1. ## Substitution

A friend gave me this procedure, but I'm in doubt with something. Can someone tell me how they got the values for u, dv, du, and v?

Thanks

2. Google L.I.A.T.E, but this is less important than seeing why the choice of u and v that works works. Which is about working backwards through the product rule. Just in case a picture helps...

... where (key in spoiler) ...

Spoiler:

... is the product rule.Straight continuous lines differentiate downwards (integrate up) with respect to the main variable (in this case x).

... is lazy integration by parts, doing without u and v.

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!

3. Thanks tom!