

 

[stapel]

Try this lesson. The author's explanations are pretty good.

 

[markraz]

thanks, yeah I get it now