Why not do parts right away (twice) - integrate 1/x^2 and differentiate ln^2(x) (with the chain rule). Pic in a mo

btw for ,

Edit: excuse the delay, anyway, just in case a picture helps...

... where

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

... is the product rule, straight lines differentiating downwards (integrating up) with respect to x.

Full size:Spoiler:

Zooming in on the chain rule (in a jiff)...

Key and full-size:Spoiler:

I'll look at the subbing first, also.

_________________________________________

Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!