@r9m The answer is not important, but the way and the core idea behind it.

ಠ_ಠ :-)

@Chris'ssis please enlighten me ? :D

@r9m How did you arrive at that solution

@ಠ_ಠ its of the form $\int f'(x).f(x)^n\,dx$

@r9m The core idea is that the primitive has the form $g(x) (x^5+3)^{6/5}+C$, where $g(x)$ is a polynomial. Using this simple fact, one can construct thousands of tricky questions ...

I'm not aware of this form

Where do you learn about these special tricks

Is there like a book on it

@r9m Is there any reason to believe that @DanielFischer would promote fascism? Why would you read such a book? :-)

@Chris'ssis aha !! @Chris'ssis .. although while solving a similar problem my instincts would be getting an expression like $\int \sum_n f^{(n+1)}(x)f^{(n)}(x)\,dx$

@ಠ_ಠ I create them- self-learning.

I mean I don't understand the significant of the form $\int f'(x) \cdot f(x)^n dx$

Isn't there like a book where you can learn about these special forms

@ಠ_ಠ there is nothing special about it.

I've never seen it before and don't understand where it comes from

@r9m I see. I'm glad you got my point ;)

I've just finished another proof ... (finally)

@Chris'ssis There is art in an art ;)

Anyone minds helping me understand a bit the transition from a description of bounds, to the actual bounds on a triple integral, and finally into cylindrical bounds? I have a specific problem I can't figure out how to do it with, quite lost

@r9m Indeed. Interesting. :-) Are you that one in red?

@Chris'ssis nope .. I'm taller .. but there is a lot of red and I'm not sure if I'll fit anywhere :)

:-)

Dang it's frustrating when I can't find references nor people answering a question of mine.

It's actually even more frustrating that I can't do it myself

I mean, if I managed to translate some cartesian boundries to two cylindrical (and in this case also polar) boundries: $r(cos\theta +sin\theta )=1, r(cos\theta + sin\theta )=2$, how do I know how to bound the integral over $r$?

@Chris'ssis I just went through the proof of $\lim\limits_{n \to \infty}\int_{[0,1]^n} f\left(\frac{n}{\frac{1}{x_1}+\cdots+\frac{1}{x_n}}\right)\,dx_1\cdots\,dx_n = f(0)$ by O.Furdui from Crux TOTTEN-03. [2009 : 320, 323], .. our proof is 'shorter' :P[raspberry] lol (thats all I want to say)

@r9m Do you have a link?

@Chris'ssis ah .. no (its among the relatively new crux stuff .. so inaccessible from the crux site) .. I had to request user mixedmath for it (he has subscription) .. but I have the pdf :)

@r9m Nice. I don't have access ... :-(

@Chris'ssis Do you find it more fun to create problems than to solve some question asked by, I don't know, others?

@BalarkaSen Let me remind you that the last problems I created are based upon the integral question you asked me in the past that I recently evaluated. Well, I wanted to go further and study things for other similar cases ... :-)

Would the bounds above translate to bounds like $\int_\frac{1}{cos\theta +sin\theta}^\frac{2}{cos\theta +sin\theta}$, especially since I can say in this case that $0\le \theta \le \frac{\pi}{2}$?

@r9m Great! Thank you!

@Chris'ssis Quite true, quite true, but often you come up with problems which seem unrelated to me. Isn't it more interesting to relate a few things other than doing unrelated problems from a competition or something?

.

Well, I like the diversity, and out there are lots of interesting questions. I'm not sure what you mean by "relate a few things", and the same thing to "unrelated problems". It's all about diversity.

Hear hear, @Mike

What, @MikeMiller? Have you come up with something topologically contractible to a point?

@Chris'ssis I think I made myself clear enough above. What I mean is this : You have a few problems, like solving a cubic equation, then finding logarithm of 2 upto 60 decimal places and then doing a tough polylog summation ending up with a problem of determining what is 2 to the power of 436 modulo 112. Cool, that's really some fun mathematics, but isn't it more fun to do question which are "related"?

Like, after solving the cubic ask yourself if you can do the same for a quartic, a quintic, and higher degrees. That'd be really something interesting, non?

@BalarkaSen This is exactly what I'm doing. I don't have a few questions, but more than ten thousands questions (I mean those created by me) ... :-)

You know, I try to generalize a lot of problems, not only to solve particular cases.

@Chris'ssis The number of question doesn't matter really, the question is : do they all come from some single interesting problem you are trying to solve?

@BalarkaSen Sometimes when I'm on chat on my phone, I forget to click away notifications, and when I get home I have something like ten of them.

So I say something to make them go away.

just make it all go away

i wish i could do that in real life

@MikeMiller Aha. That's a good idea.

Oh eyeglasses, it's never that bad.

those are eyebrows

I will fight anyone who disagrees

@MikeMiller You know what Pedro will say now.

fight fight fight

I'll bring the oil. I never miss a good old oil wrestling.

I'm not sure what kind of glasses have hooks on top of them

@BalarkaSen Anyway, I think we talk, understand different things here. Maybe the language is a barrier to clearly understand each other our ideas. I have no idea what you mean by "some single interesting problem".

@N3buchadnezzar Let me bring a matchbox too.

@BalarkaSen Massage oil ._. Good luck putting that on fire

._o

@MikeMiller Do you know the effect of the ESCape key?

@N3buchadnezzar Hell.

@Chris'ssis Perhaps, I don't know, you have never done such related problems, thus you can't understand.

@BalarkaSen Fire

@DanielFischer I do now, but I will have forgotten by tomorrow.

@MikeMiller I have a problem for you.

@BalarkaSen I have too many problems as is.

For instance, my hair is too long.

@BalarkaSen I think you begin to make assertions that I don't like that much. What I do and what I can understand you might hardly appreciate/evaluate since you don't know me.

@Chris'ssis Oh, no, I am not evaluating your works, don't get me wrong. I am merely pointing out that it might be more interesting to you if you try out problems like the one I mention.

@BalarkaSen you better try some of the integrals above instead of keeping this unproductive discussion. ;)

@Chris'ssis I am not interested, thank you.

@Chris'ssis But in terms of research how is solving integrals useful, what does it contribute to various branches of mathematics. Except being fun brainteasers?

@N3buchadnezzar Point taken.

I mean ofcourse it could give you as an individual greater insight into some specific topics, or functions. But thats not what research is about, is it?

I don't underestimate integrals. For example, in study of complex analysis or number theory, several integrals arise to which you need closed forms but individually, it's pretty boring as, for example, a putnam problem.

@N3buchadnezzar I think the best way is to find the answer to this question on your own.

The $\frac{x}{x^s} \frac{\zeta'(s)}{\zeta(s)}$ one

Yes, @N3buchadnezzar, that's an example.

@BalarkaSen Using a shovel is fun, studying the shovel on its own is boring?

Hahaha

The mathematics I do is an art (I love very much). End of story.

For everyone who does what they love, what they do is an art, isn't it so?

@Chris'ssis Art is ok. Just don't get into abstract art.

Pollock's convergence or number 8 is nonsense to me.

what is like space, and meaning and stuff right?

@Chris'ssis Actually, what you do is fine by me. I am really asking you to peek at what is going on outside what you do. Have you seen Elkies' answers to some integral questions here and there? Does it not inspire you to learn the stuffs that relate to the art you do?

Elkies?

Noam Elkies

Noam D. Elkies.

@BalarkaSen Why do ask me this kind of questions? Do you know what new things I learn every day? It's a disrespectful attitude. I'm going to ignore you (from now on).

one of the world's best computational number theorists

@MikeMiller computational algebraic number theorist, i'd say

and the best of the best.

his pass time job seems killing mosquito integrals/inequalities by heavy elliptic modular atomic explosions.

@Chris'ssis I am not sure what disrespectfulness I have shown to you.

You guys are crazy. Also, I think I have my bounds wrong sigh

I didn't know it was disrespectful to point out that there are branches in mathematics other than computing integral and series.

I think it's either wrong with the bounds for r, or with the bounds for z.. not sure why for either. Maybe it's right and I can't do algebra..

@Studentmath What problem are you doing?

This one is pretty cute.

@balarka Trying to turn some triple-integral to cylindrical one to solve it. Let me repost it..

Argh, have to do the latex again.

Which makes me think it's wrong

Either the first bound (over z) or the second bound (over r).

Let $a,b,c$ be the lengths of the sides of a triangle. Compute the integer part of $$\frac{(a^2+b^2+c^2)(a+b+c)}{a^3+b^3+c^3}$$

This one was given to a middle school contest (very cute).

@Studentmath æææwhy not post it on le mail ?

You mean main?

y

Since I think it's something really stupid that I am missing and I will find out sooner or later. Probably will give up in a few and post it, but I am sure it's something minor in the bounds or with opening up the $(cos+sin)^3$ that fools me here.

@Studentmath I think you forgot a factor of $r$ in the integrand

$(r^2 \cos^2 \theta - r^2 \sin^2\theta)^2 r \mathrm{d}r \cdots$

See. Something stupid.

I admire you @N3b! Thank you

I am tired but otherwise it looks correct

Thank you very much :)

@Studentmath This might be easier

I want to practice the transition to cyndrical boundries and triple-cyndrical integrals though - otherwise that certainly looks easier

Hi Folks. Anyone know why do I get +2 to my reputation for "User removed"?

@Jeff maybe .. user had downvoted a question of yours ..

@Studentmath Do you know the answer?

do i lose 2 points for a downvote?

and then if they get kicked off, for who knows why, i get my 2 points back. cool :)

Unfortunately no - I will compare it with the solution for the integral you suggested though, so thanks again :P

@Studentmath They are different, yours however simplify greatly

Ah.

o_o !!

Have you guys checked out cloud.sagemath.com

Didn't look into trying in cartesian - does it actually complicates it? Just used a gut-feeling to try it out in cyrindical.

@Studentmath cant really spot any obvious mistakes either, sigh

Why in the given bounds x is from 1 to 2 and not 0 to 2, by the way? @N3b

ah, silly me

Well that only made it worse

haha

Where are you computing it?

Maple

So the bounds are either wrong in yours or in mine..

Which means they're wrong in mine.

@Studentmath Nah

That some strong program.

I can't see any faulty in your bounds and they're rather direct unlike mine - the result is different as it seems, so one has to be wrong.. no?

That's how you get polynomials in sage nb

@Studentmath YEah

Probably with mine then as again, yours are rather direct..

Try for a second with x going from 0 to 1 instead of 0 to 2, if you can bother

@r9m It just came to mind another way to that question. When I find some time to dedicate to it, I'll try to put it on paper.

@Chris'ssis Cool !! :D (y)