Studying for complex analysis, I stumbled upon this problem. Evaluate $$\int_{0}^{\infty} \frac{\log(1+x^2)}{1+x^2}~dx.$$ So the integrand suggests that I need to use the function $f(z)=\frac{\log 1+z^2}{1+z^2},$ which has two branch points and two simple poles at $z=i$ and $z=-i,$ which lead me to use a semi-circle contour in the right-halfplane having branch cuts at $i$ and $-i.$ But then the process become too lengthy. Is there any other method to go by doing the problem. I was thinking of making a substitution and reducing this to a form to use Gamma function, but wasn't successful. Any help is appreciated.
How would I go about evaluating this integral? $$\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx.$$ What I've tried so far: I tried a semicircular integral in the positive imaginary part of the complex plane, excluding the negative real axis, but had trouble calculating the residue at $z=i$ (perhaps there is a way of doing this that I don't know of). After that didn't work, I tried a rectangular box integral from $\epsilon$ to $R$, from $R$ to $R+i/2$, from $R+i/2$ to $-S+i/2$, from $-S+i/2$ to $-S+i\epsilon$, from $-S+i\epsilon$ to $-\epsilon+i\epsilon$ and finally a semicircle around the origin, radius $\epsilon$.   Any help would be appreciated.
Does one need a visa to transfer between two airports during a transit through the Schengen area? I am an Indian citizen travelling from New York to Delhi with a layover in Paris where I need to transfer between Paris Orly Airport (ORY) and Paris Charles de Gaulle Airport (CDG).  Do I need to have a visa to make this transfer?  I didn't notice that while booking the ticket. How can I delete all files from a directory when it reports "Argument list too long" Optimal tiling of polygon using ArcGIS Desktop? I am trying to tile a polygon with a minimal number of fixed sized squares.  Currently I am creating a fishnet over my polygon then spatially joining the squares that intersect the polygon. This is not optimal.  Also note the squares can be shifted vertically/horizontally but not rotated.  My end goal: The polygon represents a clipped image and I want a tiling of the clipped image. Where each tile is 300px by 300px. Some overlap is fine if that makes the problem easier.  Current    Manually optimized    Are there any tools or algorithms that would help with this? I am proficient with Python and ArcMap.  The polygon was created from line features so I also have access to those segments. Maybe that would will help for generating the squares.  The entire polygon must be covered. Is there a general rule for determining the direction of tension force? Tension, for me, is a tricky thing.  After finishing a related chapter of my book and watching a video, I still can't get a hang of it.  Here is a situation:   My knowledge is that tension, just like normal force, happens in  just the same way, but with the difference of a string attached.  It is understandable that in the picture, the string attached to the hanging mass has a tension directed upward, because it's weight is directed downward. (Action and reaction)  But what intrigues me is that applying the same logic, the horizontal mass is being pulled to the right, it would have been understandable if the tension is directed to the left.   also Can I think of tension as the reaction force when you pull, and normal force when you push?  update If I was to think tension as a reaction force in the first picture for the horizontal mass, then can the frictional force be the action force? (Ehh, I don't think that makes sentence. Friction is always reaction) Recently I have installed an older version of Ubuntu on my old machine. Whenever I try to install any software, I get an error saying it couldn't be found:  $ sudo apt-get install vlc Reading package lists... Done                Building dependency tree        Reading state information... Done     E: Couldn't find package vlc Radical change of favourite tags doesn't reflect in questions list Why does the logo not show up when signing up for a site and confirming the account? How to check if a column exists in a SQL Server table? Is the Hogwarts Express in the magical or non-magical realm? This question is related to  and explores an apparent inconsistency, given only the Harry Potter movies as source material.  The Hogwarts Express line seems to have an inconsistent existence between magical (invisible to ordinary humans aka muggles) and non-magical (muggle) realms; platform 9-3/4 is clearly hidden from muggles, but in Chamber of Secrets, when Harry and Ron take the car (in the muggle world) to catch up to the train, they make no explicit crossing into a magical realm, suggesting that the train is traveling the muggle world despite its departure from a magical platform.  In which realm (magical or muggle) does the Hogwarts Express exist? How is this apparent inconsistency resolved? Using `\input` to insert a section of a document into another Is there any way one can use \input to insert only a specific section of a document into another? I intend on using this to improve the readability of an article with lots of pgfplots graphs in it, by moving all of my graphs to another file, and using something like \input{file.tex:graph1} to insert each graph where it is needed, rather than have all of them displayed together Short story where time is accelerated and characters have to get back to ship? Looking for a short story where time is accelerated on a planet.  The characters are actually born at the beginning of the story and then grow up quickly and inadvertently learn that their forebears came from a rocket ship nearby.  After having aged to "teenagers" they try to reach the ship?  At some point there is a war between confused aging survivors.  I think it was in a compilation which included a story called "Cousins". Find $ P(Z>X+Y)$ where $X,Y,Z \sim U(0,1)$ independently I'm trying to follow a line in a derivation for $P(Z&gt;X+Y)$ where $X,Y,Z$ are independent continuous random variables distributed uniformly on $(0,1)$.  I've already derived the pdf of $X+Y$ using the convolution theorem, but there's a line in the answer that says:  $P(Z&gt;X+Y) = \mathbb{E}[\ P(Z&gt;X+Y\ |\  X+Y )\  ]$ where $\mathbb{E}$ is the expectation.  I'm not familiar with this result. Could anyone give a pointer to a similar result if one exists?  Thanks. Black screen on boot after AMDGPU-Pro install (16.04) I have been having some screen freezing issues on my new Ubuntu 16.04 system, and have been in the troubleshooting process for this issue. I thought it was a graphics driver problem, as I am running an AMD R9 380x card which was supposed to be fully supported by the open-source AMDGPU driver preinstalled with 16.04, but after looking around online, many people seem to have issues with. I thought the answer would be to install the recently released AMDGPU-Pro driver , following the instructions from . However, when I reboot I am getting a black screen. Is there an easy way to revert my changes back? My machine was semi-functional with the freezing issue but now with no video at all is useless to me. How to proceed? Recursively rename all the files without changing their extensions? How to recursively rename all the files in several layers of subdirectories without changing their extensions?  Below's a toned down version (to save room) of what I've got.  For argument's sake, I want all the files to have the same title, yet retain their original extension. There's never more than a single file per directory, so there's no chance of doubling up.  For simplicity, we'll just call them all foo, followed by their current extension.    So just to clarify: Asset\ 1.pdf, Asset\ 1.png, Asset\ 1@4x.png, Asset\ 1.svg Will become: foo.pdf, foo.png, foo.png, foo.svg And so on in that fashion.    I would typically use parameter expansion and a for loop, like:    for f in */*; do mv "$f" "${f%/*}/foo.${f##*.}"; done     But it's not recursive. So I would prefer to use something with find..-exec or similar.    ~/Desktop/Project/Graphics/ ├── Huge │   ├── PDF │   │   └── Asset\ 1.pdf │   ├── PNG │   │   ├── 1x │   │   │   └── Asset\ 1.png │   │   └── 4x │   │       └── Asset\ 1@4x.png │   └── SVG │       └── Asset\ 1.svg ├── Large │   ├── PDF │   │   └── ProjectAsset\ 2.pdf │   ├── PNG │   │   ├── 1x │   │   │   └── ProjectAsset\ 2.png │   │   └── 4x │   │       └── ProjectAsset\ 2@4x.png │   └── SVG │       └── ProjectAsset\ 2.svg ├── Medium │   ├── PDF │   │   └── ProjectAsset\ 3.pdf │   ├── PNG │   │   ├── 1x │   │   │   └── ProjectAsset\ 3.png │   │   └── 4x │   │       └── ProjectAsset\ 3@4x.png │   └── SVG │       └── ProjectAsset\ 3.svg ├── Small │   ├── PDF │   │   └── ProjectAsset\ 4.pdf │   ├── PNG │   │   ├── 1x │   │   │   └── ProjectAsset\ 4.png │   │   └── 4x │   │       └── ProjectAsset\ 4@4x.png │   └── SVG │       └── ProjectAsset\ 4.svg └── Tiny     ├── PDF     │   └── Asset\ 5.pdf     ├── PNG     │   ├── 1x     │   │   └── Asset\ 5.png     │   └── 4x     │       └── Asset\ 5@4x.png     └── SVG         └── Asset\ 5.svg  30 directories, 20 files When I open the game, the screen stays at the Mojang sign and then crashes. It has something to do with my texture pack, but I can't start the game to change it and it won't let me delete the texture pack folder alone.  I've already deleted the bin and resources folders in the minecraft folder and downloaded the game again. I opened it but the same problem was still there.  How do I properly perform a clean uninstall of the game? The question is to calculate the radius of convergence of $\sum\limits_{n=0}^\infty n!x^{n^2}$.  I dont know how to calculate R.O.C for such type of questions involving $n^2$ as power of x. How do we do this? Any help appreciated. How do I turn off some formats in GeoServer's WMS? I have published a couple of layers on my Geoserver.  To be complaint with the T&amp;C of my data provider, I need to block the access of some of those layers as Vector data. Hence I have already blocked the WFS services on these Layers.  I came to know that even on the WMS service, you can get Vector Data, if you use GeoRSS and some of the .   How do I block GeoRSS, SVG &amp; UTFGrid as formats in the WMS Service? Why is Lightroom not rendering what I see in every other JPG viewer? This is the PATH variable without sudo:  $ echo 'echo $PATH' | sh  /opt/local/ruby/bin:/usr/bin:/bin   This is the PATH variable with sudo:  $ echo 'echo $PATH' | sudo sh /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/X11R6/bin   As far as I can tell, sudo is supposed to leave PATH untouched. What's going on? How do I change this? (This is on Ubuntu 8.04).  UPDATE: as far as I can see, none of the scripts started as root change PATH in any way.  From man sudo:      To prevent command spoofing, sudo   checks ``.'' and ``'' (both denoting   current directory) last when searching   for a command in the user's PATH (if   one or both are in the PATH). Note,   however, that the actual PATH   environment variable is not modified   and is passed unchanged to the program   that sudo executes. I almost always want the profile correct applied, but it's an extra step. Any ideas on how to apply these automatically?