Solving $\int_0^\infty 1/(1+x^4)\,dx$ using elementary high school methods
How can I compute the integral $\int_{0}^{\infty} \frac{dt}{1+t^4}$?
QGIS apply style to shapefile Identify a catastrophic sci fi story written before 1980: ruptured spleen, alien moon base, time and space travel, antimatter tool I read a sci fi short story sometime between 1974-1980 but it may have been written long before that.  I believe it was in a paper back anthology of sci fi stories, but I'm not certain.  I think the protagonist is facing the final climactic conflict when we meet him.  Most of the story is memories and flashbacks.  The first flashback is to his childhood.  He and his younger brother are sled riding.  His brother crashes, ruptures his spleen and dies.  He feels responsible and is wracked with guilt.  Much later, as an adult, he is exploring a long-deserted alien base on the moon.  There are unfamiliar artifacts on the base, including a time-travel device/vehicle, and a tool with an anti-matter tip.  It carves neat holes and eliminates matter simply by moving it through matter.  He accidentally drops the tool, which plummets unimpeded to the center of the moon.  He realizes that over time, it will consume and destroy the moon, which will be catastrophic for Earth.  He uses the time-travel device to travel to the moon at an earlier time so that he can prevent himself from dropping the tool.  He makes bigger problems for himself, forcing him to travel back further and further in time.  He travels so far back that he encounters the original alien inhabitants of the base.  Now we are at the present time in the story.  This is his final conflict, he has to escape, travel forward in time and resolve all of the problems he created.  Unfortunately, the alien inhabitants capture him, and the story ends.  Can anyone identify the story and author? Will links to images be kept permanently when added to a comment and nothing else? I assume, that Stack Exchange have some clean-up subsystem, which deletes all "abandoned" images (stored at i.stack.imgur.com), that is, all of them, that were initially uploaded, but no post is actually having link to them. Am I right?  If such subsystem is implemented and is doing its job on regular basis, then what about following scenario:   Start a new question or answer, anywhere. Hit button and upload an image. Copy generated image's URL  to clipboard. Close tab and drop editing post. Go to question on answer, you actually planned to reply. Post a comment to it and paste copied image's URL from clipboard to comment's body.   Will uploaded image, with URL pasted only to comment, be kept permanent? Does clean-up subsystem (if exitst) take care of checking for image's URLs in comments as well? How to solve this recurrence $T(n) = 2T(n/2) + n\log n$ How can I solve the recurrence relation $T(n) = 2T(n/2) + n\log n$? It almost matches the Master Theorem except for the $n\log n$ part. I'm new to blender and have been studying and starting with low poly modeling. Recently I changed my GPU from a GTX 960 to an RX 580. I uninstalled the drivers and installed new ones using DDU.  Problem: Rendering using OpenCL produces these unwanted lines. The attached image is a product of CPU + GPU render then the GPU only render, respectively. When I render using only the CPU the results are as expected, no unwanted black vertical lines, using only the GPU adds more lines on the image.  Any help is appreciated, thank you! Whenever adding a new wireless network, android seems to forget the network after disabling then re-enabling wifi. I am forced to manually connect to the network and enter the password each time. This also happens with open networks. The problem occurs on any wireless network, at home, work, public networks, etc.  Further inspection on the /data/misc/wifi/wpa_supplicant.conf file shows "disabled=1" added to the end of each network.    click image for larger version  This has been going on for weeks. Any help would be much appreciated.  Phone: Nexus 4 Version: 4.4.4 Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$ What is given?  $$\text{Let P be a prime}$$ $$\text{Let} \space f(x)= 3x+1$$ $$\text{Let} \space g(x)= 6x+1$$  Show that: If there exists $x \in \mathbb{N}$ such that $f(x) = P $ , then there exists a $y \in \mathbb{N}$ , such that $g(y) = P$  What have I tried?   Given the question says 'show that', that leads me to believe I need to do a proof of sorts. I'm guessing it might be a proof by either strong induction, or just induction (or maybe just a direct proof?).  I don't even know how to set this up If $f(x) =$ $3x + 1 = $ prime...for any integer $x$, then there exists an integer $y$ such that $g(y) = 6y + 1 = $ prime?   Any hints or starting points would be greatly appreciated.   $$\text{Thanks in advance!}$$ In Java, what is the best way to determine the size of an object? I have an application that reads a CSV file with piles of data rows.  I give the user a summary of the number of rows based on types of data, but I want to make sure that I don't read in too many rows of data and cause OutOfMemoryErrors.  Each row translates into an object.  Is there an easy way to find out the size of that object programmatically?  Is there a reference that defines how large primitive types and object references are for a VM?  Right now, I have code that says read up to 32,000 rows, but I'd also like to have code that says read as many rows as possible until I've used 32MB of memory.  Maybe that is a different question, but I'd still like to know. How can I make a bash script executable by double clicking just like .exe files in Windows? I tried , but there are two consequences:   the terminal twinkles, disappears, and nothing is done. you must specify to run in terminal in order to work.   I have a script that installs tomcat on an offline PC, including all dependencies of tomcat in the script. I need to make the script work on double clicking like windows since most who use the script will not be familiar with Ubuntu.  Forget the above explanation. I want to make a script that can be run by double-clicking on it, without using the terminal. Anybody knows how? How to flag a typo question I came across  today. In reading the answer and the comments it turns out that the issue was just a simple typo that the OP made. So that being the case I decided that this question probably needs to be closed since this will not be helpful to any future vistors. However, in looking at the flag reasons (I don't have the close ability yet), I don't see a flag that would be appropriate.   I know some of these options might still be influx because of the . However, until a different off-topic flag description is created, how should this be flagged? Or should this not be flagged at all and just allowed to live on or wait for a user with close votes to use a custom off-topic close option? Hisoka hinted that Gon is his treasure and also his prey, but it can't be both, right? Because in the end, he didn't want Gon to die no matter what.  So it's weird that he didn't want Gon to die but also made him his prey to fight till death. Is it sexual for Hisoka or what? I still remember the 'Schwing' thing. Why is OpenJDK 10 packaged as openjdk-11-*? While looking to compile OpenJDK from source, the newest General Availability version () insists on OpenJDK 9 or 10.  JDK 11, however, is not due to be released until .    However, to my surprise, when I do apt search openjdk the result is:  ... openjdk-11-jdk - OpenJDK Development Kit (JDK) ... openjdk-8-jdk - OpenJDK Development Kit (JDK) ...   No OpenJDK 9 or 10!  And wait, is that OpenJDK 11?  Maybe a Beta release?  Nooo....  So I looked at apt show openjdk-11-jdk:  Package: openjdk-11-jdk Version: 10.0.1+10-3ubuntu1 ...   Why has OpenJDK 10 been packaged as openjdk-11-*?? Hyperspace travel is a norm in Star Wars universe. Even small ships have that capability and without this capability galactic-scale economy isn't possible.  My educated estimates say that at any point of time at least billions of ships are in hyperspace across the galaxy. Now, talk about economic hubs like Coruscant during Clone Wars Era. The number of ships arriving here should be enormous. Millions in an hour? If one person small ship can have warping capability, then the number can exceed even billions in a peak hour. You can go shopping on a neighbor planet five times a day or you can live on a cheap planet even if you have a job on Coruscant (there are public transport cabs featured in Rebels TV show in case you aren't rich enough to have own ship).  Now, the famous quote:     "Traveling through hyperspace ain't like dusting crops, boy! Without precise calculations we could fly right through a star or bounce too close to a supernova, and that'd end your trip real quick, wouldn't it?"   That's fine. Calculations prevent you from hitting a star, supernova or planet which are already on map, but how does a ship avoid hitting another ship? Provided that number of ships arriving near a planet is that much high, the probability of two ships jumping to the same co-ordinate can't be zero. In fact, the probability should be very very high.  Is there a central body which controls the traffic by coordinating the hyperspace calculations of different ships? This seems unlikely because everyone seems to go anywhere they want while maintaining the destination privacy (there are countless examples). Or, is there really a traffic control body and those who travel privately actually gamble? Is there any other protocol if not traffic control body?  Has the canon ever addressed it? What about Legends? Question is pretty much in the title: is it possible for an alliance to win as one, instead of a single player being the winner?  And if there is such way, is there a difference between classic and disharmony? How do shock waves form in space? Today my aerodynamics professor mentioned that the equations we were learning for atmospheric shock waves can also be applied by astrophysicists to study black hole-related shock waves in space.  How is this possible? Isn't space too rarefied for shock waves? What is an example application? He mentioned something about the density limit before/after a relativistic shock approaching 6. Average distance between two random points in a square replacement wood threshold insert for metal door I have some late 70's doors and one is missing a threshold insert (the adjustable wood kind), anybody know of where one could by just the "wood strip" that goes in and screws down (there is a metal piece that sticks up into the wood, though you can't see it)?    They have about 4 screws that go down into them? Let $a,b,c>0$ such that $a+b+c=3$, find max/min of $\frac1{a^2+1}+\frac1{b^2+1}+\frac1{c^2+1}$ What is the best way to unit test a method that calls into multiple methods, for example:  modify(string value) {     if(value.Length &gt; 5)  replaceit(value);      else changeit(value); }   This pseudo code has a modify method that (currently) calls either replaceit() or changeit(). I have already wrote tests for replaceit and changeit, so writing a new test for modify will be 99% the same set of code.  I need to test it thought because it may change in the future.    So do I copy paste the existing test code?  Move the test code to a common function?  Any other ideas?  I'm not sure of the best practice here. Daily reputation cap doesn't account for reputation * loss* due to bounty awarded? There are many Q&amp;A's around this and the best explanation of daily cap model is from this answer that uses . It is an old answer but gives a good understanding.   My confusion is in applying this model to my situation yesterday.    On 31/12/2019, I awarded a bounty to , since it became eligible for bounty (2 days after posting it). Subsequently, I got more upvotes (including one accept) which exceeded the daily cap of 200. I am confused about this-loss of reputation due to bounty awarded by me preceeded subsequent gain of reputation so going by the bucket analogy, I should have my rep adjusted accordingly and those 6 up votes (at the bottom of table) should have been credited (rep should have been 177 instead of 117),  /reputation shows this   2 219845 (10)  1 219884 (2)  2 170717 (10)  2 219621 (10)  2 219845 (10) 2 219845 (10) 2 218537 (10)  2 219845 (10)  2 219892 (10)  2 219845 (10) 8 219821 (-100)  2 219845 (10)  2 219621 (10)  2 219845 (10)  2 219821 (10)  2 219845 (10)  2 219845 (10)  2 219845 (10)  2 219912 (10)  1 219912 (15)  2 219845 (10)  2 219845 (10)  2 219892 [10]  2 219845 [0]  2 219621 [0]  2 219845 [0]  2 219845 [0]  2 219845 [0]  2 219845 [0]  -- 2019-12-31 rep +117 = 27089 --   It is not the 6 votes I am bothered about, it is more about trying to correct my understanding  or have I stumbled upon an anomaly?