Solve this:     $$\int\sin(\cos x)dx$$   I checked on Maxima, mathematica but both cannot find its integral though numerical approximation is available in later. Has someone faced similar problem? Also, I saw that such problems are not stated in books also, no function can be expected to be invalid to integrate !!
I've been wondering, what is the general form for the integral of $\sin(\cos x)$? I tried integrating it myself and couldn't, tried with Wolfram Alpha and it couldn't either. If you think about it conceptually, it should have a general form as it's graph if just like sin and cos, which both have general forms. If it doesn't have a general form, I'd like to know why. Thanks!
What does “pull sb. out of the hat” mean? I found the phrase, “pull her out of the hat” in the following sentence of the quote from Frank Bailey, the most relied-upon former aide of Ms.Sarah Palin, whose memoir, “Blind Allegiance to Sarah Palin: A Memoir of Our Tumultuous Years” is due out on Tuesday this week.  “I doubt if there's anything new in this book, just more detailed views of the gruesome story of her rise and fall. What would really be interesting is an account of who made the decisions in the GOP to pull her out of the hat. It certainly wasn't McCain.”  I don’t find the idiom, “pull one out of the hat” in any dictionaries at hand. Does it mean to “pick up” (Sarah Palinfor (vice) presidential candidate) or “remove her from (the candidate seat)? Can somebody teach me the meaning of this phrase? Do local flows of left-invariant vector fields satisfy $\Phi_X^t\circ L_x=L_x\circ \Phi_X^t$? Given $G$ a lie group and $X$ a left-invariant vector field. Let $\Phi_X^t$ be the local flow of $X$. Why can we conclude that $\Phi_X^t \circ L_x=L_x \circ \Phi_X^t$? Thanks! Flatten an irregular list of lists My Windows 7 has suddenly stopped displaying Unicode symbols For some strange reason, my computer suddenly doesn't show certain unicode characters anymore! I have no idea what happened.  Affected applications include Windows Explorer (should be Japanese characters), Google Chrome (should be a heart), and Winamp (should be stars):      Russian, German etc. characters are displayed normally. Chrome also displays Japanese script on websites, but not in the GUI. How can I fix it?     TL;DR: A workaround is to put a shortcut with a Unicode name on the desktop so that explorer.exe is the first process to display a Unicode string after booting.     Update: I have tried to use System Restore to fix it. I needed to go back in time quite a while because the most recent restore points didn't solve it so I used one from the middle of November. After that restore, Unicode symbols were displayed again. Then I updated my system with Windows Update again because those were removed during the restore. After that, the error occurred again! I then did a restore to a point before my new updates, but the error persists, and the old restore point (which I used before) is gone and there are currently no other snapshots of the system. Any suggestions on what to do now?  Update 2: I could find a workaround:      Control Panel → Region and Language → Administration → Change Language for Unicode-incompatible programs to Japanese (Japan).    All mentioned programs display their symbols correctly again. However, I don't consider this a fix because these programs are not usually Unicode-incompatible, and it also leads to some (non-serious) artifacts in some programs. I still welcome an answer that tells me what went wrong here and how to fix the issue.  Update 3: I think I have isolated the particular Windows Update which causes the error. It is . I have installed all other updates except this one, and the error did not occur again.  Update 4: The true origin of this problem was Chrome, see accepted answer. Workaround: put shortcut with Unicode name on desktop so that explorer.exe is the first process to display a Unicode string after booting. Undefined control sequence and \chapter error I’m getting an “undefined control sequence” error with the following code, using TeXstudio:  \documentclass[11pt]{article} \begin{document} \begin{center} \chapter{CHAPTER 6} \end{center} \end{document} Direct observations of a black hole? Notation question: $\ll$ Omission of "the" in "elected him president" and "made captain" In Days Of Future Past, Quicksilver spends a lot of time playing with electronics.  In his famous tour de force scene in the Pentagon, he specifically puts his headphones on before running around the kitchen.  But why?  Does the music on his Walkman speed up with him as he uses it, or is it still operating at "normal" speed? Or indeed, does any electronic device that he touches speed up? How do I find out command line arguments of a running program? I'm looking for a tool or method to find out what command line parameters have been passed to a program, for example when it was run by another program (launcher-application scenario). Suppose that $f$ is a function defined in $[a;b]$ to $[a;b]$ and continuous on $[a;b]$. The problem is I haven't the definition of the function, this is more abstract, but even if how can I prove that $f$ would have a fixed point? What happens with the force of gravity when the distance between two objects is 0? so I had my first approximation to the gravity equation  \begin{equation} F=GmM/r^2 \end{equation} and some questions arose that my teacher couldnt respond: if r approximates to 0 with mM being constant, then the force should tend to infinity, right? so that being true, then if we would travel to the center of the earth, we would be crushed by gravity? if so, how can there be anything right in the center of the earth? wouldnt anything there be compressed and destroyed by the infinite force?  having that in mind, my next question is as gravity force is measured from the center of an object, any part of the same object which is not at the center would be affected by the same object's gravity? if so, how can we differentiate between two objects that are not in a vacuum? my question originated thinking in us standing on the earth, in contact with it, are we, in a gravitational sense, one object? this lead to the last question, if gravity is a property of matter, then how applying the same logic as before, how does it work between two neutrons?(chose neutrons because i assumed it would be more difficult obtaining gravitational force if there was electrostatic forces from charges inbetween) do two newtrons in contact count as 1 gravitational object? and how thats its own gravity affect the newtron from center and out? Can't read filenames in save dialog box. Names are too faint I want to click on file to inherit the name for the file being saved. I can't read file names in the dialog box because the color is too faint. This is the same question as   That question does not have an answer but I don't have enough points to interact there so I have to post a new question.    Edited to add screen shots I tried to calibrate the monitor which no effect and did not change the readability of "unavailable" file names. I have added screenshots of previous operating systems to compare: Please tell me how Mojave is not to blame here: Is there a way to save composite node presets? Is there any way in Blender to save settings in your compositing node setup. For example say for my shadow catcher I have it setup for a hard shadow for sunlight, and then I also have a setting for diffuse light shadow for indoors. Is there any way I can save these settings individually so I can quickly switch to them rather than having to individually change the nodes every time. How to code around known MMa special-case failures? workspace switching via ctrl + alt + arrow not working after upgrade to 13.04, how to fix this? Dynamic loading of python modules Should the weight of downvotes be increased? Electron shells in atoms: What causes them to exist as they do? I have seen similar posts, but I haven't seen what seems to be a clear and direct answer.  Why do only a certain number of electrons occupy each shell? Why are the shells arranged in certain distances from the nucleus? Why don't electrons just collapse into the nucleus or fly away?  It seems there are lots of equations and theories that describe HOW electrons behave (pauli exclusion principle), predictions about WHERE they may be located (Schrödinger equation, uncertainty principle), etc. But hard to find the WHY and/or causality behind these descriptive properties.  What is it about the nucleus and the electrons that causes them to attract/repel in the form of these shells at regular intervals and numbers of electrons per shell?  Please be patient with me, new to this forum and just an amateur fan of physics. Why is the spoken German in many US films and TV shows so inaccurate? Is there a reason why in so many English-language movies and TV series, whenever someone is speaking "German", they (actors, writers etc.) just don't care about if what they say is right or wrong? This can range from:    just minor grammatical errors e.g. "Schieß dem Fenster" in "Die Hard":                                rambling some made-up words and claiming them to be German e.g. "Lebenslangeschicksalssatz" in "How I met your mother"                                wrong German paired with a bad accent e.g. in "Scrubs"                                up to native German speakers talking complete nonsense e.g. Heidi Klum in HIMYM                                  I don't know if this is the same with other languages (for example there is a scene in Scrubs where the cast speaks Spanish, but there might be similar mistakes:                                 Do the creators and actors just not want to speak correct German and at least use correct German words, or is there simply no money in a $100,000,000 movie production to ask a native speaker to look over your script and maybe correct some of the lines?