How do I prove that the integral ${\displaystyle\int_0^1}{\dfrac{ln(x)}{1-x^2}dx}$ converges? I tried to find a converging on $[0,1]$ function $g(x)$ such as $g(x) &gt; \dfrac{-ln(x)}{1-x^2}$, but I couldn't succeed in finding it as of yet.
Find whether the integral converges or diverges. $$\int_{0}^{1}\frac{\log(x)}{1-x^2}dx$$  I simplified it to $$\int_{0}^{1}\frac{\log(x)}{(1-x)(1+x)}dx$$  Here I have $2$ "bad" bounds (both $0$ and $1$).  I think, to prove such integral converges, I should find something that is equivalent to or less than $\log(x)$ so I can exchange them, maybe $\sqrt{x}$, so it may cancel out the fraction, and I can compare it to $$\int_{0}^{1}\frac{dx}{x^p}$$  Also I had an idea to substitute $x$ with $u+1$ so I can use $\log(1+u) \sim  u$ when $u \rightarrow 0$. I'm allowed(not familiar with anything else) to use direct comparision test, limit comparision test, Cauchy test and Abel-Dirichlet's test.   Any hints are much appreciated, I just want to get the big picture.   Thank you.
I saw her dance/dancing? I saw a flash of lightning strike/striking? I caught her steal/stealing? Is there a way to show statistic info? Say I am logged into a remote system, how can I know what it's running? On most modern Linuxes (Linuces?), you have the lsb_release command:  $ lsb_release -ic     Distributor ID: LinuxMint Codename:       debian   Which as far as I can tell just gives the same info as /etc/lsb-release. What if that file is not present? I seem to recall that the lsb_release command is relatively new so what if I have to get the OS of an older system?  In any case, lsb stands for Linux Standard Base so I am assuming it won't work on non-Linux Unices. As far as I know, there is no way of getting this information from uname so how can I get this on systems that do not use lsb_release? How do I remove hidden backup files? I have files ending in ~ in my home directory, and I want to delete them. How do I do that? How do I prevent this backup functionality? How do I make an object face the mouse position, but only on one plane? I want a game object to turn and look towards where the mouse was clicked (in world space).  It works well when considering all 3 dimensions, but I really only care for the plane formed by the x and z axis, not the y.  I've tried to fix this by setting the y of the directionTarget to the y of the object's position, but that gives weird results.  My code looks like this:  Quaternion rotationTarget;     float rotationLerpProgress;     float rotationLerpDuration = 1f;      // Use this for initialization     void Start ()     {      }      // Update is called once per frame     void Update ()     {             if (Input.GetMouseButtonDown (0)) {                     var ray = Camera.main.ScreenPointToRay (Input.mousePosition);                     RaycastHit rayHit;                      if (Physics.Raycast (ray, out rayHit)) {                             var rayHitPoint = rayHit.point;                              var rotationDirection = transform.position - rayHitPoint;                                                            rotationDirection.Normalize ();                             //rotationDirection.y = transform.position.y;                             rotationTarget = Quaternion.LookRotation (rotationDirection);                             rotationLerpProgress = Time.deltaTime;                     }                     //targetPosition = Camera.main.ScreenToWorldPoint (Input.mousePosition);                                     }              if (rotationTarget != transform.rotation) {                      transform.rotation = Quaternion.Lerp (transform.rotation, rotationTarget, rotationLerpProgress / rotationLerpDuration);                     rotationLerpProgress += Time.deltaTime;                       if (rotationLerpProgress &gt;= rotationLerpDuration) {                              transform.rotation = rotationTarget;                     }              }      }   I must be missing something. How do I do this right? This lock notice about collaborative effort is partly misleading is locked  with the following notice:     This question and answer are a collaborative effort: if you see something that can be improved, edit it!    Except that while the answer can be edited because it's a Community Wiki question, the question itself  can't be, because it's locked. I don't know the reason why it was locked, but maybe the notice's text should be changed or omitted? (I have no opinion on whether the question should stay locked or not.) I have two users, user1 and user2, that are both members of groupA. user2 has a folder in their home directory called folderA. If they wish to allow read-write-execute permissions for all members of groupA, how would they do this?  What if folderA contains many files and additional folders that also need to have read-write-execute permission?  Information regarding groups is a little 'spotty' across the web, so I am putting my question here in the hope someone posts a clear answer that might help others out too.  Thanks! Ethernet: how important is the magnetics topology? I have some Ethernet issues with a set of boards (6/10 are bad). They're possibly just assembly house mistakes... but I'm very concerned about my magnetics jack.  I could have sworn I saw a example schematic with my jack's topology used with my PHY before, but I can't find it. The PHY's datasheet and suggested magnetics jacks are all identical in topology, and very different than what I have.  I'm using a SMSC  PHY, with a Bel  magnetics jack.  The transformer ratios on my jack vs. a suggested jack for this PHY like the  are the same (1:1).  The inductance is the same, 350uH. However, the choke on mine is on the circuit side, not network side. Also, while the TLA has four 75 ohm resistors from taps tied to a single 1nF/2kV cap, mine has an extra set of 1nF caps between the taps and the 75 ohm resistors.  The main difference is that my jack is a POE jack, and I thought I found an example that used one exactly like it. So, the topology is obviously different just because of that feature.  At the moment, I have 4 good boards, 1 'sometimes' board, and 5 boards that just blink a LED at 11.68Hz representing some error that no datasheet explains.  How important is this? Of course there's no other jack with that footprint.  EDIT  I added some detail on the magnetics jacks above. I was just recommended the SI-60152-F, so I'll compare to that one. Of course like all the other recommendations... it also has no stock at anyone on FindChips.  LATE EDIT  It turns out my problem was the crystal layout that fed the Ethernet PLL.  On the respin, I went with a more standard non-POE jack. Onguard U-lock jammed I'm currently trying to unlock my bike that has been sitting on my porch for a while, the key works and turns, and I can hear the lock engaging/disengaging, however I cannot get the shackle to come out. I think their might be dust/sand stuck in the mechanism however I'm not sure how to get it off now to check. How many ways can you divide $9$ students into three unlabeled teams where one team contains $4$ people, one contains $3$ people and the last contains $2$ people? Unlabeled, meaning that groups with abc = bca = cba, etc  I understand how to do this if the teams are labeled:  $$\frac{9!}{4!3!2!}$$  But there is a term missing in the denominator when the teams are unlabeled and I'm having difficulty understanding how to calculate how many ways the teams can be organized.  There are $3!$ ways to organize the same first group of $3$, $4!$ ways to organize the same second group of $4$ and $2!$ ways to organize the last group of $2$. Why wouldn't you multiply $3!4!2!$ in the denominator?   For instance:  (ABC, DEFG) = (ABC, DEGF)  = (ABC, DFEG) = (ACB, DFGE), etc Making 3 points stick on a plane / flag with wind I have a flag I want to waft in the wind. I imported the shape as an SVG from Adobe Illustrator.  I converted the mesh to a curve.  It wouldn't let me make some subdivisons but it still seems to work with the cloth property.    When I press play, you can see the structure of the flag stops.  How can I make those last 3 points intact? Also the fill colour seems to have disappeared, do you know why and how I can bring it back?    Thanks  Steve  File here: When can I make opportunity attacks? What provokes an opportunity attack?  In 3.X moving out of a threatened square, standing up from prone, casting a spell (unless cast defensively), or making a ranged attack provoked, while in 4e moving out of a threatened square or making a ranged/area attack provoked. Installing Cygwin packages from the command-line Possible Duplicate:        I'm looking for a "yum"-link method to install additional Cygwin packages from the command-line. Let's say I want to add the package "Math/bc", then ideally I'd like to be able to do it  using one command as in:  yum install bc   Currently the only way I've found to install new packages is to locate and run the installation file SETUP.EXE file and then scroll to the relevant package, add it, etc. This is  quite cumbersome so I'm sure there is a smarter command-line way to add an additional package. No surname in my passport How to rename file as below  AS1100801000002.RAW7AGS  AS1100801001008.RAW7AH4 AS1100801002001.RAW7AH9 AS1100801003002.RAW7AHE AS1100801004009.RAW7AHT AS1100801005002.RAW7AHY AS1100801010002.RAW7AJ3   to new name  AS1.txt AS2.txt AS3.txt AS4.txt AS5.txt AS6.txt AS7.txt Average distance between two random points in a square A square with side $a$ is given. What is the average distance between two uniformly-distributed random points inside the square?  For more general "rectangle" case, see . The proof found there is fairly complex, and I am looking for a simpler proof for this special case. I expect it could be significantly simpler.  See also . Detect edits to add [SOLVED] or [RESOLVED] to the title and direct the user to add an answer Users often ask questions that they answer for themselves. Good for them. And good for us.  Symptom  The correct procedure seems to be:   Write new answer to own question  Wait two days Accept own answer   The incorrect, but fairly popular, procedure seems to be:   Edit the question to include the solution Put "[SOLVED] or [RESOLVED]" in the title   Proposed solution  Users should be warned when using the word "solved", delimited in any way, in a question title. This could be "[SOLVED]", "(solved)", or even "Solved - ". I imagine this:   The user tries to submit an edit that adds "solved" such that the word "solved is delimited. The user is brought to a warning page. If the only edit to the question was appending new lines (such as adding an "edit:" paragraph), that edit is copied into a text box The page mentioned in 1 is shown as follows:     $StackSite marks questions as answered when you accept an answer. You can accept an answer by clicking the green check mark next to that answer. There's no need to put "SOLVED" or "RESOLVED" in the title!      Are you answering your own question?      Create a proper answer to your question:         Move your edit to a new answer.   Write your answer.   If nobody writes a more correct or thorough answer after two days, come back and accept your answer.         By doing this, you remove your question from the Unanswered Questions list. You also allow other $StackSite users to vote your answer up. Thanks for helping out!      TEXT BOX WITH EDITS GOES HERE, FOLLOWED BY "POST YOUR ANSWER" BUTTON      Not answering your own question?      Sorry for slowing you down.      OVERVIEW OF EDIT, FOLLOWED BY "SAVE EDITS" BUTTON    Discussion  This would likely reduce the number of [RE]SOLVED questions that appear. However, it's unclear whether this should be a community moderation issue or a feature request issue. The increased engineering work required in building in the interstitial page is probably quite nontrivial, whereas this type of question makes up well under .  Note: Google also provides a . How can you reduce ambient noise from servers? Why didn't the mirror universe's tech progress past the main timeline's? In Star Trek TOS, we see the Defiant disappear to unknown parts  ('The Tholian Web'), and Star Trek: Enterprise revealed that the Defiant went back in time to the mirror universe ('In a Mirror Darkly', parts 1 &amp; 2).   Because of this, one might wonder why (in-universe) the mirror universe didn't obtain (and maintain) technological superiority over the main timeline. (Granted, the out of universe answer is that TOS depicted the two universes as having essentially the same level of tech)  So does any work (whether STO, or a pocket books work) address why the mirror universe didn't simply leap frog the main universe's technology?   (Or to put it another way, why did the mirror universe's technology appear to stagnate for a century after obtaining access to the Defiant's advanced technology?) A sequence of real numbers such that $\lim_{n\to+\infty}|x_n-x_{n+1}|=0$ but it is not Cauchy