How can I solve $\int \sqrt{1+x^2}\,dx$?
How to integrate $\int\sqrt{x^2+1}dx$
Prove that $\lim_{n\to\infty}a_n\le \lim_{n\to\infty}b_n$ When something gets wet, it usually appears darker. This can be observed with soil, sand, cloth, paper, concrete, bricks...  What is the reason for this? How does water soaking into the material change its optical properties? How do I expire a PHP session after 30 minutes? I need to keep a session alive for 30 minutes and then destroy it. I have a 32-bit machine, can I use programs that are meant for 64-bit processors? I am using a 32-bit machine, but I am having to use a relatively obscure semantic database which only comes in 64-bit versions.  What are my options for running it in my local dev environment?  Currently when I try to run it, I get an error message that looks like this:  cannot execute binary file   and when I check my machine info, I get this:  $ uname -a Linux slabrams-desktop 2.6.32-29-generic #58-Ubuntu SMP Fri Feb 11 19:00:09 UTC 2011 i686 GNU/Linux How can I install Ubuntu on a second hard drive with Windows being on the first? I have recently got an Alienware M17x R4 and since it has two hard drive bays I was thinking of putting my hard drive from my old laptop and installing Ubuntu on it without making any changes to the drive that has Windows on it. Also if possible to add a entry to the Windows boot loader to boot Ubuntu instead of using GRUB. Prove homotopic attaching maps give homotopy equivalent spaces by attaching a cell Prove: If $f,g:S^{n-1} \to X$ are homotopic maps, then $X\sqcup_fD^n$ and $X\sqcup_gD^n$ are homotopy equivalent.   I think it can be proved by showing they are both deformation retracts of $X\sqcup_H(D^n\times I)$ where $H$ is the homotopy between $f$ and $g$.  However, I have difficult in proving that the deformation retracts are continuous map. In fact, I have difficulty in representing a map in quotient spaces like $X\sqcup_fD^n$. I think a map from $X\sqcup_fD^n$ to $W$ can be represented by two maps: $m_1: X\to W$, $m_2: D^n\to W$, where for $x\in S^{n-1}$, $m_1\circ f(x)=m_2\circ i(x)$.  Then I construct the deformation retract this way: $m_1: X\to X$. For $x\in H(S^{n-1},t)$, $m_1(x)=H(S^{n-1},0)$, otherwise $m_1(x)=x$.  $m_2: D^n\times I\to D^n\times {0}$: $m_2((D^n,t))=(D^n,0)$.  It is easy to verify that $m_1$ and $m_2$ define a map from $X\sqcup_H(D^n\times I)$ to $X\sqcup_fD^n$. As long as this is a continous map, obvioulsy then we find a deformation retract. But it seems such a map is not continous? Updating list definition using features I have a feature that deploys content types, a list definition and template that uses these content types and finally a list instance. This feature is already in production.  Now we have a change request to add new views to this existing list. So I make the changes to schema.xml and upgrade the solution. But alas, the new views don't show up. If I create a new site, the list instance is created with the new views. I tried deactivating/reactivating, iisreset but still no success. Is there anything I'm missing? Call a javascript function after 5 sec of last key press How to prove Fibonacci sequence with matrices? I have a registered StackOverflow account which I normally log into using OpenID.  Recently I logged out in order to post a question anonymously (supplying a fake name and of my secondary email addresses).  The problem now is that I'm logged in to StackOverflow as this "dummy" user, unable to see a way to log out.  The top menu normally has a "logout" link, but when you aren't fully registered this link is replaced with "register".  There is no "logout" link for me. :(  So..   When logged out there is a "login" link. When logged in there is a "logout" link. When "logged in" with an unregistered account, there is only a "register" link (no "logout"). Can I use variables inside {} expansion without `eval`? What is the evidence that dark energy exists? (as of 2020) Astrophysicists believe that dark energy exists and makes up ~70% of the universe's energy content. What is the evidence that dark energy exists? Wikipedia gives :   Supernovae. A specific type of supernovae (type 1A) are supposed to be standard candles - that is, their luminosity is known. In turn this lets us measure distance to faraway galaxies, check how fast those galaxies are receding from us, and check if that recession speed is increasing over time. CMB. Data from the Cosmic Microwave Background indicates the universe is approximately flat. Visible matter + dark matter can account for ~30% of the energy content required to make the universe flat, leaving ~70% for something else - dark energy. BAO. Baryon acoustic oscillations act as a "standard ruler" that lets us measure how the Hubble constant varies with redshift (i.e. time), and see if the recession speed is increasing with time. Late-time ISW. ISW stands for integrated Sachs-Wolfe effect. The idea is that, usually, a photon that enters a potential well gains energy as it falls in and loses energy as it emerges, and gain/loss exactly cancel. If a universe is expanding in accelerated fashion, then this is untrue; the potential wells / hills are smoothed out and there is a permanent shift in the photon's energy and therefore temperature. If we see a correlation between hot and cold spots on the CMB and the locations of superclusters and voids, then it's a sign of accelerated expansion. Galaxy evolution. This uses (known) evolution of early-type galaxies as a standard clock. Once we know how long it takes for a galaxy to evolve from one state to another, as well as their redshifts, we can reconstruct how the Hubble constant varies over time, and see if the recession speed is increasing with time.   Two questions:   Did I understand any of these five methods wrong? Are there any other lines of evidence for the existence of dark energy? ADC0808 IC working correctly occasionally I am using  for a project on converting analog signal to digital signal. It has an inbuilt multiplexer using which we have to provide an analog signal to one of the pin. However what happens is ;  Sometimes it latches to a particular value say 1000000 and remains at there no matter how many times Start of Conversion is pressed which should set the inner counter to 0.  Sometimes it gives slightly wrong output off by 100 or 1000 and when I press Start of conversion, it gives correct output, so its not reliable every time.  And most seriously , Suppose the control for multiplexer according to Datasheet are such that input pin 1 should be active, instead, it works only when the input is given to pin 5 for one particular IC and pin 3 for other. I have been trying to fit it in logic since 3 days however each day some new error happens. I have replaced it twice from my college lab and now the technician doesn't want to replace it anymore . What is amiss here ? Integral of $\frac{\sqrt{x^2+1}}{x}$ So I have to do the integration of $\frac{\sqrt{x^2+1}}{x}$. Give me a hint. What should I replace? Should I do it with integration by parts? Export nodes from Drupal 4? $$|a\sin x+b \cos x|\leq \sqrt{a^2+b^2}$$   I have tried: $$|a\sin x+b \cos x|\leq |a+b|\leq \sqrt{a^2+b^2}$$  enough to prove: $$|a+b|\leq \sqrt{a^2+b^2}$$  But I can find how to continue from here Is the following equivalent to the axiom of choice? My machine is continously making udp dns traffic request. what i need to know is the PID of the process generating this traffic.  The normal way in TCP connection is to use netstat/lsof and get the process associated at the pid.  Is UDP the connection is stateles, so, when i call netastat/lsof I can see it only if the UDP socket is opened and it's sending traffic.  I have tried with lsof -i UDP and with nestat -anpue, but I can't find wich process is doing that request because i need to call lsof/netstat exactly when the udp traffic is sended, if i call lsof/netstat before/after the udp datagram is sended is impossible to view the opened UDP socket.  Call netstat/lsof exactly when 3/4 udp packet is sended is IMPOSSIBLE.  How I can identify the infamous process? I have already inspected the traffic to try to identify the sended PID from the content of the packet, but is not possible to identify it from the contect of the traffic.  Anyone can help me ?  I'm root on this machine FEDORA 12 Linux noise.company.lan 2.6.32.16-141.fc12.x86_64 #1 SMP Wed Jul 7 04:49:59 UTC 2010 x86_64 x86_64 x86_64 GNU/Linux Is it a good approach to call return inside using {} statement? Where to put my code: plugin or functions.php? Is there an easy to understand scheme to decide what kind of code belongs to a plugin or the theme’s functions.php?  There    and many  about that topic, mostly because there are some misconceptions about the inner workings of WordPress. I am asking for an answer based on facts, not on opinions.  It should explain how to handle these points (and probably more):   custom post types and taxonomies contact forms shortcodes custom widgets  SEO functions like custom meta elements theme switch   There are often pros and cons for both sides. Our most popular question  got a lot of code snippets as answers that are at least debatable. We need criteria a beginner can understand, maybe a check list – with reasons.  See also the related question by Chip Bennett on our meta site:   Related: