The primitive of xtan(x) (1 Viewer)

[Captain pi]

If anyone has a coherent proof for the result found @ http://integrals.wolfram.com/ after computation of the integral of x*Tan[x], I would be very grateful if he could post it.

Please note Trev: if you copy the infra proof, you will have to explain it to the class before I award you $15.

 

[KeypadSDM]

PolyLogs would have to be substantially beyond what you know, right?

But even then it's astoundingly simple:

Since we know that:

d/dx PolyLog[2,-(e^2ix)] = 2i * Sum[n=1,infinity] [(e^(2inx)/n) * (-1)^n]

 

[Trev]

Please note Trev: if you copy the infra proof, you will have to explain it to the class before I award you $15.

Haha, I saw this thread and knew it was you!
So you expect me to read up on 'polylogs' and whatnot, and even then after all that effort - explain it to the class. HP, you know how much of a crap public speaker I am
Hmmm, I'll have a go!

 

[Trev]

Wait, looking at the brief example
"d/dx PolyLog[2,-(e^2ix)] = 2i * Sum[n=1,infinity] [(e^(2inx)/n) * (-1)^n]"
I have already been confused, and have decided I won't bother, haha. I'll tell someone else to and make them suffer

 

[Captain pi]

PolyLogs would have to be substantially beyond what you know, right?

But even then it's astoundingly simple:

Since we know that:

d/dx PolyLog[2,-(e^2ix)] = 2i * Sum[n=1,infinity] [(e^(2inx)/n) * (-1)^n]

My dear Thomas, I don't even know how to differentiate complex numbers (bows head in shame), let alone call myself amongst the 'we' you so confidently assumed above.

Could you expand (tremendously) on this proof? Could you file a .pdf? Or, at least, give me some reading material?

Love,

pi.