Calculate $$\int\limits_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}}dx$$   First I tried the substitution $t=x+2$ and obtained $$\int\limits_{0}^{2} \frac{t-2}{\sqrt{e^{t-2}+t^2}}dt$$ and than I thought to write it as $$\int\limits_{0}^{2} (t-2)\frac{1}{\sqrt{e^{t-2}+t^2}}dt$$ and use the fact that $$2(\sqrt{e^{t-2}+t^2})'=\frac{1}{\sqrt{e^{t-2}+t^2}} \cdot(e^{t-2}+2t)$$ Using integration by parts we get that we have to calculate (excluding some terms we know) $$\int\limits_{0}^{2} \sqrt{e^{t-2}+t^2}\cdot \frac{6e^{t-2}-2te^{t-2}+8}{(e^{t-2}+2t)^2}dt$$ which is uglier then the initial problem. Do you have any idea how to solve the problem?
$ \int_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}} dx $ = -$  2.887270... $  The function has no antiderivate and there's no symmetry here to help, if you solve this I would be thankful if you would for a highschooler ^^
Is there a word for someone with the same name? If a person shares my name, in Dutch there is the word &quot;naamgenoot&quot;, meaning roughly 'member of the same name'.  John A: Hi, my name is &quot;John&quot;  John B: O, then we're insert solution word here!  Similarly,  'classmate' is 'klasgenoot' in Dutch 'roommate' is 'kamergenoot' in Dutch  I'm pretty sure I cannot call someone with the same name as mine a 'namemate' :)  Edit Because sceptics appear to be frustrated mightily by an apparent lack of research, there was  in chat, with no satisfactory conclusion. /Merriam Webster namesake appears to be linked to intentional name correspondance (being named after someone). There may be a US/UK English divide there.  &quot;I was named after my grandfather. I am his namesake.&quot; -   Also, the introduction seems to hint at much broader meaning:  &quot;Namesake is a term used to characterize a person, place, thing, quality, action, state, or idea that has the same, or a similar, name to another&quot;   Do you know of a better word/phrase to describe this succinctly? Confused between Nested Quantifiers I am reading nested quantifiers. I am confused in between two cases,   1. Existential Quantifier before Universal Quantifier  2. Universal Quantifier before Existential Quantifier   I would be very thankful if someone highlights the difference between them and also give an example.   Thanks in advance. PDF editing within Apex/Visualforce Executing user-supplied ruby code on a web server So far, I didn't have the chance to use either of these services. Before starting, I would like to hear your opinions. What are the advantages and disadvantages? Why should I choose one over the other? I am mainly interested in the technical side, but I would also love to hear comments also regarding the plans and prices. Should I remove non-significant variables from my regression model I have run a multiple linear regression using stepwise regression to select the best model, however the best model returned has a non-significant variable. When I remove this the AIC value goes up indicating the model without the significant variable is a worse fit. Should I remove the non-significant predictor or should I leave it in as it is a better model? I Roll To Seduce The Dragon! (or, Do doublings of proficiency bonus stack?) Lets say there exist some enterprising young bard 3/ sorcerer 1 named Kirk.   Deciding to uphold (long past) family tradition, he has chosen to go out and have a little half-dragon of his own.   He chose Persuasion as his expertise skill, and is of a dragon bloodline himself, gaining the Dragon Ancestry perk.  Do they stack? Not the same ability, and both say "Your proficiency is doubled" when they activate. Granted, it would only happen when dealing with dragons. But there are certainly worse times to ramp up your charm. I'm seeing red dots everywhere On all Stack Exchange sites where I have review privileges, the review queue menu icon has a red dot. No matter what I try, it doesn't go away.     on Meta Stack Overflow might or might not be related. How to force a table into page width? I have the following table:  \begin{table}[htb] \begin{tikzpicture} \node (table) [inner sep=0pt] { \begin{tabular}{ l | l }   {\bf Symptom} &amp; {\bf Metric} \\ \hline Class that has many accessor methods and accesses a lot of external data &amp; ATFD is more than a few\\ Class that is large and complex &amp; WMC is high\\ Class that has a lot of methods that only operate on a proper subset of the instance variable set &amp; TCC is low\\ \end{tabular} }; \draw [rounded corners=.5em] (table.north west) rectangle (table.south east); \end{tikzpicture} \caption{God class symptoms} \label{tbl:god_class} \end{table}   Now I want to force the width of the table to be the same as the \textwidth, either by linewrapping of table text or by scaling. How can I achieve that? In fact, of these, only Charcoal shows a recent time stamp. The positive integer solutions for $2^a+3^b=5^c$ What are the positive integer solutions to  the equation     $$2^a + 3^b = 5^c$$    Of course $(1,\space 1, \space 1)$ is a solution. The most efficient way to implement an integer based power function pow(int, int) java.io.Console support in Eclipse IDE I use the Eclipse IDE to develop, compile, and run my Java projects. Today, I'm trying to use the java.io.Console class to manage output and, more importantly, user input.  The problem is that System.console() returns null when an application is run "through" Eclipse. Eclipse run the program on a background process, rather than a top-level process with the console window we're familiar with.  Is there a way to force Eclipse to run the program as a top level process, or at least create a Console that the JVM will recognize? Otherwise, I'm forced to jar the project up and run on a command-line environment external to Eclipse. Prove that $\lim_{n \to \infty} \int_0^1{nx^nf(x)}dx$ is equal to $f(1)$. Intuitive explanation for how could there be "more" irrational numbers than rational? Install Numpy for Python3.4.0 on Ubuntu 14.04.01 LTS Excel: I need a formula that will count months between two dates. If it's 1-15 it should be a half month. Any ideas? So I am trying to find a formula for excel. Bascically I have two dates and I need to know the number of months between them. But to add complexity, I need a rule in there that if the earlier date is the 1st to 15th it will be a whole month but if it is 16th to end of the month it will be a half month.  For example: Date 1: April 4, 2012 Date 2: December 31, 2012 Answer: Number of months would be 9 months  If Date 1 was April 16, 2012, with the same Date 2 of December 31, 2012, then the number of months would equal 8.5.  Can anyone help me with this one? You help would be greatly appreciated. many thanks It seems that panel shadow is somehow hardcoded in KDE 4 and devs do not have any plans to change it and/or make it customizable. So, what I'm actually asking is some kind of hack (if there is any) which will remove the shadow of the panel in KDE 4.x completely (but without need to disable all desktop effects in the process).  Possible application: When a user wants a completely transparent panel, no top/bottom borders at all, the shadow is completely out of place and destroys the experience. I am planning an hour and a half ride with my 1 month old baby girl. I heard that being in the car seat for a long time is not good for newborns.  Is an hour and a half too long? Should we do a stop in the middle of the trip? I encountered such a formula for pooled variance:  $$\frac{(n-1)s_x^2+(m-1)s_y^2}{n+m-2}\left(\frac{1}{n} + \frac{1}{m}\right)$$  Here we have two samples of the following sizes $n$ and $m$. $s_x, s_y$ are the sample variances.  I understand that the first term is a weighted average, but from the second term comes?