I have to calculate the integral $\int \frac{2-3x}{2+3x} \sqrt{\frac{1+x}{1-x}}dx$. I tried the following substitutions: $x \rightarrow \frac{1+t}{1-t}, x \rightarrow \frac{1-t}{1+t}, x \rightarrow \frac{t^{2}+1}{t^{2}-1}$ but with no good result. Also I observed the symmetry in the integral, by $x\rightarrow\frac{x}{3}$. However I am unable to end it.
Evaluate $$\int \frac{2-3x}{2+3x}\sqrt\frac{1+x}{1-x}d x$$ What substitution should I use ? $\sqrt\frac{1+x}{1-x}$ suggests $x=cos2\theta $ but its not useful in $\frac{2-3x}{2+3x}$
How to include time factor in a mixed model (investigating the interaction between two factors and time)? Most people spend part of each day standing, and if they have normal anatomy their heads are over their heels in this position.  Even sitting or lying down, the head is higher than the heels (if not over the heels).  Yet the phrase "head over heels" is used in ways implying it is an unusual situation.  How did such usage come to be, and why does it persist?  Why is the more obvious "heels over head" not used? Orthographic Camera Zooming In XNA I am using a spritebatch to render a board. I have created a camera class which can provide me a view and projection matrix. Currently I am supplying the view matrix to my sprite batch when I call begin.  I can get the view matrix to correctly move everything around and do some zooming in and out. My problem is that I want to zoom in on a specific point (for now the center of the screen) but currently zooming just zooms in on the coordinate 0,0.   Here is how I am constructing the view matrix;          _ViewMatrix =             Matrix.CreateTranslation(                 new Vector3(                     (-_Position.X + _Width * _Zoom / 2),                     (-_Position.Y + _Height * _Zoom / 2),                     0) ) *             Matrix.CreateScale(new Vector3(_Zoom, _Zoom, 1));   How could this be altered to make it scale correctly relative to the given point. Later I will probably want to zoom to the mouse position, but if someone has a simple example I'm sure I can work out how to adapt it. Subfields of finite fields Headless linux install operators as strings I need to evaluate a mathmatical expression that is presented to me as a string in C#.  Example noddy but gets the point across that the string as the expression.  I need the evaluate to then populate an int.  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(To yield a numbering in the style of Tractatus Logico-Philosophicus).  \def\on{} \def\down{} \def\up{}  \on This is the first paragraph, paragraph number 1.  \on This is paragraph number 2.  \down This is paragraph number 2.1  \down 2 This is 2.101  \up This is 2.11  \down 2.111  \up 3 3  \bye   If \down is starred, begin with zero.  If \up is followed by an integer, it should take it as an argument, unless there is a newline between \up and the integer.  An indefinite number of decimals should be possible.  PS.  I apologize for changing the question after (2) answers have been given, but I realize I failed to appreciate a feature of Wittgenstein's numbering: the last decimal is never 0.  Therefore, \down &lt;n&gt; is better than \down*, as now demonstrated above.  I think the 0 is supposed to indicate an additional level of unimportance. Possibly offensive usernames I flagged  as having a  ():    I said "possibly offensive" because it's possible it's a genuine surname I wasn't aware of, but googleing didn't show any evidence and  pretty much matched my definition of it which seems offensive.   Is this really a genuine name? If not how is it possibly not offensive and thus a bad flag?   (I flagged in good faith so even if it is a genuine name declining seems harsh) There are $k$ penguins, $k\ge 3$. They are all different heights. How many ways are there to order the penguins in a line, left to right, so that we cannot find any three that are arranged tallest to shortest (in left to right order)? The penguin triples do not have have to be adjacent.  This problem is courtesy of someone I know only as "DaMancha." The question is:      Prove that if $p \in \mathbb{Z}$ is irreducible, then $p$ is also prime.    Irreducible is defined as follows: $n \in \mathbb{Z} $ is irreducible iff the only way to write $n=ab$ for some integers $a$ and $b$ is if $a = \pm1$ or $b = \pm1$. Prime is defined as follows: an integer $n$ is prime iff whenever $a,b \in \mathbb{Z} $ and $p\mid ab$ then it must be true that $p\mid a$ or $p\mid b$ (or both).    Hint: Prove that if $n\mid ab$ but $n$ does not divide $a$, then $\gcd(a,n) = \pm1$. Then use Bézout's theorem and prove $n\mid b$. I need an appearing effect for text like the one (in javascript) here .  However I don't know how to insert js code into LaTeX (apart from using the AcroTeX Bundle) and that would also force me to use Acrobat Reader, so I'd like to implement a similar effect in Beamer. Is it possible?  (of course I would love to see alternative approaches to this) Does an HDR environment texture affect the Shadow pass? I am compositing a scene using a standard process in Cycles, and it worked correctly as long as I had my lighting setup in the scene, however when I switched to HDR, my Shadow pass seems to become a solid black. Why is this, and how can it be avoided?  My node setup: Citing papers, that are cited within a paper? I am reading a paper which discussing the change in a specific idea in a field of science over time. I would like to basically summarize the points in the paper but in a smaller fashion by taking some quotes and explaining how they relate to my situation.   For instance, in the paper I am reading the author said "in 2002, Stanley and Miikkulainen [SM02b] argued that the topology of a neural network also affects their functionality" where the tag [SM02b] is a reference to a entry in the author's bibliography.   Is it sufficient to only cite the author of the paper, or do I need to cite both the author of the paper and the author of the paper the author cited in the paper? What is syntax highlighting and how does it work? Moment generating functions/ Characteristic functions of $X,Y$ factor implies $X,Y$ independent. This is solely a reference request. I have heard a few versions of the following theorem:     If the joint moment generating function $\mathbb{E}[e^{uX+vY}] = \mathbb{E}[e^{uX}]\mathbb{E}[e^{vY}]$ whenever the expectations are finite, then $X,Y$ are independent.   And there is a similar version for characteristic functions. Could anyone provide me a serious reference which proves one or both of these theorems? No package php-imap available on CentOS 7 I'm running a dedicated server with CentOS 7 64bit, here is the output when trying to install IMAP:    yum install php-imap   Loaded plugins: fastestmirror   Loading mirror speeds from cached hostfile    * base: ftp.ciril.fr    * extras: ftp.ciril.fr    * updates: ftp.ciril.fr   No package php-imap available.   Error: Nothing to do       Also the same when disabling exclusions:    sudo yum install --disableexcludes=all php-imap Loaded plugins: fastestmirror Loading mirror speeds from cached hostfile  * base: ftp.ciril.fr  * extras: ftp.ciril.fr  * updates: ftp.ciril.fr No package php-imap available. Error: Nothing to do Is a droid a ‘he/she’ or an ‘it’? Inspired by  question.  Are droids in the Star Wars universe referred to with gendered pronouns (i.e. he or she), or are they referred to as objects (i.e. it)? Why is plain-hash-then-encrypt not a secure MAC? It seems that even in MAC-then-encrypt systems like SSL, something like HMAC is used rather than a plain hash. Why?   Suppose we use some stream cipher; then why can't we use $Encrypt(m | H(m))$ as the MAC-then-encrypted version of the message? Assuming no bad relations between $Encrypt$ and $H$, what are the possible weaknesses? 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I've just installed Ubuntu and I need either video, wireless, or some sort of other manufacturer (non-opensource) driver. How can I run the tool that will fetch all of these for me? I'd like graphical instructions.  Related: