Integral $\int_0^{\infty}\frac{\ln(x)}{x^2+nx+n^2}dx=\frac{2\pi}{3\sqrt{3}}\frac{\ln(n)}{n}$
Compute $ \int_{0}^{ \infty }\frac{\ln xdx}{x^{2}+ax+b}$
How do I go about proving this? I know one method is:  $\eqalign{    \cos (90^\circ + \theta ) &amp;\equiv \cos90^\circ \cos\theta  - \sin90^\circ \sin\theta   \cr    &amp;  \equiv (0)(\cos\theta ) - (1)(\sin \theta )  \cr    &amp;  \equiv  - \sin \theta  \cr} $  I'd appreciate others, particularly ones that will allow me to visualize this identity on the unit circle.  Thanks alot. Prerequisites for AIC model comparison What are exactly the prerequisites, that need to be fulfilled for AIC model comparison to work?  I just came around this question when I did comparison like this:  &gt; uu0 = lm(log(usili) ~ rok) &gt; uu1 = lm(usili ~ rok) &gt; AIC(uu0) [1] 3192.14 &gt; AIC(uu1) [1] 14277.29   This way I justified the log transformation of variable usili. But I don't know if I can AIC-compare models when for example the dependent variable is different?  Ideal answer would include the list of prerequisites (mathematical assumptions). Atheros AR9485 wifi disconnects randomly Failed to download repository information due to missing CDROM Support for hardware components How can I find out if Ubuntu supports a particular hardware component, that is, if it works in Ubuntu?  I am going to put together a computer and I am choosing components.   How do I know if Ubuntu supports this or that motherboard, or this or that sound card, or this or that graphics card, etc? How do I know that there is no conflict in Ubuntu between this and that hardware component?   What resources are there to help with such situations?  I know that there are computers with Ubuntu pre-installed and that there are  for whole computers but this is not what I'm looking for. I'm looking for resources to find out support for particular hardware components and conflicts among particular hardware components. What is a "static" function in C? The question was about plain  functions, not  static methods, as clarified in comments.  I understand what a static variable is, but what is a static function?  And why is it that if I declare a function, let's say void print_matrix, in let's say a.c (WITHOUT a.h) and include "a.c" -  I get "print_matrix@@....) already defined in a.obj", BUT if I declare it as static void print_matrix then it compiles?  UPDATE Just to clear things up - I know that including .c is bad, as many of you pointed out. I just do it to temporarily clear space in main.c until I have a better idea of how to group all those functions into proper .h and .c files. Just a temporary, quick solution. Rotate group of objects over an edge Environment variables when run with 'sudo' What is the use of multiple main methods? How does virtualizing differ from emulation, in terms of structure? Someone told me that a virtualizing program like VirtualBox does not work like an emulator does in the sense that it doesn't emulate registers and uses the actual ones for the virtualized data that are on the CPU. Emulators must emulate the registers since they are mostly to execute software that depends on a foreign environment (e.g. a Genesis emulator needs Motorola 68000's registers and memory addresses, so developer must make these resources available as emulated registers).  My main question is, how is virtualization developed? How do we enable an entire OS to run as a process in a virtual machine, but get it to run independently while still making use of the actual CPU? I only know emulation, not virtualization, so if anyone could help that'd be nice!  PS: I am not asking solely what the difference is, but differences in how they run software. What are the different widely used RAID levels and when should I consider them? This is a  about RAID levels.    What are:   the RAID levels typically used (including the RAID-Z family)?  deployments are they commonly found in? benefits and pitfalls of each? How to initialize private static members in C++? What is the best way to initialize a private, static data member in C++?  I tried this in my header file, but it gives me weird linker errors:  class foo {     private:         static int i; };  int foo::i = 0;   I'm guessing this is because I can't initialize a private member from outside the class.  So what's the best way to do this? Reputation widget crash I have an issue with crashing reputation widget when it's added to the home screen. When I add it for the first time, it says "Please login before using this widget" (even though the app itself is logged in already). So I open the app, go back to the home screen, add the widget again and it crashes (and it's not added to the home screen). When I'll try to add it again, it says "Please login before using this widget" again. And then it just repeats - "Please login...", execute the app, crash, "Please login...", etc.  Restart of the device didn't make any change.  I have found .  My set up:  Stack Exchange app version: 1.0.89 Android version: 5.0.1 Device: Samsung Galaxy S4 Output of getent group Example of $\deg(fg)<\deg(f)+\deg(g)$ Let $R$ be an integral domain and $f,g\in R[X_1,...,X_n]$ where $n&gt;1$. What is an example of a pair $f,g$ such that $\deg(fg)&lt;\deg(f)+\deg(g)$?   Moreover, I have proven that the units of $R[X_1,...,X_n]$ are just the units in $R$. (Proof is done inductively) Is it true?  EDIT    Even though the each term in the underlined summation is nonzero, isn't it possible that the summation is 0? Why is this impossible ? Vertical spacing in floats I am using a float inside the text. As I found out, using \intextsep I could set space above and below the float and the texts. But when I am using \setlength{\intextsep}{5mm}, the space below the float is more than the one above it. Why they are not equal?  % Preview source code  %% LyX 2.0.0beta1 created this file.  For more info, see http://www.lyx.org/. %% Do not edit unless you really know what you are doing. \documentclass[english]{report} \usepackage[T1]{fontenc} \usepackage[latin9]{inputenc} \setcounter{secnumdepth}{3} \setcounter{tocdepth}{3} \usepackage{graphicx}  \makeatletter  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands. %% A simple dot to overcome graphicx limitations \newcommand{\lyxdot}{.}   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands. \usepackage{setspace} \setlength{\intextsep}{5mm} \setlength{\belowcaptionskip}{0mm}  \setstretch{2}  \makeatother  \usepackage{babel}  \begin{document} Text Text Text Text Text Text Text Text Text Text Text Text  \begin{figure}[h] \begin{centering} \includegraphics[scale=0.5]{\lyxdot \lyxdot /Pictures/fedora} \par\end{centering}  \caption{}  \end{figure} Text Text Text Text Text Text Text Text Text Text Text Text \end{document} I have a script that does a number of different things, most of which do not require any special privileges. However, one specific section, which I have contained within a function, needs root privileges.  I don't wish to require the entire script to run as root, and I want to be able to call this function, with root privileges, from within the script. Prompting for a password if necessary isn't an issue since it is mostly interactive anyway. However, when I try to use sudo functionx, I get:  sudo: functionx: command not found   As I expected, export didn't make a difference. I'd like to be able to execute the function directly in the script rather than breaking it out and executing it as a separate script for a number of reasons.  Is there some way I can make my function "visible" to sudo without extracting it, finding the appropriate directory, and then executing it as a stand-alone script?  The function is about a page long itself and contains multiple strings, some double-quoted and some single-quoted. It is also dependent upon a menu function defined elsewhere in the main script.  I would only expect someone with sudo ANY to be able to run the function, as one of the things it does is change passwords. prime divisor of $3n+2$ proof I have to prove that any number of the form $3n+2$ has a prime factor of the form $3m+2$. Ive started the proof  I tried saying by the division algorithm the prime factor is either the form 3m,3m+1,3m+2.  Case 1: $3m$      suppose $3m$ does divide $3n+2$. That means $3mr=3n+2$ where $r$ is some integer. But we get $mr-n= 2/3$ and since $mr-n$ is an integer that's a contradiction. Thus $3m$ does not work.  Case 2: $3m+1$ Same argument here  Case 3: $3m+2$ By the fundamental theorem of arithmetic every integer is divisible by a prime. But not sure what to do from here. Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$ Prove that if $d$ divides $n$, then $2^d  -1$ divides $2^n  -1$.  Use the identity $x^k  -1 = (x-1)*(x^{k-1}  +  x^{k-2}    + \cdots + x +1)$ Exactly half of the elements of $\mathcal{P}(A)$ are odd-sized