Integral $\int \frac{dx}{x^4+1}$
Evaluating $\int \frac{1}{{x^4+1}} dx$
When interacting with different elements and applying multiple actions it  may be quite convenient in some situations if we could do:  WebElement myInput = driver.findElement(By.id("my-input-id")); myInput.clear().sendKeys("test");   Instead of:  WebElement myInput = driver.findElement(By.id("my-input-id")); myInput.clear() myInput.sendKeys("test");   But, the problem is , sendKeys() and other "action" methods cannot be chained as is - they return void and not the current WebElement.  What would be the easiest way to achieve chaining multiple actions? Pluralization issue on new question statistics underneath title, with views It looks like the new question statistics underneath the question title introduced a pluralization issue with views:        To be clear here, this was not an issue with the old sidebar-based question statistics; that used to properly say "viewed 1 time". While moving custom profiles using eclipse from dev org to partner org found following errors Intuitive explanation for dividing by $n-1$ when calculating standard deviation? I have a card that is 50% used with 7% interest. The max credit limit on the card is $10,000, and I used $5000. I have another card that is $14,000 and I have $2900 used, but the interest is 14.9%. I want to move the $2900 card to the other card that has a lower interest rate (7%). This will bring the balance close to the max, but the idea is to focus on this one card and bring the balance down as quickly as possible. is this a wise choice? I am looking to purchase a house in 6 months so I thought that this might be enough time to pay it off and keep my score up. My scores are currently in the low 700s. Use a concatenated (dynamic) string as JavaScript object key? The "Satellite Paradox": Twin paradox in orbiting satellites I want to simply eliminate the effect of acceleration, which is the cornerstone in resolving the traditional twin paradox, through the following thought experiment: Assume twins $A$ &amp; $B$ are located in the same orbital height, far away from the surface of a massive planet, on a long concrete column at rest WRT the planet. A rapid explosion that happens between the twins makes them orbit the earth with a high velocity, say, $0.6 \ c$, in the same orbital path but in different directions. According to relativity, since the orbiting satellites are completely inertial frames, each twin attributes a variable time dilation to the other one, and each twin expects the other one to be younger. Nonetheless, these twins are automatically reunited after traveling half of the orbit's circumference without being affected by additional accelerations. Which twin is younger in this case? Indeed, If each twin sees the other's clock as running slow all along the way, how can the clocks agree when they meet? For this configuration:  The acceleration due to the explosion does not affect the twins' clock rates since it occurs abruptly in the same place on the column where the twins are located back-to-back. The clocks have been synchronized just before the explosion.  The traditional gamma factor, attributed to one twin from the viewpoint of the other, is variable because the resultant velocity of one twin complying with the relativistic velocity addition is a variable measured from the viewpoint of the other one. However, whether or not the corresponding time dilation is varying, each twin anticipates the other one to be younger. There is no breaking of symmetry!  The $g$-field of the planet has nothing to do with orbiting satellites since they are inertial, and thus GR corrections are not inserted. (Remember the GPS settings!) Why is "ask" sometimes pronounced "aks"? We've recently moved from New Zealand to New York City, and have noticed that many people (most of whom have good English) pronounce "ask" as "aks". For example:     Could you please go aks her tomorrow?   Sure, I'll ax her! :-)  What's the origin/etymology of "aks"? It seems to be more common among African Americans, but it's definitely used by others too. In a bash shell script, writing a for loop that iterates over string values Is there is any way to prove the Faraday's law of induction? I want to know if there is any way to prove the Faraday's law or is it just an experimental observed phenomena?  More specifically, is there any reason why the proportionality constant is 1? How did Faraday discover it? I also heard that we can prove Faraday's law using the principle of least action, but is that true? $IS \mid JS$ implies that $I\mid J$ where $I$ and $J$ are ideals of a number ring contained in another number ring $S$ AIC versus Likelihood Ratio Test in Model Variable Selection The software that I am currently using to build a model compares a "current run" model to a "reference model" and reports (where applicable) both a chi-squared p-value based on likelihood ratio tests and AIC values for each model.  I know that one advantage of AIC over likelihood ratio tests is that AIC can be compared on non-nested models.  However, I am not aware of any reason why AIC couldn't or shouldn't be compared on nested models.  In my model, when comparing nested models for variable selection, I'm finding several cases where the likelihood ratio test and the AIC comparison are suggesting opposite conclusions.  Since both are based on likelihood calculations, I'm struggling to interpret these results.  However the documentation of my software says (without explaining),   "If two models are nested (i.e. one is a sub-set of the other) then the more usual chi-squared test is the most appropriate to use. If the models are not nested, the AIC can be used..."  Can anyone elaborate on this and/or explain why AIC is not as helpful as likelihood ratio tests on nested models? Pre & post increment operator behavior in C, C++, Java, & C# Prove $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^n = n!$ and $\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^m = 0$ Prove $$\sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^n = n! \qquad\text{and}\qquad \sum_{k = 0}^{n}(-1)^{n - k} \binom{n}{k} \cdot k^m = 0,$$ where $m \in \{0, 1, 2, \cdots, n - 1\}$.  To be honest, I tried to use some combinatorial ideas but was not able to see interconnections. Also, I had an idea to prove it using induction but failed to do that either. Help will be much appreciated! I just got stuck and don't see any continuation of solution for this problem Execute bash commands over SSH while staying in interactive mode afterwards Probably it is a weird thing I would like to achieve but: I would like to SSH to a remote host and then execute some bash commands like "alias" automatically to use them afterwards in an interactive mode. The remote host does not allow the personal environment.    Is this possible? Would "expect" do it? Or is there any other way to achieve this? Basically I would like to have my bashrc without modifying any files on the remote host. I've already tried clicking and holding the left button of my mouse, and it just won't work! Whenever I press it, it opens the game menu instead. My son is almost 3 (33 months) and for the past few months, he has been holding his poop in, to the point that he won't go for many days a time. When this started, the doctor advised us to give him Miralax to make his stool softer so it comes out more easily. Even with the Miralax, he still managed to hold it for two days at a time sometimes, but at least it was coming out at all, so we continued with it.  Anyway, we've been giving him the Miralax for months now, and now he's (supposed to be) going to preschool in September, which of course requires that he be potty trained. We don't want to hold him back since he's developmentally ready otherwise, so we started potty training a few weeks ago.  He picked up the potty training really quickly – for peeing – but he still holds his poop in no matter what. If he's sitting on the potty, as soon as he's about to do it, he stands up and just keeps holding it in (and once he starts to stand, if we even so much as ask him to sit back down, he screams and cries).  We have tried everything to convince him (or distract him enough) to sit and poop: reading books, singing songs, playing games, playing with toys, offering him snacks/treats (graham crackers), giving him stickers, etc. Nothing works.  As of today, it has been a week since the last time he pooped, with the exception of a little bit today and a little bit yesterday (both of which ended up all over the bathroom floor since he won't sit down). The doctor says now we should give him an enema to force it all to come out, but even so, that won't solve anything going forward since he still won't go in his diaper or on the potty in the first place (what are we going to do, give him an enema every week, indefinitely?).  The issue isn't that he's scared of the potty itself, since (a) he was holding it before we started potty training, and (b) he knows exactly what he's supposed to do, since he has no problem with peeing (he sits down himself, points it out afterward, knows that it gets emptied into the big potty, etc.).  It's that he just won't poop, ever – not in his diaper, not on the potty – and the only reason why anything comes out at all is because we've been giving him the Miralax every day (and even then, these aren't "full" poops, just whatever happens to come out because it's soft enough that he's unable to hold it all in).  I'm at a complete loss as to why this even started, and what if anything we can do that would actually help. Is it a behavioral problem? Medical? Both?? Help!    UPDATE: I just wanted to update this question since a lot has changed since I originally posted it. We discovered there was a specific situation where he would go in his diaper voluntarily: in our bedroom closet with the door closed. So we knew then that the withholding was intentional, since it was now established that he could go if he wanted to.  So we let him continue going in the closet and, over time, found that he usually went around the same time each day. Based on that, we then had him sit on the potty when we knew it was most likely he would need to go. We also managed to find two things that distracted him enough to sit (blowing bubbles and playing with his toy laptop).  By doing this, we were able to get him to go on the potty without really realizing it (so he didn't try to fight it), and then made a big deal out of it every time he did. Over time, that helped establish that that's what he was supposed to do, and now he does so voluntarily. He hasn't pooped in his diaper in probably 3 weeks by now.  I wouldn't say he's "fully" potty trained, in that an adult still needs to go with him and distract him (and occasionally remind him when he needs to go in general), but finally we made progress. My professor was lecturing today and he made this statement which I was unable to verify.  (I worded it nicer)  There is no map which is both smooth and onto from $S^1$ to $S^1$$\times$ $S^1$.  When he said this he included the original "one can clearly see" statement which is usually when the most people seem to be confused in his class.  Thus, I was hesitant to ask why.  So, please no one lecture me on the fact that I should have asked anyway.  If it is really that obvious, I would rather look stupid here than in class :) Update #2: Seems that it was my secondary screen the one that didn't show the color! Tried with another screen and I could see the progress clearer... perhaps a stronger color will make it easier to see across different devices?  Update: Seems to be an issue in Firefox, as I tried on Chrome and the progress is visible.    I just noticed that the badge progress on your user profile had it's style changed (don't know when but it seems that recently).  However, seems that the progress of gold badges is not working properly. If we see the Bronze and Silver badges, they are "filled with color" as you progress on the badge, however golden ones are not colored (just the border).   Here a picture illustrating what I say:    Is there a reason for this behavior? Why does this PNG image on twitter look different when clicked? This morning on twitter there was a tweet with the text "click on this picture".  When picture is clicked, it's opened in wider viewer, but looks completely different.  I tried to analyze this picture in ACDSee, and I also tried uploading on Facebook, but it's happening only when embedded on twitter. I don't have much knowledge about graphics so please explain this to me. Why does this PNG image change only when clicked on Twitter?  Screenshots (left = before clicking; right = after clicking):     Here's the original .