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Evaluating the indefinite integral $ \int \sqrt{\tan x} ~ \mathrm{d}{x}. $ I have been having extreme difficulties with this integral. I would appreciate any and all help. $$ \int \sqrt{\tan x} ~ \mathrm{d}{x}. $$ Logical volume is not mounted but is in use. Please close all applications using this device (eg iscsi) How do I resize a LVM partition using system-config-lvm?  As per   I clicked on the partition and tried to resize, but got a pop-up error from system-config-lvm.     Logical volume is not mounted but is in use. Please close all applications using this device (eg iscsi).     What's the problem and how can I fix it?    See also . "Was" or "were" in subjunctive clauses I'm not a native english speaker, so even though I'm decently proficient at it, I don't really "know the rules" sometimes, and this is one that's been confusing me for a long time.  Which one is correct in each sentence?     If the movement [was/were] to continue uncorrected, the tower would   one day topple.      If I [was/were] rich, I would buy a yacht.   NOTE: I care not only about the case of "I", but also "she", "them", "it", etc, as in the example of the tower. Would it be any different if instead of the tower, it'd be me who'd topple if uncorrected?  I'm pretty sure it's "were" in both cases. That's what they taught me, I think. I started to doubt when I saw a lot of "was", but it sounded like the typical intentional mistake used "stylistically". ("If I was a rich girl...")  Then I saw it some more and thought it came down to an American/British English difference (I was taught British, in theory, and most of what I read is American).    But that tower sentence came straight from "The Guardian"...  When do you use was and when do you use were? Once a lead is converted it automatically creates an account, contact and one opportunity. But in my case i want to display the result without creating an Account. Please provide me with a sample code.  Any help will be appreciated... An example for a homomorphism that is not an automorphism Every vector space has a basis Prove that every vector space has a basis. I am going to use Zorn's lemma for this also here is a necessary definition regarding totally ordered subsets: one element will be contained in the other.   proof: A basis for $V$ is a maximally linearly independent set. Let $X$ be equal to all linearly independent subsets of $V$. On, $X$ define $A\leq B$ means $A\subset B$. Let $S$ be a totally ordered subset of $X$, let $T = \bigcup_{A_{s}\in S} A_s$ then $A_s\subset T$ for all $s\in S$. Does $T\in S$? i.e. is $T$ a linearly independent set?. Let $$O = \alpha_1 v_1 + \alpha_2 v_2 + \ldots + \alpha_n v_n \ \ \text{where} \ \ v_i\in T = \bigcup_{A_{s}\in S} A_s$$ Then there exists $S_i$ such that for all $i\in A_{s_{i}}$ all $i$ $A_{s_{1}},A_{s_{2}},\ldots, A_{s_{n}}$ (these will have one contained in the other then we would take the larger). So, there exists $A_{s_{k}}$ such that $A_{s_{k}}\supset A_{s_{i}}$ all $i$ just compare two at a time. Therefore, $V_i \in A_{s_{k}}$ all $i$, but $A_{s_{k}}$ is a linearly independent set. So, $\alpha_i = 0$ all $i$. Hence, $T\in X$ so $T$ is an upper bound for $S$. Hence every totally ordered subset of $X$ has an upper bound, hence by Zorn's lemma, there exists a maximal element and this would be the basis.  I am not sure if my proof is right, I apologize if it is a bit messy. If it is right, any suggestions on cleaning it up would be greatly appreciated. For example, here are top five accounts in each site (this picture was taken when I was in Biology SE).    As you can see, all the badges are DNA, while Academia's badges should be hats, so on.  What do you think? Theorem style with name as argument Is there some way to get a theorem type which will make a theorem with the name passed as a parameter? In other words, is there a way to define "named" such that   \begin{named}[NAME] text \end{named}   will print   "NAME: text"?  I tried using the definition \newtheorem*{named}{}, but that results in   "(NAME): text", which is quite different from what I am trying to do.  I know that I could also create a new instance of \newtheorem for each named theorem I want to use, but that is clunky and inconvenient. Is there a better way? Prove or show a counter example for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$ I'm working on my Discrete Mathematics homework and they are asking me this:  Prove or show a counterexample for: $\forall a, b, c \in \mathbb Z$, if $ab\mid c$ then $a\mid c$ and $b\mid c$  I'm not completely sure how to prove it. I was thinking to find a counterexample like zero but I'm not sure if that it's going to work. Or maybe try to approach it backwards?   I'm a little bit lost Is the use of "one of the" correct in the following context? How to proof that $\forall n \ge 1: \sum_{i=1}^n (i(i+1))^{-1} = n(n+1)^{-1}$ using mathematical induction So for a better presentation:   I need to prove this using mathematical induction, so i started with a base of $n=1$  Since $i$ starts at $i = 1$ I got this:  $$\frac{1}{i(i+1)} = \frac{n}{n+1}$$ $$\frac{1}{2} = \frac{1}{2}$$  So since this was true I went to the induction part: I chose $n = k$ and assumed this was true:  $$\frac{1}{i(i+1)} = \frac{n}{n+1}$$ $$\frac{1}{i(i+1)} = \frac{k}{k+1}$$  but I got stuck here since I didn't know if I needed to increment $i$ or not and because I didn't know if I needed to add the summation symbol or not and needed to do a few things with it. Compute the limit $\lim_{n \to \infty} \frac{n!}{n^n}$ Determining members of local groups via C# I wondered whether anybody knows how to obtain membership of local groups on a remote server programmatically via C#. Would this require administrator permissions? And if so is there any way to confirm the currently logged in user's membership (or not) of these groups? How can I vertically center a "div" element for all browsers using CSS? I want to center a div vertically with CSS. I don't want tables or JavaScript, but only pure CSS. I found some solutions, but all of them are missing Internet Explorer 6 support. &lt;body&gt;     &lt;div&gt;Div to be aligned vertically&lt;/div&gt; &lt;/body&gt;  How can I center a div vertically in all major browsers, including Internet Explorer 6? A method for evaluating sums/discrete functions by assuming they can be made continuous and differentiable? Test for convergence of the series $\sum_{n=2}^\infty\frac{1}{(\ln n)^{\ln n}}$ Generating data with a given sample covariance matrix how to permanently disable ubuntu updates & hide install updates button pic included how to permanently disable ubuntu updates pop up &amp; hide or remove Install Updates button pic included see below: Create a tar archive split into blocks of a maximum size I need to backup a fairly large directory, but I am limited by the size of individual files. I'd like to essentially create a tar.(gz|bz2) archive which is split into 200MB maximum archives. Clonezilla does something similar to this by splitting image backups named like so:  sda1.backup.tar.gz.aa sda1.backup.tar.gz.ab sda1.backup.tar.gz.ac   Is there a way I can do this in one command? I understand how to use the split command, but I'd like to not have to create one giant archive, then split it into smaller archives, as this would double the disk space I'd need in order to initially create the archive. I've read and have heard of both 'as per' and 'per' being used conversationally, both with the same connotation of either 'according to' or 'on authority of'  Examples:  "Tell Ron to start molding new rollers for the mecanum wheels, as per me"  "Per Mr. Crane, you need to start the molds for the new rollers."  They both establish the same context by setting that something should be done on the authority of someone else (or the speaker, per the first example (see what I did there?)). Or it acts as a way to cite a source of a statement, directive or fact in conversational speech.  My question is, what is, if any, the functional and syntactical difference between as per and per. If there are no differences, which is apropos to use?