I don't know how to integrate $\displaystyle \int\frac{1}{x^{4}+1}\mathrm dx$. Do I have to use trigonometric substitution?
Just doing this for revision, seems much harder than it should be, should I use $x=\tan u$ ? Any help appreciated.
Overlapping matches in Regex Does the Google spider render JavaScript? Proving convergence of sums: If $\sum_{n=1}^{\infty}a^2_n$ and $\sum_{n=1}^{\infty}b^2_n$ converge then $\sum_{n=1}^{\infty}a_nb_n$ converges I was trying to experiment with docker, Ubuntu 14.04, 64-bit. I managed to run an image, and I gave it the path on one of my removable drives, /media/Drive1.  Now, whenever I reboot, I see there is a /media/Drive1 with only a docker directory inside it, and the actual drive which should be Drive1 ends up mounted on /media/Drive11, and this happens every reboot - even when I unmount these drives, and do a sudo rm -rfv /media/Drive1 before rebooting!  So something probably creates /media/Drive1 before it is fully mounted, and I guess that something is docker, because when I boot, I have:  $ ps axf | grep docker  2085 ?        Ssl    0:00 /usr/bin/docker -d   So, how can I disable the docker autostart, so it doesn't interfere with the mounting of external USB drives at boot? Find out which application listens to specific key bindings? mariadb Unknown system variable 'server_uuid' Im trying to setup replication between mariadb(10.1.31-MariaDB - MASTER) and mysql(5.7.12-log - SLAVE). After executed the start slave, I got the below error.     Fatal error: The slave I/O thread stops because a fatal error is   encountered when it tries to get the value of SERVER_UUID variable   from master.   Then I tried to get the value of master_uuid.  MariaDB [(none)]&gt; show variables like '%server_uuid%'; Empty set (0.00 sec)   Then tried to setup this in mysql prompt.  MariaDB [(none)]&gt; set global  server_uuid = 11123c25-cac0-3523-8089-4c54d9b46f33; ERROR 1193 (HY000): Unknown system variable 'server_uuid'   And also I tried to setup auto.cnf in data directory.  [auto] server_uuid = 11123c25-cac0-3523-8089-4c54d9b46f33  chmod 644 auto.cnf   But still im getting the fatal error is encountered when it tries to get the value of SERVER_UUID variable from master. Should the first word after a colon be capitalized? Which of the following is correct?   For example: This. For example: this. Sanity check question about correlation between log-normal random variables Recently I came across the following result in a paper, which I can't seem to find right.  Anyway the authors had cited  by Johnson &amp; Kotz, page 20 as the source. Since I do not have access to this book I am unable to check on the derivation of this result. I was hoping someone could shed some light on how to prove this.  Let $X$ and $Y$ denote a pair of bivariate log normal random variables with their means and variances given by the ordered pairs $(\zeta_{X}, \eta_{X})$ and $(\zeta_{Y}, \eta_{Y})$ and with correlation coefficient $\rho_{(X, Y)}$, derived from the bivariate normal with marginal distributions having parameters $(\xi_{X}, \nu_{X}^2)$ and $(\xi_{Y}, \nu_{Y}^2)$ and correlation coefficient $\rho_{N}$.  The expression for $\rho_{(X, Y)}$ is given as \begin{equation} \rho_{(X, Y)} = \dfrac{\mathrm e^{(\rho_{N} \nu_{X} \nu_{Y})} - 1}{\sqrt {(\mathrm e^{\nu_{X}^2} - 1)(\mathrm e^{\nu_{Y}^2} - 1)}} \end{equation}  The below is a manipulation I came up with, any error in that would be completely mine.  Upon rearranging we get \begin{equation}\begin{aligned} \rho_N &amp;= \dfrac{\ln (1 + \rho_{(X, Y)} \sqrt {(\mathrm e^{\nu_{X}^2} - 1)(\mathrm e^{\nu_{Y}^2} - 1)})}{\nu_{X}\nu_{Y}}\\ &amp;= \dfrac{\ln (1 + \rho_{(X, Y)} \frac{\eta_{X}\eta_{Y}}{\zeta{X}\zeta{Y}})}{\sqrt {\ln ((\frac{\eta_{X}}{\zeta_{X}})^2 + 1)\ln ((\frac{\eta_{Y}}{\zeta_{Y}})^2 + 1)}}. \end{aligned} \end{equation}  I am very interested in learning if this result would hold true between $X$ and $Y$'s correlations if we had a quad-variate situation as in there were 2 more random variables which are also correlated with $X$ and $Y$ would this result still be true ? I suspect it should be, but I am newbie and due to lack of a credible source I was wondering if some one would be kind to confirm it. I know how to , but I'd like to add a bunch of different extensions and avoid the tedious job of adding every single one. Is there a command line tool or registry key I can use to accomplish this? When I tried to connect my Ubuntu 13.10 to my VM Centos 6.5 using ssh appear the message "Connection refused" or "No route to host" even than I change the port, noting change.    I need to use SSH, VPN and Samba, but this IP in my VM Centos do not work.  How Can I resolve this problem? Which is correct: "drive safe" or "drive safely"? In QGIS, I want to make polygons from a set of intersecting lines. Looking at the screenshot here, I want chop the purple line (it's a closed line, not a polygon) where it crosses the green and blue lines. The result hopefully would be a polygon where I have hatched in red. I have quite a few to do.    I have tried the QGIS tool previously called Polygonizer (see ), but now called Polygonize. This is a tool that, given a layer containing a set of crossing lines arranged essentially like a # symbol, should create a polygon from the enclosed space in the middle.  (In QGIS 2.01, Polygonize is in the top menu bar: go to Processing -> Commander, then type "Polygonize" on the command line, select "Processing algorithm: Polygonize" from the list that appears, and press Enter.)   At the momemt Polygonize doesn't work properly. Is there another way to do what I want to do?   For example, wouldn't it be great if the QGIS 'Split Feature' command was able to work like MapInfo's 'Polyline Split', where you select the polygons to split, then select an already-drawn polyline to split by, and voila. But Split Feature seems not to work that way.    UPDATE: Detail of problems with running Polygonize.  I have 64-bit QGIS 2.01 installed to Windows 7 from the installer package, QGIS-OSGeo4W-2.0.1-3-Setup-x86_64.exe.  The routine processed an output from my shapefile, but did not create a polygon from the region enclosed by intersections between the blue, green and purple lines. (Note: in the actual input file, all these lines are on the same layer; the screenshot just colours them differently for illustrative purposes). What I got instead was a simple conversion of the purple outline to a polygon, as though the program completely ignored the blue and green lines.  When I node-edited the closed purple line, to open it so that I had a set of open crossing lines like in the # symbol, and then ran Polygonize again, nothing happened. No crash, but no visible polygon in the output file.    When I used Nick Hopton's own  data, I got a crash; see screenshot: From what I understand, the frequency of light coming from the source moving towards an observer increases. From $ E=hv $ , this implies increase in energy of photon.  What really is confusing, is where does that extra energy come from? And also where is the energy is lost during opposite Doppler effect (red shift)? Why doesn't this violate the conservation of energy? Roll a 6-sided die until the total $\geq M$. Mean amount by which $M$ is exceeded? Here is the question:  You roll a fair 6-sided dice iteratively until the sum of the dice rolls is greater than or equal to M. What is the mean and standard deviation of the sum minus M when M=300?  Should I write a code to answer these kind of questions?  Please give me some hints on that. thanks! Why does this excerpt say that unbiased estimation of standard deviation usually isn't relevant? Why do I need 50 reputation to comment? What can I do instead? Users with less than 50 reputation points cannot write comments on questions and answers that they don't own.  Why does this limit exist? But I want to contribute now. What should I do instead? But I can't write a good answer without more information! Shouldn't I be allowed to post comments if I have reputation on a different site? But I saw a new user posting a comment! How did they do it? Why do I need 50 reputation to comment on my own post?   See also:    in the Help Center How come I can't give more than 500 rep? Why can't I give more than 500 reputation as a bounty at a time? The system won't let me choose an option more than 500.  Also, how were some users able to do so? On  the OP has given a single bounty worth 550 rep, but at the moment I have 844 rep and I can't give any more than 500 rep on a bounty.  Can you please tell us if this is a bug or not? Resizing an image in a post? Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$ Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$.   This is my proof to show that a ring is commutative if it has the property that ab = ca implies b = c.  We need to show that if x, y ∈ R then xy = yx. Let a = x, b = yx and c = xy. Then ab = x(yx) = (xy)x = ca. Thus, by the hypothesis, b = c, or xy = yx. Thus, for x, y ∈ R we have xy = yx.   How would I show when $a\neq 0$? How can I deploy a connected app from my sandbox environment to my production environment? I built a changeset and I was able to include all my classes, but it was a surprise that salesforce has not provided any option to deploy a connected app.  So how do I go about deploying a connected app? Do I need to create it in every other environment?