Why is it that differentiation of a function that is a composition of elementary functions (such as $\sin \:2^x$ or $\ln(\mathrm{arcsec}\: x^3)$ or $x^{1/x}$) always produces a composition of elementary functions, while integration sometimes does not? For example, the derivative of $\sin \:x^2$ is $2x\cos \:x^2$, but the integral of $\sin \:x^2$ produces the Fresnel sine function, the definition of which is simply the integral? To put it loosely, why does differentiation make functions simpler and integration make functions more complex? I guess what I'm trying to get at is what fundamental aspect of integration sometimes produces a non-elementary function from an elementary function?
If a function is a combination of other functions whose derivatives are known via composition, addition, etc., the derivative can be calculated using the chain rule and the like. But even the product of integrals can't be expressed in general in terms of the integral of the products, and forget about composition! Why is this?
ID for Contact portion of Person Account Is it possible to get the ID of a Contact which is part of a Person Account?  I have a custom object which has a custom field referencing the Person Account, though it seems to be referencing the Contact directly. I have created a button which I am using to pass the ID into a Visualforce Page.  With the Insert Field drop-down on the create/edit button page I can put in {!Account.Id} or {!Contact.Id} but neither of these work. The Account ID is placed in the URL but is not the correct ID and the Contact ID is blank, which I assume is because the button is on a Person Account page and not a Contact Page. Can a willing lycanthrope be True Polymorphed? Can a lycanthrope or other shapeshifter be willingly affected by the spell True Polymorph? I know that it can be affected by regular Polymorph, but the text for the enhanced version seems to differ. How to keep the console window open in Visual C++? I'm starting out in Visual C++ and I'd like to know how to keep the console window.  For instance this would be a typical "hello world" application:   int _tmain(int argc, _TCHAR* argv[]) {     cout &lt;&lt; "Hello World";     return 0; }   What's the line I'm missing? I wonder is it legal to register a domain name that contains a company name. For example cococola.cc (considering that this domain name is available). Can I buy and use any domain names that contain a name of a trademark? What's wrong if I fit the auto-regression with OLS? I am doing auto-regress by usual linear regression package. e.g.  $y_t=φx+ε_t$ with $x =y_{t-1}$  My reason is that, Auto-regression does assumes iid errors, same for linear regression. Linear Regression doesn't have assumption on independent variables. What's different is merely that the independent variables is replaced with lagged dependent variable y.  But I see AR always is fitted by specific methods, I am afraid I'm doing wrong. Wikipedia mentions several English words that have been :   Anime comes from animation and has been reborrowed into English to mean Japanese-style animation. Puroresu comes from professional wrestling and is a term for Japanese-style professional wrestling. Kosupure comes from cosplay (an abbreviation of costume play) and refers to the practice of dressing in costumes of anime and video game characters.    Do you know other examples of word reborrowings from Japanese or other languages back into English, or vice versa? Evaluating the infinite product $\prod\limits_{k=2}^\infty \left ( 1-\frac1{k^2}\right)$ How do I move child windows without moving or minimizing parent in GNOME 3? I have Ubuntu 17.10 with GNOME 3.  What happens: I have (for example) LibreOffice Calc open, with some data columns in it.  I highlight the columns I want to chart, then I select INSERT > CHART.  The chart child window dialog pops up on top of my data, so I want to move it to the side.  When I grab the top bar and move it, the parent (spreadsheet) window minimizes (I think it actually disappears).  Continuing the above example, if I click FINISH on the chart window, I can then see the minimized spreadsheet application, which is the window title bar plus the menu bar just below it.  This seems like really odd behaviour and certainly falls under the category of "not being useful to the user", since the whole idea of moving the child window in the first place was just to be able to better see the spreadsheet!  In other applications, for example the PDF viewer, a slightly different problem occurs.  When I try to move the child window (for example the print dialog) the parent does not minimize but instead follows the child window around.  This is less surprising than having the parent disappear entirely but equally useless in terms of allowing the user to see the information present in the parent window.  Update 2017/11/06  Pomsky's answer below fixes the problem, but leaves me wondering why the window manager is making the decision that all child windows have modal behaviour (or don't), and not the applications themselves; and further, why modal behaviour prevents moving the child screen around when it obscures useful info on the parent screen.  Neither of these seem like good design to me... Assume that $X$ and $Y$ are two random variables such that $Y=E[X|Y]$ almost surely and $X= E[Y|X]$ almost surely. Prove that $X=Y$ almost surely.   The hint I was given is to evaluate: $$E[X-Y;X&gt;a,Y\leq a] + E[X-Y;X\leq a,Y\leq a]$$  which I can write as: $$\int_A(X-Y)dP +\int_B(X-Y)dP$$ where $A=\{X&gt;a, Y\leq a\}$ and $B=\{X\leq a,Y\leq a\}$.  But I need some more hints. My Prof wrote that   $\sum_{n=2}^{\infty} n(n-1)x^{(n-2)} = \frac{2}{(1-x)^3}$  when $-1&lt; x&lt;1$  I do not understand where the above formula comes from. Can someone please explain the steps or provide a hint?   Thanks! Why are the IV (constant) values fixed for HMAC/SHA? Why do HMAC/SHA IV's have a fixed value? I refer to the arbitrary H constants which are included in the algorithm prior to any data being fed in.  Why aren't they exposed to the user, so one can decide on an IV and modify it accordingly (for example, in java they are provided at hash function specification, instead of being supplied by the user at init)?  How does modifying these IVs affect the algorithm? In how many different ways can you split $10$ people into two groups of $5$ people? In how many different ways can you split $10$ people into two groups with the same amount of people?  My attempt: Since the order in which you choose someone doesn't matter, I chose to calculate the combinations: $10 \choose 5$ How to use downloaded fonts with pdfLaTeX on Ubuntu I want to use the  font in my pdfLatex document.  What steps should I do for using a downloaded font   Should I download the TTF or the OpenType version? Where should I store the font? Should any font processing be done? How can pdfLatex find this font?   I am using TexLive 2011 installed in a custom location (/somepath/texlive/2011) on Ubuntu amsalpha-like bibtex style with manual labels I have from Exercise 1 pg 33 - "Algebra - T. W. Hungerford" following:      Question to proof: Show by example that the first conclusione may be false if $G,\, H$ are monoids that are not group.   I thinked:     Proof: let be for example two monoids $(G:=\{\emptyset\}, \bot)$ and $(H:=\{\emptyset, \{\emptyset\}\}, \top)$ with: $$\begin{array}{c|c} \bot &amp; \emptyset \\ \hline \emptyset &amp; \emptyset \end{array} \, \, \, \,\, \,\, \,\, \,\, \,\, \,\, \,\, \,\, \, \begin{array}{c|cc} \top &amp; \emptyset &amp; \{\emptyset\}\\ \hline \emptyset &amp; \emptyset &amp; \emptyset \\ \{\emptyset\} &amp; \emptyset &amp; \{\emptyset\} \end{array}$$ $G$ with $e_G:=\emptyset$ like neutral element and $H$ with $e_H:=\{\emptyset\}$ like neutral element. Let be $f$ a function from $G$ to $H$ with $\emptyset \mapsto \emptyset$ (namely $x \mapsto x$), the function is Homomorphismus in fact $$ \begin{align} {\color{Red}f}{\color{Red}(}{\color{Red}x}{ \color{Red}\bot }{\color{Red}y}{\color{Red})}=&amp;f( \emptyset \bot \emptyset)= {\color{Green}f}{\color{Green}(}{\color{Green}\emptyset}{\color{Green})}= \emptyset \\ {\color{Red}f}{\color{Red}(}{\color{Red}x}{\color{Red})} {\color{Red}\top} {\color{Red}f}{\color{Red}(}{\color{Red}y}{\color{Red})}=&amp;f(\emptyset) \top f(\emptyset)= \emptyset \top \emptyset= \emptyset \\ &amp;\text{with }x,y \in G \end{align}$$ but it means that $$ \begin{align} f(e_G)&amp;\neq e_H \\f(e_G)={\color{Green}f}{\color{Green}(}{\color{Green}\emptyset}{\color{Green})}=\emptyset &amp;\neq \{\emptyset\}= e_H \end{align}$$ Therefore $f$ ist Semigroup-Hom but not Monoid-Hom...   Is it correct? What did my neural network just learn? What features does it care about and why? Why should I avoid multiple inheritance in C++? Is it a good concept to use multiple inheritance or can I do other things instead? I'm using Ubuntu 12.04 &amp; everything about it is great except that it just won't resume after suspend. I've tried the suggestions listed in this thread  but none worked. I'm using Lenovo Y510P. I'm new to Ubuntu, or unix for that matter, so please let me know if there's anymore  information that I should be posting. Thanks.  update  I tried the suggestion by Dima on this post . The machine wakes up from hibernation but immediately the screen gives a screen like this     Wondering if this is an issue with the graphics card or something. Is it correct that "etc." can not be used together in a sentence with "for example" and "such as"? I just read an article from a Chinese website for English teaching which mentions  that point. For instance, one can't say:     "I can play quite a few musical instruments, for example, the flute, the guitar, the piano, etc.".    The correct one should be:     "I can play quite a few musical instruments, for example, the flute, the guitar, and the piano."    Is it possible to find any references to prove that? Renaming hundreds of files at once for proper sorting I have a ton of files, all named stuff like 1.jpg, 2.jpg, 3.jpg, and so on up to 1439.jpg, however, I have a problem with one of my projects and alphabetizing. It will usually go in the order 1.jpg, 10.jpg, 11.jpg and so on.  What I need is some way to name the files so they are in the format such as 00001.jpg all the way up to 01439.jpg.  How would I be able to do this quickly and efficiently?