@Anastasiya-Romanova: It is really easy to say "I'd never do anything like that". Believe me, there was an age when I was convinced I would never want to kiss a girl. Or drink beer. People change as they become older. Completely absurd things are more likely to happen, sometimes.
@Anastasiya-Romanova: They gave him detention plus cleaning bathrooms. Whilst it does not fix what he has done, he will hopefully realise that what he did was wrong.
@Sawarnik: What kind of hints are you looking for? She was at my flat yesterday. Does that help?
@Sawarnik: I only have a bigger brother, and we used to beat each other up. I'd do the same with you if you were my smaller brother, if that's what you want?
What real analysis tools would you recommend me for getting the closed form of the integral below?
$$\int_0^{\infty} \frac{\log(x)}{\cosh(x) \sec(x)- \tan(x)} \ dx$$
@JasperLoy: You know, when I was younger, I was in love with a girl in my class. One time, we were on some sort of school trip and there were too few pillows, so I gave her one I brought with me because my mother had anticipated a pillow-shortage. I would sniff at it every day after the school trip because I loved her smell so much. Unfortunately, at some point, my mother decided to wash the cover when I was in school. I was devastated when I found out. :-(
How to compute the following integral
\begin{equation}
\int_0^\pi\frac{\cos nx}{a^2-2ab\cos x+b^2}\, dx
\end{equation}
I have been given two integral questions by my teacher. I cannot answer this one. I have also searched the similar question here but it looks like nothing is similar so I ...
@UserX I myself find this question hard to answer. My brother is very hard to define and understand (at least to me). Of course, he loves math like me.
@Huy Oh ok good. I thought you haven't seen her for a while. "Wow I have not seen you for almost 10 years!". "By the way, when I was 13 I sniffed a pillow you slept on many times".
@Chris'ssis re : $\int_0^{\infty} \frac{\log(x)}{\cosh(x) \sec(x)- \tan(x)} \ dx$ .. the log x is spelling trouble .. I don't know how to sum that crazy series with $\log \frac{x}{n}$ (I expanded on $\frac{\cos x}{\cosh x - \sin x}$ in its (trig,exp) seires) .. :O
stuffs crazy ... maybe it can't be done like that .. :O
@Chris'ssis okay .. my idea is $\displaystyle \frac{\cos x}{\cosh x - \sin x} = \sum\limits_{n=0}^{\infty} (a_n \cos nx + b_n \sin nx)e^{-nx}$, where, $a_n = \frac{1}{2i}(i^n + (-i)^n)$ and $b_n = \frac{1}{2i}(-i^n+(-i)^n)$ ...
after that I want to evaluate .. $\displaystyle \int_0^{\infty} e^{-x}(\sum\limits_{n=0}^{\infty}\frac{1}{n}(a_n\cos x + b_n\sin x)\log \frac{x}{n})\,dx$
@TedShifrin Heya. Three of the four I've just looked at are reasonable, first edits adding sensible tags to two new questions, one extending his own answer for the first time. The fourth smells a bit, but seems defensible. I'll wait with flagging for worse edit-spamming.
@r9m you might like this one (I have an attitude as described here, that's why I succeded in many very tough taks - sometimes they were integrals, series and limits :) )
@Mike: I don't really have one, but it's definitely not Petersen. Spivak is long-winded, but has good stuff. Kobayashi-Nomizu is good, when you know what you're doing. Chern's book from China has some nice stuff (moving frames approach, which I usually teach). There is the 3-volume Russian book, and some French texts, too, which I have on my shelf but don't remember the authors of. I don't follow any text when I teach ... But also remember I'm more interested in complex geometry.
@TedShifrin The reason I ask is because I've come to the conclusion in your first sentence ;) What do you mean by "when I know what I'm doing"? And is doCarmo off your list for a reason?
Well, @Sawarnik, I get accused of stalking "young boys" on MSE ... by an idiot, to be sure.
Yao is one of the differential geometry stars from the 70's to now ... his work is on the analytic side of differential geometry and much of it is quite technical, but deep.
It's not mine, either, @Mike. But to some people, the differential forms stuff I do for pages is no different. To me, it is :P Because to me, it's all totally intuitive.
What real analysis tools would you recommend me for getting the closed form of the integral below?
$$\int_0^{\infty} \frac{\log(x)}{\cosh(x) \sec(x)- \tan(x)} \ dx$$
@Chris'ssis: I appreciate your words. I know I shouldn't take them personally, but there are things that even said over the internet by a stranger can hurt a lot.
What real analysis tools would you recommend me for getting the closed form of the integral below?
$$\int_0^{\infty} \frac{\log(x)}{\cosh(x) \sec(x)- \tan(x)} \ dx$$
How to compute the following integral
\begin{equation}
\int_0^\pi\frac{\cos nx}{a^2-2ab\cos x+b^2}\, dx
\end{equation}
I have been given two integral questions by my teacher. I cannot answer this one. I have also searched the similar question here but it looks like nothing is similar so I ...
