How is answering a question possible after even question closed? I just saw a bizarre situation on Stackoverflow.  question was closed at 14:36:35 but   at 14:36:39  How is this possible? Closing a question take a few seconds?
How was this answer posted after this question was closed? Question:   Answer:   The question was closed at 11:57:57 (according to the hover-over-"x-mins-ago" bar) and the answer was posted at 12:16:35. It's a fairly lengthy answer, so it's possible that it was started to be written before it was closed but I swear I've started to answer a question then I got a banner along the top saying "this question has been closed" and the answer was no longer post-able.
Why can't the indefinite integral $\int\frac{\sin(x)}{x}\mathrm dx$ be found? I came across a list of functions in my calculus textbook whose indefinite integral cannot be found. It was written that the integral $$\int \frac{\sin(x)}{x} dx$$ cannot be evaluated without any explanation as to why.  I did some research over the internet and found out that the definite integral $$\int_{0}^{\infty} \frac{\sin(x)}{x} dx$$ can be evaluated using Laplace transformation and is equal to $\pi /2$. But I still couldn't find answer to my original question. I read somewhere that the integral cannot be expressed using 'elementary functions'. A little help is appreciated, I'm in Calc 1 going advanced than my course but I am sorry if my post shows lack of research. Thank you! App version: 1.0.35 Device: Nexus 7 Problem: Users with weird/unusual name won't display on the Android app, there will just be a blank space where the username should be. For example,  user is showing as:   On a question:   On their profile: Proof of $\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1}$ It's a standard result that given $X_1,\cdots ,X_n $ random sample from $N(\mu,\sigma^2)$, the random variable $$\frac{(n-1)S^2}{\sigma^2}$$ has a chi-square distribution with $(n-1)$ degrees of freedom, where $$S^2=\frac{1}{n-1}\sum^{n}_{i=1}(X_i-\bar{X})^2.$$ I would like help in proving the above result. Thanks. How to execute two mysql queries as one in PHP/MYSQL? Generalized Tube Lemma Why do shell script comparisons often use x$VAR = xyes? Proving that if $G$ has a Hamiltonian circuit, then the line graph $L(G)$ also has a Hamiltonian Circuit I have a graph G = (V, E). I know that the line graph L(G) of G is defined as follows: each vertex in L(G) corresponds to an edge in G, and two vertices are connected by an edge in L(G) if and only if the corresponding edges in G are adjacent.  Now I am trying to (a) prove that if G has a Hamiltonian circuit, then L(G) also has a Hamiltonian circuit, and (b) give an example of a graph G such that G does not have a Hamiltonian circuit but L(G) does.  However, I'm extremely stuck on how to do this, and any help would be greatly appreciated. Thanks so much! let's say that I have a following file structure:  ~/DIR1 -fileA -DIR2 --fileB   Then, being in ~, I run this script:  cp DIR1 NEWDIR2   And just an error happens:  cp: omitting directory ‘DIR1’   I understand why nothing from DIR1 gets copied (because I didn't use -r switch that would enforce recursion) but I'd expect the DIR1 folder itself copied to NEWDIR2 (so practically a creation of a new "NEWDIR2" in ~ or a creation of ~/NEWDIR2/DIR1).  Could someone explain to me why is my expectation wrong? Anime about a boy and a girl who ride ostrich-like creatures through a valley I can not remember much but I have had this film in my head for years I searched everything I can remember on every website I can think of.  I don't remember the exact story but I'll list everything about it can   Apocalyptic future possibly Two main characters: a boy and a girl riding ostrich-like creatures through a valley An old blind lady that senses things Crashed spaceship looking like a submarine Giant creatures looks like yaks with blue eyes, whose eyes turn red when something is about to happen The old lady says "Some say they went to the stars" while looking at the spaceship The two main characters do something and their eyes turn blue in the distance and the village cheers   This film is at least ten years old and I would appreciate it so much if you knew anything about it, or could help me find the title. It's easy to set inline CSS values with javascript. If I want to change the width and I have html like this:  &lt;div style="width: 10px"&gt;&lt;/div&gt;   All I need to do is:  document.getElementById('id').style.width = value;   It will change the inline stylesheet values. Normally this isn't a problem, because the inline style overrides the stylesheet. Example:  &lt;style&gt;    #tId {       width: 50%;    } &lt;/style&gt;  &lt;div id="tId"&gt;&lt;/div&gt;   Using this Javascript:  document.getElementById('tId').style.width = "30%";   I get the following:  &lt;style&gt;    #tId {       width: 50%;    } &lt;/style&gt;  &lt;div id="tId" style="width: 30%";&gt;&lt;/div&gt;   This is a problem, because not only do I not want to change inline values, If I look for the width before I set it, when I have:  &lt;div id="tId"&gt;&lt;/div&gt;   The value returned is Null, so if I have Javascript that needs to know the width of something to do some logic (I increase the width by 1%, not to a specific value), getting back Null when I expect the string "50%" doesn't really work.  So my question: I have values in a CSS style that are not located inline, how can I get these values? How can I modify the style instead of the inline values, given an id? nginx open reverse proxy? Somehow, and I'm not sure how, we have configured an nginx reverse proxy that is acting as an open proxy.  The log files tells us the matching requests are going against the following conf file:  map $http_upgrade $connection_upgrade {         default upgrade;         ''      close; }  access_log      /var/log/nginx/access.p.log; error_log       /var/log/nginx/error.p.log;  proxy_next_upstream     error timeout invalid_header http_500 http_502 http_503 http_504; proxy_buffers           8 32k; proxy_buffer_size       64k; proxy_http_version      1.1; proxy_set_header        Host            $host; proxy_set_header        X-Real-IP       $remote_addr; proxy_set_header        X-Forwarded-For $proxy_add_x_forwarded_for; proxy_redirect          off; proxy_set_header        Upgrade         $http_upgrade; proxy_set_header        Connection      $connection_upgrade;  server {         listen          80;         server_name     ~first.*\.second\.com;          location / {                 resolver                172.16.1.1 172.16.1.2;                 proxy_pass              http://$host;                 proxy_read_timeout      7200s;         } }  server {         listen          443;         server_name     ~first.*\.second\.com;         ssl             on;          location / {                 resolver                172.16.1.1 172.16.1.2;                 proxy_pass              https://$host;                 proxy_read_timeout      7200s;         } }   The top-level conf file looks like this:  user nginx; worker_processes 8; pid /var/run/nginx.pid;  events {         worker_connections 4096;         # multi_accept on; }  http {      ##     # Basic Settings     ##      sendfile on;     tcp_nopush on;     tcp_nodelay on;     keepalive_timeout 65;     types_hash_max_size 2048;     # server_tokens off;      # server_names_hash_bucket_size 64;     # server_name_in_redirect off;      include /etc/nginx/mime.types;     default_type application/octet-stream;      ##     # Logging Settings     ##      access_log /var/log/nginx/access.log;     error_log /var/log/nginx/error.log;      ##     # Gzip Settings     ##      gzip on;     gzip_disable "msie6";      # gzip_vary on;     # gzip_proxied any;     # gzip_comp_level 6;     # gzip_buffers 16 8k;     # gzip_http_version 1.1;     # gzip_types text/plain text/css application/json application/x-javascript text/xml application/xml application/xml+rss text/javascript;      ##     # nginx-naxsi config     ##     # Uncomment it if you installed nginx-naxsi     ##      #include /etc/nginx/naxsi_core.rules;      ##     # nginx-passenger config     ##     # Uncomment it if you installed nginx-passenger     ##      #passenger_root /usr;     #passenger_ruby /usr/bin/ruby;      ##      include /etc/nginx/conf.d/*.conf;     #include /etc/nginx/sites-enabled/*;   }  what here is causing this? What's the difference between passing by reference vs. passing by value? Prove that ${x dy - y d x\over x^2 + y^2}$ is not exact Is there a way to show that $\sqrt{p_{n}} &lt; n$?  In , I show that $f_{2}(x)=\frac{x}{ln(x)} - \sqrt{x}$ is ascending, for $\forall x\geq e^{2}$. As a result, $\forall n \geq 3$ $$\frac{p_{n}}{ln(p_{n})} - \sqrt{p_{n}}\leq \frac{p_{n+1}}{ln(p_{n+1})} - \sqrt{p_{n+1}}$$ Also (and as a result), $\forall n \geq 3$ $$ \frac{p_{n}}{ln(p_{n})} - \sqrt{p_{n}} &gt; 0$$ Or $$ \frac{\pi (p_{n})}{p_{n}/ln(p_{n})} &lt; \frac{\pi (p_{n})}{\sqrt{p_{n}}}$$  According to  $$\displaystyle\smash{\lim_{n \to \infty }}\frac{\pi (p_{n})}{p_{n}/ln(p_{n})}=1$$ Or, $\forall \varepsilon &gt;0$, $\exists N(\varepsilon )$: $\forall n&gt;N(\varepsilon )$ $$1- \varepsilon &lt; \frac{\pi (p_{n})}{p_{n}/ln(p_{n})} &lt; 1+ \varepsilon$$ Or $$1- \varepsilon &lt; \frac{\pi (p_{n})}{p_{n}/ln(p_{n})} &lt; \frac{\pi (p_{n})}{\sqrt{p_{n}}}$$ As a result $\forall \varepsilon &gt;0$, $\exists N(\varepsilon )$: $\forall n&gt;N(\varepsilon )$ $$(1 - \varepsilon ) \cdot  \sqrt{p_{n}} &lt; \pi (p_{n}) = n$$  But this is not enough.  Interestingly,  is true iff function $f_{4}(x)=\pi (x) - \sqrt{x}$ is strictly ascending ($x &lt; y \Rightarrow f(x) &lt; f(y)$) for prime arguments.  If $f_{4}(p_{n}) &lt; f_{4}(p_{n+1})$ then $$\pi (p_{n}) - \sqrt{p_{n}} &lt; \pi (p_{n+1}) - \sqrt{p_{n+1}}$$ Or $$\sqrt{p_{n+1}} - \sqrt{p_{n}} &lt; \pi (p_{n+1}) - \pi (p_{n}) =1$$  And vice-versa, if $$\sqrt{p_{n+1}} - \sqrt{p_{n}} &lt; 1$$ Then $$-\sqrt{p_{n}} &lt; -\sqrt{p_{n+1}} + 1$$ Or $$\pi (p_{n})-\sqrt{p_{n}} &lt; \pi (p_{n}) + 1 -\sqrt{p_{n+1}} = \pi (p_{n+1}) -\sqrt{p_{n+1}}$$  So, if Andrica's conjecture is true then $\forall n \geq 3$ $$\pi (p_{n})-\sqrt{p_{n}} &gt; 0$$ Or $$\sqrt{p_{n}} &lt; \pi (p_{n})= n$$ Can open sets and closed sets of $\mathbb{R}^n$ be homeomorphic? Positive euphemism for "harped on" How can I replace harped on with a more positive expression?  The production manager harped on the new quality assurance regulations for nearly an hour. What does --shell-escape do? I stumbled upon an example, which needed to be compiled with the additional option --shell-escape. Using this option it worked just fine, but I'm curious:     Why or when is this option needed and what does it actually do? Limit of $L^p$ norm when $p\to0$ Let ($\Omega$, $\cal{F}$, $\mu$) be a probability space and $f\in L^1(\Omega)$. Prove that  $$\displaystyle\lim_{p\to 0} \left[ \int_{\Omega}|f|^pd\mu \right]^{\frac{1}{p}}=\exp \left[ \int_{\Omega}\log|f| d\mu  \right],$$  where $\exp[-\infty]=0$. To simplify the problem, we may assume $\log|f|\in L^1(\Omega).$ How can I add a right-click desktop menu entry to create a text file to Gnome 3 in Ubuntu 16.04.02? The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$ How to calculate: $$\int_0^\infty \frac{x \sin(x)}{x^2+1} dx$$ I thought I should find the integral on the path  $[-R,R] \cup \{Re^{i \phi} : 0 \leq \phi \leq \pi\}$.  I can easily take the residue in $i$ $$  Res_{z=i} \frac{x \sin(x)}{x^2+1}  \quad = \quad \frac{i (e^{ii}-e^{-ii})}{2i}  \quad = \quad \frac{i(\frac1e-e)}{2i} \quad = \quad \frac1{2e}-\frac e2 $$ I know that the integral on $[-R,R]$ will get nearby the real value of $ \frac12\int_0^\infty \frac{x \sin(x)}{x^2+1} dx$. That means that I'm done if I show that the integral on the other part of the path will be small, here is an attempt to do so:  $$ \left|\frac{x \sin(x)}{x^2+1} \right|  \quad \leq \quad  R \cdot \frac{|\sin x|}{R^2-1} $$ I could rewrite $\sin x$ but it becomes nasty. Can you help me with this?