Evaluate $\int_{0}^{\frac{\pi}{2}} x\ln(\tan(x))dx $
How to evaluate $\int_{0}^{\pi }\theta \ln\tan\frac{\theta }{2} \, \mathrm{d}\theta$
How could I write a command in LaTeX, so after compiling it will be shown as a text in PDF and not executed?  For Example, I would write \it This is how you write in italic and the compiled pdf would contain the exact same text between the quotation marks without \it being executed. Auto delete spam email from a domain in Gmail Proof: Every convergent sequence of real numbers is bounded Should Stack Exchange have a spam filter? (Does it already and I’m not aware?) Of course spam posts should be flagged, and if they come up in review, rejected.  Over on Mi Yodeya during the past 24 hours I’ve helped delete and reject four spam posts through the review queue, and I can only imagine that others were posted over the course of the night. To clarify, I’m referring to edits and answers that were about 99.274% words that I don’t think any decent person would use in everyday discussions, even if someone got them really angry.   Thing is, if the only thing we can do as a community is delete his posts/reject his edits, and as moderators to ban his account, can’t he just create a new account? Further, some of these posts . Maybe the mods can ban his IP address? I’m not one, so I have no idea what kind of power they wield in that respect. But he can always just get a new computer.   I don’t have the numbers to see what this is like on other sites, but I know this doesn’t happen often on Mi Yodeya. I wonder, then, whether this is the optimal solution, or whether an automatic spam filter be put into place - say, a new review queue that automatically deletes posts or rejects edits that can then be voted on whether to be reposted if it’s a false alarm. Perhaps it can be automatically triggered by certain keywords (like ****, %$#^, or @$+^).   Now, all of these posts that I voted to delete/reject came up in Suggested Edits and First Posts. Maybe such edits would show up in Low Quality in general, and that just wasn’t the case here because of precedence rules. I don’t know. But perhaps the above would be a better solution, if this is even as big of a problem as I’m making it out to be. Storing C++ template function definitions in a .CPP file Input password into SSH without typing Gmail App in my Android device shows correctly all the labels that I created using Gmail through web interface.  Can I create new labels in Gmail on Android device using Gmail App?   Also, ideally, once I create these new labels in Gmail App, I obviously should be seeing the same in Web Interface of Gmail too (Sync!!).  Any ideas? How do I check if a string contains a specific word? MLE for Poisson-binomial distribution I am looking for the maximum likelihood estimator (MLE) for the .  I understand the derivation of the MLE for a  and a , but I am unable to derive the MLE equation for the Poisson-binomial distribution. I get double question marks when referring to labels inside figures I have some charts embedded in figures, and I want to be able to refer to them easily using the "Figure x" notation. I'm doing it like this (in this order):  \documentclass[12pt,letterpaper]{article}  ...  \section*{Results} ...we performed a linear regression to obtain a standard curve  (Figure~\ref{0:stdcurve})....  \pagebreak \section*{Results (Graphs)} \subsection*{Construction of Standard Graph for PNP} \begin{figure}[h]   % Figure 1     \centering     \includegraphics[scale=1]{kinematics-res/graph0-1}     \caption{The standard curve for PNP.}     \label{0:stdcurve} \end{figure}   However, instead of getting the output "...to obtain a standard curve (Figure 1)...", I just get "...to obtain a standard curve (Figure ??)..."  I also noticed that the PDFLaTeX compiler is generating warnings saying that it couldn't find the reference of the name 0:stdcurve. Why am I getting these warnings? To quantize a scalar field theory with the action:  $$S=\int \mathrm d^Dx\mathscr{L}(\phi,\partial_\mu\phi)=\int \mathrm dx^0L(\phi,\partial_0\phi)$$  we promote $\phi(\vec{x})$ and $\pi=\frac{\delta L}{\delta(\partial_0\phi)}=\pi(\vec{x})$ to be field operator at fixed time $x^0$ (with the canonical commutation relation $[\phi(\vec{x}),\pi(\vec{y})]=\delta^{D-1}(\vec{x}-\vec{y})$), then we use the classical equation of motion to find $\phi$ and $\pi$ at all time.  What principles lie behind this? Why can we assume that the field operators satisfy the classical equation of motion?    By example if we have a classical theory with $S=\int \,\mathrm dtL(\phi,\partial_t\phi)$, momentum $\pi=\frac{\delta L}{\delta(\partial_t\phi)}$ hamiltonian $H=\pi\phi-L$, the classical equation of motion is:  $$\frac{\mathrm d\phi}{\mathrm dt}=\frac{\delta L}{\delta(\partial_t\phi)}$$  When we do the canonical quantization, we promote $[\phi,\pi]=\delta(\vec{x}-\vec{y})$ and the equation of motion for $\phi$ is $$\frac{\mathrm d\phi}{\mathrm dt}=i[H,\phi]$$  Why should $i[H,\phi]$ has the same form as $\frac{\delta L}{\delta(\partial_t\phi)}$? This fact comes from where? What is the best way to add options to a select from a JavaScript object with jQuery? Show that if terms of a series have ratio less than the ratio of convergent series, then the series converges We have two infinite series $\sum a_n $ and $\sum b_n$, such that $a_n &gt; 0,\ b_n &gt; 0$ and $a_{n + 1}/a_n \leq b_{n + 1}/b_n$ for all $n$. Show that if $\sum b_n$ converges, then $\sum a_n$ also converges.   Any hints on how to prove this? I can sort of picture why this must be true, but I'm not sure how to prove this rigorously. I'm not sure using the ratio test would help here.. In a batch file I need to extract a month, day, year from the date command.  So I used the following, which essentially parses the Date command to extract its sub strings into a variable:  set Day=%Date:~3,2% set Mth=%Date:~0,2% set Yr=%Date:~6,4%   This is all great, but if I deploy this batch file to a machine with a different regional/country settings, it fails because month, day and year are in different locations.   How can I extract month, day and year regardless of the date format? At what point is a creature's toughness calculated? If I have  where I can sacrifice a creature and put X 1/1 token creatures onto the battlefield, where X is the sacrificed creature's toughness.  If I have a creature that is 4/4 and cast  to give it +3/+3 then sacrifice it? Do I get 4 tokens or 7?  Also what if my 4/4 creature was dealt 2 combat damage before I sacrificed it? Do I get 2 or 4 creatures?  Finally, what about counters? If my 4/4 had a +1/+1 do I get 4 or 5 tokens? biblatex: Cite commands with the same author prints authors name twice I'm using biblatex 1.4b, and Biber 0.9. However, I think the problem is with my settings, not with the versions of those programs.  I'm trying to cite a single author, and produce their name, followed by the dates of two papers, using the authoryear-ibid style, and natbib compatability. Here's my biblatex preamble:  \usepackage[style=authoryear-ibid,natbib=true,backend=biber]{biblatex}   What I want is for the following command: The works by \citet{Blau81, Blau88} ... to produce: The works by Blau (1981; 1988) ... however, what I'm getting is: The works by Blau (1981); Blau (1988)...  I know that biblatex knows they're the same author, since in the bibliography they fall under the same name (i.e. after the first instance of the name, there's just a dash instead of the name)  What am I doing wrong here? I've also tried it with the commands \cite and \cites, and neither produces what I want.   (crossposted with comp.text.tex) List of Ubuntu Versions with Corresponding Linux Kernel Version how to Query parent to child I have process in salesforce in such a way opportunity we can relate this opportunity to this lookup field parent_opportunity__c . Which relates opportunity to other parent opportunity.  I want to write a query parent to child :  select id,(select id from opportunity where parent_opportunity__c!=null) from opportunity where parent_opportunity__c=null   I have worked with different scenarios i cant able to crack it  select id,name,(select id,name from parent_opportunity__r) from opportunity this is showing error and   select id,name,(select id,name from opportunity) from parent_opportunity__c this is also error Is there a website listing the location of all the Windows 10 lock screens? Windows 10 has an extensive collection of lock screen photos, many of which have  here on Travel.SE.  Is there a website which lists the location of all of these photos? I imagine Microsoft has purchased an official license, so they should have a record about the photographer and the place where the photo was taken. Why is polyploidy lethal for some organisms while for others is not?