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...
... 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.
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!