How to find $\int_0^2\frac{\arctan x}{x^2+2x+2}\,dx$?
Use of substitution into the integral $\int_0^2 \frac{\arctan x}{x^2+2x+2}dx$
Capitalization of explanation of abbreviations SSH Permission denied (publickey) I am trying to connect to a Linode (running Ubuntu 12.04 LTS) from my local machine (also running Ubuntu 12.04 LTS)  I have created a private and public key on my local machine and copied my public key to my Linode's authorized_keys file.  However, whenever I try to ssh to my Linode I get the error message Permission denied (publickey).    It's not a problem with how ssh is set up on my Linode because I can ssh to it from my Windows machine using key authentication.    In my .ssh directory on my local Ubuntu machine, I have my id_rsa and id_rsa.pub files.  Do I need to create an authorized_keys file on my local machine?    EDIT:  This is what I get when I run ssh -vvv -i id_rsa [youruser]@[yourLinode]:  debug3: authmethod_lookup publickey debug3: remaining preferred: keyboard-interactive,password debug3: authmethod_is_enabled publickey debug1: Next authentication method: publickey debug1: Offering RSA public key: id_rsa debug3: send_pubkey_test debug2: we sent a publickey packet, wait for reply debug1: Authentications that can continue: publickey debug2: we did not send a packet, disable method debug1: No more authentication methods to try. Permission denied (publickey). Significance of starting the Fibonacci sequence with 0, 1.... DISCLAIMER: I do not deal with in-depth mathematics on a daily basis as some of you may, so please pardon my ignorance or lack of coherence on this topic.  QUESTION: What is the significance of starting the Fibonacci sequence with $0,1$ ?  For instance, if I picked any two random integers, say 2 and 7, to start a sequence would I actually be creating some multiple or derivation of the Fibonacci sequence?  Is there a general mathematical explanation for the relationship between any sequence represented by $a[0] = x, a[1] = y, a[n] = a[n-1] + a[n-2]$ and the Fibonacci sequence?  Or, back to my example sequence, is there a general mathematical relationship between:  $2,7,9,16,25,41,66,107,173,280...$  and  $0,1,1,2,3,5,8,13,21,34...$  Perhaps the Golden Ratio explains it somehow?  Any help would be appreciated. Creating polygon from hole in QGIS? Common binaries with support for command execution, like `awk` and `vim`, not respecting setuid bit? What is the isomorphism between the fields $(Z_2[x]^{<3},+_{x^3+x^2+1},\times_{x^3+x^2+1})$ and $(Z_2[x]^{<3},+_{x^3+x+1},\times_{x^3+x+1})$? If $x$ is a positive rational but not an integer, is $x^x$ irrational? How to set a command block with a command inside using the setblock command If two coins are flipped and one gets head, what is the probability that both get head? What is meant by "Constant Amortized Time" when talking about time complexity of an algorithm? Drop shadow for text in PGF/Beamer I want to really put an emphasis on some central piece of text I'm using in a Beamer slide.  I'm using tikz and overlay to put it, enlarged, on the center of the page, using the following code:  \begin{tikzpicture}[remember picture,overlay]   \node[at=(current page.center)] {     \scalebox{2}{\Huge\texttt{{This is important!}}}   }; \end{tikzpicture}   Can I add a drop shadow to the letter themselves, so they would look even more emphasized?  Is there some other decoration that can be added to the text itself, like a glow, etc.?  Or does PGF ignores node text altogether?  The text should be in typewriter style, so using special fancy fonts is probably not the solution. A Regex that will never be matched by anything What's in "standard system utilities" in the server install? My googlefu has failed me. What packages are part of the "standard system utilities" that is preselected during install?  TIA! (-: Solution for A/C Condensate Drain Line that doesn't require emptying a bucket of water every day? Isomorphism of quotient modules implies isomorphism of submodules? Let $A$ be a commutative ring, $M$ an $A$-module and $N_1, N_2$ two submodules of $M$.  If we have $M/N_1 \cong M/N_2$, does this imply $N_1 \cong N_2$?  This seems so trivial, but I just don't see a proof... Thanks! This question was recently split into different questions for each workaround. See   meta posts for more information.   Can you use NBT tags in commands? I’ve tried commands that normally work in Java Edition like: give @s minecraft:planks 30 1 {display:{Lore:[&quot;Wooden planks&quot;]}} give @s stone_pickaxe{Unbreakable:1b} give @s item_frame{EntityTag:{Invisible:1b}} summon villager ~ ~ ~ {Offers:{Recipes:[{buy:{id:&quot;emerald&quot;,Count:5b},sell:{id:&quot;diamond_sword&quot;}}]}} summon tnt ~ ~ ~ {Fuse:20s} In the chapter on Spellcasting, there is a section called . However, despite the seeming generality of the title, the text of this section only talks about magical effects from spells:     The effects of different spells add together while the durations of those spells overlap. The effects of the same spell cast multiple times don't combine, however. Instead, the most potent effect--such as the highest bonus--from those castings applies while their durations overlap, or the most recent effect applies if the castings are equally potent and their durations overlap.   It makes sense that this section would only talk about spells, since it is in the chapter about spellcasting. However, this seems to leave ambiguous the question of how magical effects from sources other than spells combine. Such an issue could arise, for example, if two different items (or two of the same item) grant a bonus to attack rolls, or a bonus to the same saving throw.  Is there a published rule or official ruling that governs how non-spell magical effects combine?  (This question was inspired by  about the interaction between +X magical ammunition and Oil of Sharpness, and could be considered a generalization of that question.) Laptop with no battery Motivating question:    I'm aware that one can construct a hierarchy of number systems via the Cayley–Dickson process:  $$\mathbb{R} \subset \mathbb{C} \subset \mathbb{H} \subset \mathbb{O} \subset \mathbb{S} \subset \ldots $$  "Reals" $\subset$ "Complex" $\subset$ "Quaternions" $\subset$ "Octonions" $\subset$ "Sedenions" $\subset$ $\ldots$  and that at each step you're given a multiplication table that tell how the elements interact. As you move up the ladder, certain "nice" properties are lost: ordering,  commutativity, associativity, multiplicative normedness, etc... Given the multiplication table, you can show that these properties don't hold.   Eric Naslund noted that "the first 4 are very special as they are the unique 4 normed division algebras over ℝ", no surprise then that these $2^n$-ions have found quite a bit of use. I'm interested in the sequence itself however, irrespective of how useful a $2^{256}$-ion might be (ducenti-quinquaginta-sex-ion?).   I feel like something deeper is going on here though that I don't understand. Why are these particular properties lost at each step? Is it possible to quantify the process such that, at the $2^n$-ion you can say something about the symmetry of the multiplication table*?  * I'm making an ansatz that there is a connection between the symmetry of the multiplication table and these "nice" properties. What is the idiom for "as anyone can see" or "clearly"? I keep wanting to say "the handwriting on the wall," but that's not correct. The place I'm trying to use it is, "Alice likes Bob, Carol likes Bob, Alice thinks Bob likes her, but Bob dates Carol, and so as anyone can see, Bob did not like Alice."  What is the appropriate idiom here?