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Generating ordered combination of numbers Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$ I am trying to find a closed form for  $$\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx = 0.094561677526995723016 \cdots$$  It seems that the answer is $$\frac{\pi^2}{12}\left( 1-\sqrt{3}\right)+\log(2) \log \left(1+\sqrt{3} \right)$$  Mathematica is unable to give a closed form for the indefinite integral.  How can we prove this result? Please help me.  EDIT  Apart from this result, the following equalities are also known to exist: $$\begin{align*} \int_0^1 \frac{\log \left( 1+x^{4+\sqrt{15}}\right)}{1+x}\mathrm dx &amp;=\frac{\pi^2}{12} \left( 2-\sqrt{15}\right)+\log \left( \frac{1+\sqrt{5}}{2}\right)\log \left(2+\sqrt{3} \right) \\ &amp;\quad +\log(2)\log\left( \sqrt{3}+\sqrt{5}\right) \\ \int_0^1 \frac{\log \left( 1+x^{6+\sqrt{35}}\right)}{1+x}\mathrm dx &amp;= \frac{\pi^2}{12} \left( 3-\sqrt{35}\right)+\log \left(\frac{1+\sqrt{5}}{2} \right)\log \left(8+3\sqrt{7} \right) \\ &amp;\quad +\log(2) \log \left( \sqrt{5}+\sqrt{7}\right) \end{align*}$$  Please take a look . Every time I try to do something seemingly-simple in CSS, it doesn't work.  I have a content div that contains a 460x160 image. All I want to do is position the image at the bottom-right corner and wrap my text around it.  &lt;div id="contents"&gt;     &lt;img src="..." /&gt;     text text text text text text ... &lt;/div&gt;   So I want it to look like:  ------------------ | text text text | | text text text | | text text -----| | text text |    | ------------------   Doing it with a top-left or top-right image is cake:  #contents img { float:right; }  ------------------ | text text |    | | text text -----| | text text text | | text text text | ------------------   Now how do I push that to the bottom? The best I've come up with so far are:  #contents img { float:right; margin-top: 90%} // really needs to be 100%-160px  ------------------ | text text      | | text text      | | text text -----| | text text |    | ------------------   In this case the text does not print in the margin, so there is white space above the image.  #contents { position:relative; } #contents img { position:absolute; right:0; bottom:0; }  -or-  // move the img tag under the text in the html and: #contents img { float:right; margin-top:-160; }  ------------------ | text text text | | text text text | | text text -----| | text text | te | ------------------   In this case the text prints over or under the image.  So... how can I accomplish this? Existence of area-preserving diffeomorphism between two sets in $\mathbb{R}^2$ Suppose that we have open sets $A, B\subset \mathbb{R}^2$ such that $A$ and $B$ are simply connected and have smooth boundaries. Furthermore, let us assume that $m(A) = m(B) &gt; 0$, where $m$ is the Lebesgue measure on $\mathbb{R}^2$. My question is as follows: when does there exist an area-preserving diffeomorphism between $A$ and $B$? In this context, an area-preserving diffeomorphism between $A$ and $B$ is a is a $C^{\infty}$-diffeomorphism $\phi : A\to B$ such that $m(S) = m(\phi(S))$ for all measurable $S\subseteq A$. If an area-preserving diffeomorphism doesn't always exist between sets $A$ and $B$ as above, are there any extra conditions we can impose on $A$ and $B$ such that there does exist an area-preserving diffeomorphism?  My thoughts thus far are that we always have a $C^{\infty}$-diffeomorphism between $A$ and $B$: this is a consequence of the . It's also obvious to me that if we can deform $A$ linearly to get $B$, then that deformation will be area-preserving. Furthermore, it seems that aside from this case, there's no reason why an area-preserving diffeomorphism should exist. However, I'm having a hard time proving that there necessarily isn't an area-preserving diffeomorphism between $A$ and $B$ if $B$ is not a linear deformation of $A$. Does anybody have any ideas? $f(z)$ and $\overline{f(\overline{z})}$ simultaneously holomorphic Working with a huge file. Illustrator is super slow. What can I do to ease the load? How to grep for text in a file and display the paragraph that has the text? Call java program from Node.js application List all the conjugate classes in the dihedral group of order $2n$ and verify the class equation.  The dihedral group is generated by two elements $r$ and $s$.   The order of $r$ is two since $r^2=e$ and $s$ is $n$ since $s^n = e$. And I know all elements can be produced as either $s^k$ or $rs^k$. How can I list all the conjugacy class? What does an ampersand after this assignment operator mean? Using the Terminal keybindings with bash on macOS I have been trying to learn the keyboard shortcuts for the shell on macOS, but when I tried using ALT+B, it did not work.  How do you discover, configure and use keybindings in the shell? Any cheatsheets would be helpful. How do I redirect in a class sub-classing the EventSubscriber class? What's the NB30 or MM-TD in an iPhone description in GSX? What's the NB30 or  MM-TD in an iPhone description? I always see these nomenclatures Non block, etc, what does it mean? Show that $U_n:=\left(1+\dfrac{1}{n}\right)^n$, $n\in\Bbb N$, defines a monotonically increasing sequence.   I must show that $U_{n+1}-U_n\geq0$, i.e. $$\left(1+\dfrac{1}{n+1}\right)^{n+1}-\left(1+\dfrac{1}{n}\right)^n\geq0.$$  I am trying to go ahead of this step. Show that $\lim\limits_{a \to 0^+} \int^1_0 ax^{a−1}f(x)dx=f(0)$. Suppose $f$ is Riemann integrable on $[0,1]$ and continuous at 0. Show that $$\lim\limits_{a \to 0^+} \int^1_0 ax^{a−1}f(x)dx=f(0).$$   Can anyone share some insight on this one? I have no idea where to begin. Maybe a substitution? Installation of latest version R for linux First I typed  sudo gedit /etc/apt/sources.list   after that I got one sources list then I typed  deb http://cran.rstudio.com/bin/linux/debian wheezy-cran3/   then I get the error like this  No command 'deb' found, did you mean:  Command 'derb' from package 'icu-devtools' (main)  Command 'deb3' from package 'quilt' (main)  Command 'debc' from package 'devscripts' (main)  Command 'dwb' from package 'dwb' (universe)  Command 'xdeb' from package 'xdeb' (universe)  Command 'debi' from package 'devscripts' (main)  Command 'dab' from package 'bsdgames' (universe) deb: command not found   How should I proceed? Since the Stack Exchange sites run on one clock, and a clock that is not common to most of us (such as those of us in the US), can we display a clock with the site time (UTC) displayed somewhere on every page, such as at the bottom with the other text?  That way we are more aware of when the days turn over, and ecetera...  close votes, delete votes, flags, and normal votes would also benefit from this as well (thanks @Grace Note!)...    What do you guys think? yea or nay? thoughts? Install Ubuntu 12.10 instead of Windows 8 In the Landau theory of phase transitions, is the order parameter a thermodynamic variable of state? In the Landau theory of phase transitions, one typically considers a "free energy" $F$ as a function of the temperature $T$ and the "order parameter" $\psi$: $F(T, \psi)$.  For the sake of clarity, let's consider the liquid-gas transition, in which the order parameter is usually taken to be the difference of densities between the ordered phase and the disordered phase.  In this case, it looks that the order parameter $\psi$ is closely related to the the volume $V$, a global variable of state.  What is the correct interpretation of $\psi$ as a thermodynamic variable?   I consider several logical possibilities, but all interpretations look troublesome to me:    $\psi$ is a variable of state replacing the volume. In this case I have a few related concerns:   Is the "free energy" $F$ the Helmholtz or the Gibbs free energy?    If $F$ is the Gibbs free energy, $F$ should depend on the temperature $T$ and the pressure $p$ (the conjugate variable of the volume), so it shouldn't depend on $\psi$.  If it is the Helmholtz free energy, it's ok that it depends on $\psi$, but the experiments are usually carried out at constant pressure, not constant volume.  Usually, state variables are something one can select at will [for instance, think of the phase diagram $(p, T)$]. However, the order parameter $\psi$ is not selected at will, but it is selected by the system as a result of the minimization process according to the Landau theory.  $\psi$ is yet another variable of state in addition to volume and temperature.    Why the pressure is not usually taken into account as a variable of state, and only the temperature is considered? What is the conjugate variable to $\psi$? Can really $\psi$ and $V$ be taken as independent?  $\psi$ is not a variable of state, is something else.   What else can $\psi$ be from the thermodynamic point of view? Same question as above, why is pressure not usually taken into account in Landau theory? Printing a file to a printer in Ruby