How can I solve $\int \sqrt{1+x^2}\,dx$? $$\int \sqrt{1+x^2}\,dx$$  I've tried some step-by-step calculators, but what they give is way beyond my level. Is there any "simple" way to solve this?
How to integrate $\int\sqrt{x^2+1}dx$ $$\int\sqrt{x^2+1}dx$$ I've been attempting this problem for days and I've made very little progress. I understand that I should substitute $x=\tan(x)$ and $dx=\sec^2(x)dx$ but beyond that I am very much lost.
How do I turn on workspaces? (Why do I only have one workspace?) It appears that Unity on Raring only comes with a single virtual desktop (aka workspaces) by default, and CCSM's Wall plugin has no way to add more. Is this configurable at all? If $p$ is a prime and $p \mid ab$, then $p \mid a$ or $p \mid b$. Why does the beta distribution become U shaped when $\alpha$ and $\beta$ <1? In the Beta distribution (used to model Bernoulli probabilities), the $\alpha$ and $\beta$ parameters can be interpreted as the number of heads$+1$ and the number of tails$+1$ seen. So, if they were both $2$, it would lean towards the coin being fair and have a maximum at $0.5$. If they are both $20$, the distribution would become even surer we're dealing with a fair coin and peak even more at $p=0.5$.  What I don't get is its behavior when $\alpha$ and $\beta$ both become $&lt;1$.   In that case, it becomes U-shaped and the density peaks at $p=0$ and $p=1$. Meaning the coin is likely to be two-sided. I know there is an intuition for this since I think I had an idea about it a long time ago. However, I've been trying to recollect all day and can't piece it together. Does anyone have an intuition? What is the probability that all three tosses result in the same outcome? A coin is tossed three times: The probability of zero heads is 1/8 and the probability of zero tails is 1/8.  And my question is: What is the probability that all three tosses result in the same outcome?   So, if P(zero heads)= 1/8 , then that should be the same of p(all tails)?  If so, we could use the Addition Rule which is $P(A \cup B) = P(A) + P(B)$  where A and B are disjoint events, i.e. $A \cap B = \emptyset$, A is the event of tossing all heads and B is the event of tossing all tails.  I'm not sure how to continue after that... would the complement be used? Are there irreducible polynomials that are partially solvable by radicals? In general, polynomials of degree 5 or higher, with rational coefficients, are not solvable by radicals. There are some exceptions and trivial cases, for example $x^5-5x+12$ and $x^{100}+x^{25}+3$, respectively.  All irreducible polynomials with rational coefficients, that I am aware of, have either none or all roots that can be expressed by radicals.  Do partially-solvable irreducible polynomials exist? If they do, are there any examples known?  I mean, for example, an irreducible polynomial of $n$th degree that can be split over $Q(\sqrt{2})$ into two polynomials of 3rd and $(n-3)$th degrees, where the polynomial of $(n-3)$th is not solvable by radicals.    At  Alexander Gruber wrote:     Polynomials which are not solvable by radicals have (at least one) root that cannot be written by any combination of the operations of addition, multiplication, and the taking of nth roots.   I am not sure if he meant only reducible polynomials, and/or with non-rational coefficients, as polynomials that have "at least one" root that cannot be expressed by radicals. I have secured a visa for the US, be it an ESTA or another visa requiring me to go for an interview. My understanding is that obtaining a visa for the US does not guarantee me entry into the country. Rather, :  Entering the United States A visa allows a foreign citizen to travel to a U.S. port-of-entry (generally an airport) and request permission to enter the United States. A visa does not guarantee entry into the United States. The Department of Homeland Security (DHS), U.S. Customs and Border Protection (CBP) officials at the port-of-entry have authority to permit or deny admission to the United States. If you are allowed to enter the United States, the CBP official will provide an admission stamp or a paper Form I-94, Arrival/Departure Record.  What happens once I arrive in one such port-of-entry? Will I have to go through customs checks? Will I have to talk to an immigration officer explaining my reasons for visiting the US? What documentation, if any, should I bring? Is the documentation I brought for the interview enough? What if I did not attend an interview since it was not required (for example if I obtained an ESTA online)? How to delete all lines that do NOT contain a certain word in Vim? In vim I can delete all lines that contain the word "price" with this  :g /price/d   How can I delete all lines that do NOT contain the word "price"? How do I force TeX to completely use the 1st column before writing to the second column?  Right now I dont have enough content to fill one whole page. So the left and right columns are equally filled, leaving 25% symmetrical empty page at bottom. How do I fill the left column first, and then the right?  \documentclass{article}  \usepackage{multicol} \usepackage[scale=0.9]{geometry} \usepackage{amssymb} \renewcommand{\labelitemi}{\tiny$\blacksquare$} \begin{document} \begin{multicols}{2}      %lots of text goes here  \end{multicols} \end{document} How can I network two Ubuntu computers, so that they can "see" each other at an IP address? Is there a complete list of these? I've seen lots of Q&amp;A about "What does x icon mean" but it would be really useful if there were a complete list for reference! How to block specific notifications from an app? A certain app I use gives me crucial notifications that I need, but also notifies me almost daily that over 80% of my RAM is used. I would like to allow this app to send me all notifications except those that contain the string "80% of your RAM" in the text of the notification.  Obviously, there is no way to filter a certain app's notifications in stock Android (other than blocking all of a certain app's notifications, but that's not what I want!), but is there a way that I can block notifications if they contain a certain string of text?  Nexus 6P running Android Marshmallow 6.0.1, if you're curious the app in question is . I am developing my first 2D game in Unity and I have come across what seems an important question.  How do I handle data between scenes?  There seems to be different answers to this:   Someone mention using , while other people told me this should be used to store other things like screen brightness and so on. Someone told me that the best way was to make sure to write everything into a savegame everytime that I changed scenes, and to make sure that when the new scene loads, get the info from the savegame again. This seemed to me wasteful in performance. Was I wrong? The other solution, which is the one I have implemented so far is to have a global game object that isn't destroyed between scenes, handling all the data between scenes. So when the game starts, I load a Start Scene where this object is loaded. After this ends, it loads the first real game scene, usually a main menu.   This is my implementation:  using UnityEngine; using UnityEngine.UI; using System.Collections;  public class GameController : MonoBehaviour {      // Make global     public static GameController Instance {         get;         set;     }      void Awake () {         DontDestroyOnLoad (transform.gameObject);         Instance = this;     }      void Start() {         //Load first game scene (probably main menu)         Application.LoadLevel(2);     }      // Data persisted between scenes     public int exp = 0;     public int armor = 0;     public int weapon = 0;     //... }   This object can be handled on my other classes like this:  private GameController gameController = GameController.Instance;   While this has worked so far, it presents me with one big problem: If I want to load directly a scene, let's say for instance the final level of the game, I can't load it directly, since that scene does not contain this global game object.  Am I handling this problem the wrong way? Are there better practices for this kind of challenge? I would love to hear your opinions, thoughts and suggestions on this issue.  Thanks Why does evolution not make our life longer? Why does evolution not make life longer for humans or any other species?  Wouldn't evolution favour a long life? Send values from one form to another form I am trying to convince my friend that the integral of $0$ is $C$, where $C$ is an arbitrary constant. He can't seem to grasp this concept. Can you guys help me out here? He keeps saying it is $0$. Can apostrophe 's' be used with 'etc.'? Creating Inky-looking characters in Blender I'm involved in a project to do with ink animation and experimentation. I found this incredible piece of animation:    I originally thought this was some sort of After Effects compositing (is it even possible in AE?!), but found out that this particular animation was created in 3DS Max with Krakatoa and FumeFX. I'm just wonder if a similar effect is doable with Blender's smoke simulator.  There are various YouTube videos that have pretty decent results of ink renders from Blender, but I can't seem to find anything of a similar sort of movement animation. Just blobs floating around! The closest thing I found was this animation of a         but again I can't seem to replicate this. The smoke just doesn't seem to follow my character's animation. Any help with this would be greatly appreciated. Thanks. Why couldn't Doctor Strange use his sling ring in space? How many possible electromagnetic wavelengths are possible? Disclaimer: Please keep in mind that I am a young highschool student with no background in physics, this research was done in the course of an hour, and my reasoning could very well be wrong.  After a short conversation about color, I did some thinking, and read  The answer claims that there are $\infty^{\infty}$ colors   My first problem is the definition of colors, I'm going to simplify this (although it's not the same thing) as electromagnetic frequencies. This is what I mean when I refer to color in the rest of this question  The problem with $\infty^{\infty}$ colors is that the plank length exists. This causes two problems to arise with $\infty^{\infty}$. If $l_p$ is assumed to exist (as it is), this means the smallest distance in the universe is $l_p$. So, all wavelengths of light can be divided into a set, of the wavelengths produced by objects at $0^{\circ}$ Kelvin to $\infty^{\circ}$ Kelvin. According to this logic, there are simply $\infty$ colors.  Things are complicated further, when you introduce the Plank Temperature ($P_t$). $P_t$ is the theoretical limit temperature of the universe (at least for the purposes of light and color) Because an object hotter than $P_t$ will produce light with wavelengths shorter than $l_p$. This would introduce an upper limit on colors too.  Wouldn't this mean that the total number of possible colors is equal to however many plank lengths difference there is between an electromagnetic wave produced by a 0 degree object and a $l_p$ object? And therefor far less than $\infty$? Does this reasoning make sense at all? Adding vertical space at the start of a page I'd like to, first thing before writing anything on a page, add some vertical space.  Minimal (non)working example:  \documentclass{article} \begin{document}  \vspace{250px} I want to be further down on the page :(  \vspace{250px} Haha! Sucker :D \end{document}     How can I get the first \vspace to work, just like the second one?