How to calculate the integral $I=\int\limits_0^1\frac{x^n-1}{\ln(x)} \,\mathrm dx$
An integration question to be solved without using differentiation under the integral sign.
Why is my ethernet interface called enp0s10 instead of eth0? When I run ifconfig -a, I only get lo and enp0s10 interfaces, not the classical eth0  What does enp0s10 mean? Why is there no eth0? Firefox browser opens but URL is not launched What triggers the benefit of the bard's "Song of Rest" feature? In D&amp;D 5e, the benefit of the Bard's "Song of Rest" feature triggers "if you or any friendly creatures who can hear your performance regain hit points at the end of the the short rest."  Does Song of Rest's benefit apply just when spending hit dice to regain hit points? Or does it apply to any other way that a player might regain hit points at the end of a short rest (e.g. by casting a spell, using a Second Wind, eating a Goodberry, etc.)? Local Coordinate to Geocentric The ultimate question, I need a transformation matrix to take a point in local space representing a roughly 500m x 500m place in New Mexico centered at -108.619987456 long 36.234600064 lat.  The final output needs to be in geocentric coordinates and I can during initialization get any number of points on the map such as the corners, center, western most along the center etc.  During run time I would like to have a transformation matrix that can be applied to a position in local space expressed in meters and get back an approximate GCC coordinate.  The center of the point in GCC: -1645380 -4885138 3752889 The bottom left corner of the map in GCC: -1644552, -4881054, 3749220  During run time I need to be able to multiply (-250, -250, 0) with the transformation matrix and get something close to (-1644552, -4881054, 3749220).  I've spent more than a week trying to research a solution for this and so far nothing.  Given an identity matrix as our starting position and orientation. Then using geotrans and the known lat, long, and height of the starting position I get an x,y,z geocentric coordinate. A vector from the origin of (0,0,0) gives both the up and translation for the matrix. However, I need the forward and right so that I can pass a distance in meters from the origin into the transformation matrix and get a roughly accurate GCC. Do I have all of the inputs I need to calculate the right and forward?  Inputs Origin: 0, 0, 0 Global: -1645380, -4885138, 3752889 Up (Normalized): Global - Origin  Desired Outputs Right: ? ? ? Forward: ? ? ?  So with the right and forward added to the up and translation I already calculated I would have a transformation matrix.  I could then apply the matrix to a vector of say (50, 50, 0) and get something within about 0-3 cm of the output if I feed the lat/long back into geotrans.  This matrix would only ever be used small maps of about 500m x 500m so the curvature of the earth is negligible.  In reply to whuber,  I don't know your level of experience so I will start with the very basics.  An identity matrix is a 4x4 matrix that you can multiply by a vector and it returns the vector unchanged. Such as below.  1 0 0 x=0 0 1 0 y=0 0 0 1 z=0 0 0 0 1  The x, y, and z of the matrix are how much to translate the vector by and the first 3 rows and columns are the rotation.  Below is a tranformation matrix that does nothing to the orientation of a vector but does translate.  This is what you would want for two axis aligned worlds in different locations.  1 0 0 13 0 1 0 50 0 0 1 -7 0 0 0 1  If you were to multiply a vector of (10, 10, 10) with the above transformation matrix you would get an output of (23, 60, 3).  My problem is the axes are not aligned and the "plane" of the world I am trying to get the local coordinate converted to is projected on the ellipsoid of the earth.  Geotrans is library that you can use to pass a coordinate from one system such as geodetic or GDC (lat, long, height) and get back another such as geocentric or GCC (x,y,z).  For example: If my game world was representing a map centered exactly on the prime meridian and equator the transformation matrix would look something like below. I am just guesstimating the Y and Z rotations and might have them flipped and/or the wrong sign.    0 0 1 6378137 0 1 0 0 1 0 0 0 0 0 0 1 Remember all opened files with split windows and their positions in Emacs In the following figure prove that: $AK||BC$ In arbitrary triangle $ABC$, let $G$ be centroid and $AH$ be a height.We extend $HG$ beyond $G$ to intersect circumcircle at $K$.Prove that $AK||BC$       I connected midpoint of $BC$ to $K$ and $A$ to show $MA=MK$ but failed... If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c I'm trying to prove that if $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c. I tried using Bezout identity but couldn't get anywhere. I would like to open 4 Notepad++ windows at once, in the same pannel. Currently, I am only able to split it into two, and would like to know if there is a plugin that enables 4 views at at same time, or 3.   thanks How do RAM and processor speed affect overall performance on Android? Since Android can be installed on wide range of devices, I'm wondering how important RAM and the CPU speed are to the performance of a device.  There are always tradeoffs when something is increased and another one decreased!  Is more RAM or a faster processor better for general browsing and less mulititasking?  What if I'm interested in gaming or doing lots of things at once?  Will more RAM make up for a slower processor or vice-versa? Memory Usage of SQL Server SQL Server instance on my server is using almost full memory available in my Physical Server. Say if i am having 8GB of RAM than SQL Server is using 7.8 GB of RAM from system. I also have read articles and also read many similar questions regarding same on this forum and i understand that memory is reserved and it is using memory.  But i have 2 same servers and 2 SQL Servers, why this is happening on a single SQL Instance not on other. Also when i run DBCC MemoryStatus than it is showing up...  VM Reserved 8282008 VM Committed 537936   so from this we know that SQL reserved whole 8GB memory, but why this VM Committed keeps increasing. What i understand is VM Committed is:      VM Committed: This value shows the overall amount of VAS that SQL Server has committed. VAS that is committed has been associated with physical memory.   So this is the memory SQL Server has committed (from this i understand that physical memory actually SQL Server is using at instance).  So like to know the reason behind this ever increasing VM Committed memory on my server and not on another. Thanks in Advance. What are the mechanics of time dilation and length contraction? Going beyond the mathematical equations involving light and the "speed limit of the universe", what is observed is merely a phenomenon and not a true explanation of why time dilates or length contracts.  It has been proven to work out, but do we know why?  Is it something that happens at a subatomic level? I have an Excel file containing data collected over many years as latitude and longitude coordinates for archaeological sites. How can I import it into QGIS as a new layer? Does a card have a keyword if it has the same effect as said keyword? I was looking at  and found the effect surprisingly similar to the keyword Surveil. To compare, first the wording of Contingency Plan and then the wording of the Surveil keyword:       Look at the top five cards of your library. Put any number of them into your graveyard and the rest back on top of your library in any order.     And       701.41a To "surveil N" means to look at the top N cards of your library, then put any number of them into your graveyard and the rest on top of your library in any order.     They quite clearly are the same, so can I assume the card states "Surveil 5" instead? And if so, does it trigger abilities which state "Whenever you surveil ..."? A matrix inside a table Possible Duplicate:          I am trying to insert a matrix inside a table, and I am looking for a good way to do this. Usually when I write matrices in equations, I use array environment, so I naively defined an array inside tabular, and it sort of works. The only problem is that the matrix itself seems to take up a huge amount of space inside the cell. An example is   \begin{tabular}{|c|c|} \hline \textbf{EKF} &amp; \textbf{UKF}\\ \hline $Q = \left[ \begin{array}{cc} 0.1 &amp; 0 \\ 0 &amp; 0.1 \end{array}\right]$ &amp; $Q = left[ \begin{array}{cc} 0.01 &amp; 0 \\ 0 &amp; 0.01  \end{array}\right]$\\ \hline $R = 5 \times 10^{-3}$ &amp; $R = 5 \times 10^{-5}$ \\ \hline \end{tabular}   Is there any way to increase the spacing in the cell containing the matrix without that matrix taking up all the space? How to share the "Look Back" video from Facebook? On Facebook, there is a  looking back on your Facebook history. Apparently, some people have shared this video with their friends, however I and someone else cannot figure out how to do so. This URL is not unique, it's a global URL which shows the video of who's logged in. People say there's supposed to be a "share" link, but there are no links whatsoever. And, I can't share the URL because it would show them their own videos.  How do I share this video with friends on Facebook?  without using a screen recorder to capture it Use spray paint to make mask for pre-sensitised board? I'm about to etch my first simple board for a project. I have a pre-sensitised board that (as I understand the process) you expose to UV light, then develop the board in a sodium hydroxide solution, then etch. The UV light will negatively affect the protective lacquer and developing it after exposing washes away the lacquer, making the board ready to etch.  I got the lye and I got sodium persulfate for the etching but I did not have any transparent paper as I thought I did! And it's impossible for me to get a hold of it in time (= this weekend, I live far from the city and it's a small one and I haven't found any place that stocks it so I have to order online and that's sometime next week I'd get it at the fastest).   So I am looking for an alternative solution. What I am considering is printing the design to regular paper, cut out a mask carefully from this paper and place it over the board and paint a mask on. Spray paint most likely, then in theory I would have a UV mask.  Anyone see any flaws in this plan? show all my unanswered questions from SE Any way how to get    my all un-answered questions  from across all SE sites? How did the transdimensional Edo god (Edo lord) come to be the overseer of the Edo? A book in which every species on earth was rendered intelligent The 'blurb' on the back of the book was that something had boosted the intelligence of every creature on earth, to the point that at least some animals were on par with humans. I'm not sure if humans were similarly enhanced or just animals. I'm not sure whether it was done by aliens, or a side effect of something humans did, or what.   This book was on the shelves in the mid/late 1980's, so it's nothing more recent than that. Parse a Json Array in to a class in c#