Evaluate $\int_{0}^{\infty} \frac{ \sin^{2n+1} x} {x} \text dx $
Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}x}{x}\mathrm{d}x$
How do you clear a stringstream variable? I've tried several things already,  std::stringstream m; m.empty(); m.clear();   both of which don't work. $\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$ From SL Loney Trigonometry:     Prove that   $$r^2+r_1^2+r_2^2+r_3^2=16R^2-a^2-b^2-c^2$$   for a triangle with sides $a$, $b$, $c$, circumradius $R$, inradius $r$, and exradii $r_1$, $r_2$, $r_3$.   This one is a really dirty question.   I have tried a lot of stuff like $r=4R\times \Pi(\sin\frac{A}{2}$) and  $r_1=4R\times\sin\frac{A}{2}\cos\frac{B}2\cos\frac{C}2$ etc..  There are other ways like $-r+r_1+r_2+r_3=4R$,  but all these are way too cumbersome or clumsy.   Anything more intuitive? Is it adviseable to stack internal hard disk over each other (after removing them from the casing) Would it damage or cause any interference to the non-operational (whereby electricity or power is removed or disconnected from the hard disk and it will be store inside a cupboard or container either made of plastic or metal) hard disks (IDE, SATA)? Automorphism of rational numbers Let $\mathbb Q$ be group of rational numbers under addition.  Then I want to find out the automorphism group of $\mathbb Q$. In a book it is given that Aut($\mathbb Q$) is isomorphic to $\mathbb Q^*$, the  multiplicative group of rational numbers. I stuck in this. How to ssh into a server running on a home network, behind a router? Okay, so I have a PC in my home network, running Ubuntu on a VM with openssh server installed.    How can I remotely access it from another computer outside the home network, using the internet? What IP address do I use to connect to it? What kind of port-forwarding do I need to do? This is a repost with additional info of an older question that was never answered. I have stumbled upon this old question while also trying to find the name of the book series myself, as I dearly wish to read it again but for the life of me, I can't remember the name of it.      This is a long shot but I'm really in need of help for this because      it was an amazing book. It was either a kid's or YA book. A guess      from what year it was published would be 90s-mid 2000s, as I read it      around 2008-2011.         The book cover was in first person view, with the main character   holding a weapon, and was a 3D rendered image inside a dungeon or   cave (that was very reminiscent of early 90s CGI animation), though   there may be variants.    It would have been set around when computer   games were mainstream (maybe around the same time as when it might've   been published) It's about a teenage boy who is bored at home, so he   looks through an old family computer to play a game and finds one   that he has never seen before. When he plays it he gets transported   into the game which is a fantasy-medieval setting.    All that I can   remember about the game and story is that the main character is on a   quest, he rides horses a lot, (to the point where he can ride horses   perfectly in real life), at one point he eats food at an ingame   tavern/restaurant? and he tosses the ingame coin currency at the   server because he's in a hurry, (don't know why I remember that bit   specifically haha), and he meets a gnome/dwarf character who is   helping him on his journey, who has a home in an ingame mountain, and   that time goes faster in the game. (For example, if he spent 5   minutes in the real world, 3 in-game days would have passed)   Sometimes as he's playing something stops him from being able the   play the game for a few weeks, maybe a concerned parent because he's   playing too much or there's a family vacation. I remember during the   time when he's not playing the game he's on a farm and knew how to   ride the horses there.    There was a character in the real world who   was the main character's sibling, relative or friend. They were like   a rival and was also very whiny (to some extent). They were on the   farm as well with him and questioned how the main character knew how   to ride a horse when he had never done it in real life.   This is all I can remember but if you need more specific information I can try and answer. It is definitely not Space Demons or Demons Don't Dream. If anyone knows anything remotely similar please mention it, I would really appreciate it. Thank you!!            Additional info:    It is not an online game or virtual reality game. It was a normal PC game, and all other characters are (I think), just NPCs.  He woke up for the first time in a field/farm and was super confused about what happened and where he was, as he had never played the game before. He is asked a super serious question before starting the game up for the first time, like "are you sure you wish to play ___?", and then he is transported into the game.  He frequently exited the game, to continue his IRL life. And sometimes, he would lose access to the family desktop PC for a couple of days at a time, and when he went back everyone in the game (NPCs), thought he had disappeared because he was gone for ages. I think once, his family when on holidays and he couldn't take the PC, for example.  It was a book series, not a single book. In later books he would play the game again months later in the real world, and years and years would have passed in the game world.  The plot involved 2 main warring sides/factions/countries of humans, but there were fantasy/magical races and characters involved. I vaguely remember something about each side having official colours, one red and one blue. I think the main character was on the blue side.   The original question was never correctly answered, so I'm posting again to see if anyone can remember.   Books that were ruled out in original post: Eden's Gate &amp; Heir Apparent. Copyright issues if using vector art from Shutterstock? Comment on Duplicate Reference: Why would this be marked duplicate when it was asked years prior to the question referenced as a duplicate?  I also believe the question, detail, and response is much better than the referenced question.  I've been a C++ programmer for quite a while but I'm new to Java and new to Eclipse.  I want to use the  to visualize some data I'm working with.  This code is organized like this:  ./com ./com/touchgraph ./com/touchgraph/graphlayout ./com/touchgraph/graphlayout/Edge.java ./com/touchgraph/graphlayout/GLPanel.java ./com/touchgraph/graphlayout/graphelements ./com/touchgraph/graphlayout/graphelements/GESUtils.java ./com/touchgraph/graphlayout/graphelements/GraphEltSet.java ./com/touchgraph/graphlayout/graphelements/ImmutableGraphEltSet.java ./com/touchgraph/graphlayout/graphelements/Locality.java ./com/touchgraph/graphlayout/graphelements/TGForEachEdge.java ./com/touchgraph/graphlayout/graphelements/TGForEachNode.java ./com/touchgraph/graphlayout/graphelements/TGForEachNodePair.java ./com/touchgraph/graphlayout/graphelements/TGNodeQueue.java ./com/touchgraph/graphlayout/graphelements/VisibleLocality.java ./com/touchgraph/graphlayout/GraphLayoutApplet.java ./com/touchgraph/graphlayout/GraphListener.java ./com/touchgraph/graphlayout/interaction ./com/touchgraph/graphlayout/interaction/DragAddUI.java ./com/touchgraph/graphlayout/interaction/DragMultiselectUI.java ./com/touchgraph/graphlayout/interaction/DragNodeUI.java ./com/touchgraph/graphlayout/interaction/GLEditUI.java ./com/touchgraph/graphlayout/interaction/GLNavigateUI.java ./com/touchgraph/graphlayout/interaction/HVRotateDragUI.java ./com/touchgraph/graphlayout/interaction/HVScroll.java ./com/touchgraph/graphlayout/interaction/HyperScroll.java ./com/touchgraph/graphlayout/interaction/LocalityScroll.java ./com/touchgraph/graphlayout/interaction/RotateScroll.java ./com/touchgraph/graphlayout/interaction/TGAbstractClickUI.java ./com/touchgraph/graphlayout/interaction/TGAbstractDragUI.java ./com/touchgraph/graphlayout/interaction/TGAbstractMouseMotionUI.java ./com/touchgraph/graphlayout/interaction/TGAbstractMousePausedUI.java ./com/touchgraph/graphlayout/interaction/TGSelfDeactivatingUI.java ./com/touchgraph/graphlayout/interaction/TGUIManager.java ./com/touchgraph/graphlayout/interaction/TGUserInterface.java ./com/touchgraph/graphlayout/interaction/ZoomScroll.java ./com/touchgraph/graphlayout/LocalityUtils.java ./com/touchgraph/graphlayout/Node.java ./com/touchgraph/graphlayout/TGAbstractLens.java ./com/touchgraph/graphlayout/TGException.java ./com/touchgraph/graphlayout/TGLayout.java ./com/touchgraph/graphlayout/TGLensSet.java ./com/touchgraph/graphlayout/TGPaintListener.java ./com/touchgraph/graphlayout/TGPanel.java ./com/touchgraph/graphlayout/TGPoint2D.java ./com/touchgraph/graphlayout/TGScrollPane.java ./TG-APACHE-LICENSE.txt ./TGGL ReleaseNotes.txt ./TGGraphLayout.html ./TGGraphLayout.jar   How do I add this project in Eclipse and get it compiling and running quickly? How do I connect a PS3 Controller with Xperia P? Difference between be and become How to request a random row in SQL? How can I request a random row (or as close to truly random as is possible) in pure SQL? Is there a way to tell Nautilus not to generate previews of PDF files? I tend to download lots of articles as PDFs, and I find that when I browse a directory of these Nautilus takes 1 minute to load the directory. I assume that's because it's generating previews of their front pages. That feature is useless to me, alas.  I'd like to tell it not to do that. canonical-livepatch, Doesn't seem to patch anything How can I make calls related to a case display in its Chatter feed? I am using the Service Console in Lightning Experience, and using the Chatter Feed component on the Case layout to display updates to the Case.  If I use the "Log a Call" Quick Action from the Chatter publisher, these calls are displayed in the Chatter feed.  This is the desired behaviour.  However, if I insert a Log a Call record related to the Case any other way - e.g. using the Developer Console, or my CTI system's custom components - the call does not display in the feed.  If I query the record, it looks exactly the same as the record that is created with the Quick Action.  It just seems that the Chatter post is never made in this situation.  I have checked my Feed Tracking settings:   Task has Enable Feed Tracking and Subject checked Case has All Related Objects checked   How can I enable calls created with a custom component (part of a CTI system) to display in the case feed? I can't find Karliah at the Ragged Flagon During the 'Hard Answers' Thieves Guild quest, Karliah asked me to meet her at the Ragged Flagon.  However, it seems that she doesn't show up at the rendezvous point.  Where do I find her? I found this in . I've paraphrased for clarity.  There are 100 professors. Some are honest, while others are dishonest. There are more honest professors than dishonest ones. Honest professors always tell the truth, but the dishonest ones sometimes tell the truth and sometimes lie. You can ask any professor the following question about any other professor, "Professor Y, is Professor X honest?" to which he/she will answer yes or no. Design an algorithm that allows you to figure out which of the professors are honest with no more than 198 questions.  The bold part is the kicker. If liars always lied, then the problem is trivial - just ask 99 people about one guy. The majority would be the truthful answer, so you know your honest guys and your liars.  So, any advice? If you give the answer please put it in spoiler tags since I'm just looking for direction. How to show that $|D_{2n}| = 2n$ via the presentation? Consider the dihedral group  $$D_{2n}= \langle a,b \mid a^n = 1 = b^2, b^{-1}ab = a^{-1}\rangle$$  How can I show that $|D_{2n}| = 2n$?   I'm trying to show that we can write every element in the form  $$x = a^i b^j$$ where $i= 0, 1, \dots, n-1$; $b = 0,1$.   I managed to show existence, and it is clear that there are $2n$ such elements, so if I can show that every choice of $i,j$ gives a distinct element, I'll be done.  Any ideas? Removing clock from the lock-screen I'm using Ubuntu 18.04.  I want to remove the digital clock from the lock screen because I just want to see a good wallpaper there, unobstructed.   How do I go about this? Algorithms for Time Series Anomaly Detection I'm currently using Twitter's AnomalyDetection in R: .  This algorithm provides time series anomaly detection for data with seasonality.  Question: are there any other algorithms similar to this (controlling for seasonality doesn't matter)?  I'm trying to score as many time series algorithms as possible on my data so that I can pick the best one / ensemble.