You can try a substitution of
I think that will make things simpler.
I was trying to figure out a way to evaluate the following integral:
INT ( ln(lnx) + 1/[(lnx)^2] ) dx
The answer to the above is:
x ln(lnx) - [ x / (lnx) ] + c
My question is, how to get to it?
Any help/hints/suggestions will be greatly appreciated.
Yes you can - integrate ln(ln x) by parts twice, integrating 1 each time (and differentiating the integrand each time)... see what happens. Pic in a mo.
Edit: sorry for the delay. Just in case a picture helps...
... is lazy integration by parts, with...
... the product rule. Straight lines differentiate downwards (integrate up) with respect to x.
You may find it helpful to zoom in on the chain rule, inside the product rule...
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!
Yes, sorry, I made a mistake. I think that substituting x = e^u is better.
This done, I get:
If I didn't do any mistake
Then, I proceeded using by parts.
I wanted to edit my post yesterday, but my connection was not working properly
For the drawing, it's the first time I see this... it might take me some time before understanding it
Anyway, sorry for my first post, I thought it would work without actually trying