The Form of Integration by Parts

This GeoGebra applet lets you look at the first step of using the integration by parts technique. You can use it to try out different ways of looking at integrating a product. Try some of the following f(x)=x^2, g(x)=e^x f(x)=cos(x), g(x)=e^(2x) f(x)=ln(x) g(x)=1 or other functions that would be interesting. Go crazy! How would you describe which factor in the original integral problem is better as which part?