What is Lonewolf's proposed method for integrating Ln[x]dx?

[PrudensOptimus]

Integrat Ln[x]dx!

 

[Lonewolf]

Consider it as 1*ln(x) and use parts.

 

[Tron3k]

If you don't feel like doing it, you can always use:

http://integrals.wolfram.com/index.en.cgi

It gives the answer:

<br /> -x + x \ln x<br />

 

[himanshu121]

Is [x] greatest integer function??

 

[Lonewolf]

Hmm, didn't consider that. I'm not sure there'd be a closed form expression for \int ln[x] dx
where [x] is the next greatest integer function. It'd be easy enough to get a numerical answer if the interval was specified though.

 

[sam2]

You could break the integral into a summation. [x] is constant between intervals of integers, so you end up with a sum of trivial integrals.

I think this is what Lonewolf is proposing (please excuse my ignorance!)

Regards,
Sam