calculate some integral of sum of two variables
Proving the sum of two independent Cauchy Random Variables is Cauchy
I have a list of dictionaries and want each item to be sorted by a specific value. Take into consideration the list: [{'name':'Homer', 'age':39}, {'name':'Bart', 'age':10}]  When sorted by name, it should become: [{'name':'Bart', 'age':10}, {'name':'Homer', 'age':39}] On Windows 7 can one make UAC on an admin account prompt for the password, just like a limited account? I am one of the very few who likes the security of UAC and so I have the UAC set to "Always Notify" on my Admin account. But I would be even happier if the system would prompt me for a password, when notifying me.  I can get what I want by adding a second non-admin user and using that account.  But somehow it seems wasteful to have two accounts set up when I will always use the non-admin account day-to-day.  So I am wondering if there is any setting that would cause an Admin account to behave password-prompting-wise as a standard account? Convert string to Title Case with JavaScript How to prevent updating of a specific package? I frequently need to check which packages are installed, and I use the following command:  dpkg -l | grep foo  which gives the following output  Desired=Unknown/Install/Remove/Purge/Hold | Status=Not/Inst/Cfg-files/Unpacked/Failed-cfg/Half-inst/trig-aWait/Trig-pend |/ Err?=(none)/Reinst-required (Status,Err: uppercase=bad) ||/ Name                       Version         Description ii   foo                       &lt;version&gt;         &lt;description&gt;    What does the ii mean?  What other flags are there? How to read the flags? (because the explanation is quite complicated, IMO)   Thanks. How do I get attention for old, unfixed bug reports and feature requests without official responses here on Meta? C# Unsafe/Fixed Code Can you cast a spell learned from the Magic Initiate feat using spell slots? Say I play a wizard who learns cure wounds by taking the Magic Initiate feat. Could I cast that spell using the Wizard's spell slots? This is a homework problem and I'm having trouble just getting a basic understanding.  I understand that $S_6$ is a symmetric group of degree $6$.  I'm not sure how to start looking for elements. Setting nautilus-open-terminal to launch Terminator rather than gnome-terminal Separate labels in cases The error: "mount: only root can do that" while mounting a partition Get display resolution from the command line for Linux Desktop I'm looking for a method of reporting display resolution. I want to set up scripts to launch rdesktop, and I want to launch it on several machines with different resolutions, so I want a way to dynamically determine it. Ohm's law states that  electric current is directly proportional to voltage provided that physical conditions like temperature remain constant i.e. $$V = IR$$  On the other hand,  $$\text{Power = Voltage} \times \text{Current}$$  So here it seems that the higher the voltage, the lower the current, provided that the power remains constant (i.e. current is inversely proportional to the voltage here which is against Ohm's Law.).   Now my question is how do physicists explain this apparent contradiction? Or maybe this not a contradiction because I am analysing things incorrectly?   P.S.: I am a tenth grade student so please refrain from the usage of highly complicated terminologies in your answers. I was playing around with some integrals and noticed that some integrals of the form:  $$I(a,b,c)=\int_a^\infty \frac{\arctan(x+b)}{x^2+c}dx$$ Does have a closed form. I am trying to find for what constant $c$ will this work. In case you wonder why only $c$ is problematic, I will try to show by an example.  $$I=I(1,3,16)=\int_1^\infty \frac{\arctan(x+3)}{x^2+16}dx$$ Let's start by letting $x-1=t\,$ thus: $$I=\int_0^\infty \frac{{\arctan(\color{blue}{t+4})}}{t^2+2t+17}dt$$ With $\displaystyle{t=\frac{17}{y}\rightarrow dt=-\frac{17}{y^2}dy}$ $$I=\int_0^\infty \frac{{\arctan\left(\color{red}{\frac{17}{y}+4}\right)}}{\left(\frac{17}{y}\right)^2 +\frac{34}{y}+17 }\frac{17}{y^2}dy\overset{y=t}=\int_0^\infty \frac{{\arctan\left(\color{red}{\frac{17}{t}+4}\right)}}{t^2+2t+17}dt$$ $$2I=\int_0^\infty \frac{{\arctan(\color{blue}{t+4})+{\arctan\left(\color{red}{\frac{17}{t}+4}\right)}}}{t^2+2t+17}dt$$ $${\arctan(\color{blue}{t+4})+{\arctan\left(\color{red}{\frac{17}{t}+4}\right)}}=\arctan\left(\frac{\color{blue}{t+4}+\color{red}{\frac{17}{t}+4}}{1-(\color{blue}{t+4})\left(\color{red}{\frac{17}{t}+4}\right)}\right)$$ $$=\arctan\left(\frac{x^2+8x+17}{x}\frac{x}{-4(x^2+8x+17}\right)=\pi-\arctan\left(\frac14\right)$$ Above follows since the original integral is positive so we take $\arctan(-x)$ as $\pi-\arctan x $ and therefore getting a negative answer will not be an issue. $$I=\frac12 \left(\pi -\arctan\left(\frac14\right)\right)\int_0^\infty \frac{1}{t^2+2t+17}dt$$ Well, now the inner integral is not hard to compute and the final answer happens to be: $$I=\frac12 \left(\pi -\arctan\left(\frac14\right)\right)\frac14\arctan\left(\frac{t+1}{4}\right)\bigg|_0^\infty =\frac{\pi^2}{16}-\frac{3\pi}{16}\arctan\left(\frac14\right)+\frac18\arctan^2\left(\frac14\right) $$ There are more examples that I found by checking and try such as:  $$I(1,2,9)=\int_1^\infty \frac{\arctan(x+2)}{x^2+9}dx$$ $$I(2,1,6)=\int_2^\infty \frac{\arctan(x+1)}{x^2+6}dx$$ $$I(2,2,13)=\int_2^\infty \frac{\arctan(x+2)}{x^2+13}dx$$ And so on... All those can be solved by the same method: First substitute $x-a=t$, then let $t=\frac{\alpha}{y}$, where $\alpha$ is the "free of x" coefficient from the denominator.   The problem is that I tried more than $100$ combinations to get those integrals which is not that nice. How can we "smartly" find $c$ so that $I(a,b,c)$ is evaluable by symmetry? Or put in other word what should be $c$ if one wants to compute by symmetry $I(7,13,c)$? What causes the portraits of Wizards to behave interactively? Does J.K. Rowling address how the interactive portraits work? Would a portrait painted after a Wizard/Witch died become interactive, or does the painting of the portrait have to take place during the Wizard/Witches lifetime? Installing .pkg with terminal ? Is it possible to install a .pkg using a terminal ? (I wanted to install an app through ssh). Problem with sudo apt get update: The repository cdrom... does not have a Release file Every time I try update (using sudo apt-get update) my Ubuntu I get this problem:  W: The repository 'cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1) xenial Release' does not have a Release file. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use. N: See apt-secure(8) manpage for repository creation and user configuration details. W: The repository 'ppa.launchpad.net/kirillshkrogalev/ffmpeg-next/ubuntu xenial Release' does not have a Release file. N: Data from such a repository can't be authenticated and is therefore potentially dangerous to use. N: See apt-secure(8) manpage for repository creation and user configuration details. E: Failed to fetch cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1)/dists/xenial/main/binary-amd64/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs E: Failed to fetch cdrom://Ubuntu 16.04 LTS _Xenial Xerus_ - Release amd64 (20160420.1)/dists/xenial/main/binary-i386/Packages  Please use apt-cdrom to make this CD-ROM recognized by APT. apt-get update cannot be used to add new CD-ROMs E: Failed to fetch ppa.launchpad.net/kirillshkrogalev/ffmpeg-next/ubuntu/dists/xenial/main/binary-amd64/Packages  404  Not Found E: Failed to fetch ppa.launchpad.net/kirillshkrogalev/ffmpeg-next/ubuntu/dists/xenial/main/binary-i386/Packages  404  Not Found E: Some index files failed to download. They have been ignored, or old ones used instead.   How can I fix it? I use Ubuntu 16.04 LTS Is there a possibility to search when the embedded txt file was created in the word document? I'm working in Word 2010 and the extension of the document is simple: .doc  It was inserted using the Word options:  Insert -&gt; Object -&gt; Create from file -&gt; Insert as icon   Thank you, I already tried the right click and properties option, but the problem with it, that it shows only the current date for all of the 3 options (created/modified/accessed).           I also tried to get the timestamp but it is inactive when I'm on the txt object.   Sorry not to mention it before: Thank you all of you here for the help and support it is really appreciated. CSS alignment issues on close reasons with pending votes "Should" word in italics is shifted down in the vote-to-close popup when there is at least one pending close vote.  Just have a look at this:        Now without close votes:        So the issue occurs when there is a close vote on it. It doesn't look good.    Tested on Chrome 27.0.1453.116 m, Windows XP. And it looks fine on Firefox 21.0 and Opera 12.02 (Windows XP)  Here is an example of a slightly different but obviously related problem in Windows 7 SP1 and Firefox 21.0:    This seems to have something to do with how line-height and/or margin attributes are being interpreted.  Can this be fixed?