The task is to calculate the following integral:  $$\int_{1/3}^{3}{\frac{\tan^{-1}x}{x^{2}-x+1}dx}$$  However the answer me currently getting seems to be too large and odd, any ideas of more efficient solution? P.S I was using universal substitution for rational trigonometric equations
Can somebody help me calculate the following integral:  $$\int\limits_{1/3}^{3}\frac{\arctan(x)}{x^2-x+1}\;\mathrm{d}x$$  I have tried integration by parts, but I got stuck in it. Wolfram also didn't help me.  I would be happy to get some hints.
Me and my friends want to listen to music together. Two of us have Bluetooth Headphones (Beats Solo2 Wireless, Beats Studio Wireless) and one has a wired headset. Is there any way to use all three of these together? Does removing an application from Software Center do a remove or a purge When I remove an application already installed through the Software Center. Does it remove the app the same way as doing a purge to it (aptitude purge) or does it remove it like a "remove" (aptitude remove). how to auto start or enable service on next boot up or start up? in ubuntu 16.04 lts how to start or enable service on the next boot up or start up? in ubuntu 16.04 lts  without doing it manually enable or start services again everytime i start up or boot up the ubuntu 16.04 lts  thank you My work has decided to issue their own  (CA) to handle different aspects of our work securely without paying for certificates.   Cryptographically sign emails Encrypt email contents Make access to things like the company  client-certificate based. Revoke the keys of former employees automatically   They sent me a .pem file, and I'm not sure how to add it to my Ubuntu install. The instructions sent were: "Double-clicking on it on a Mac should install it."&nbsp;  How do I proceed? Do I need to do something with  to create a .key, .csr, or .crt file? Unable to install Springseed 2 on Ubuntu 15.04 Fundamental group of a torus with points removed Question 5.33 from "Topology and its Applications"  by Baesner is to compute the fundamental group of the torus ($T^2$) with $n$ points removed. I can "see" in my mind that if we remove one point we get a bouquet of two circles. Less clear is what happens when we remove two (or more) points. Any hints? How to show via inductive proof (and without the use of the binomial theorem) that $ {n\choose k} \in \mathbb{N} $? How do I show via inductive proof (and without the use of the binomial theorem) that $$ {n\choose k} \in {\mathbb{N}} $$ $$\text{ for  all }\: n,k \in \mathbb{N}_0\: \text{ with }\: n≥k .$$ For my induction proof, I would show that$$  {n\choose k-1}+{n\choose k} = {n+1 \choose k}   $$ is true. However, how do I start the induction correctly with the base cases and the hypothesis? As far as I know, I cannot simply assume $$ {n\choose k-1}+{n\choose k}, $$  so how do I come to this derivation? Change MAC address in OS X Yosemite Duplicates of an outdated question If a new question addresses the same issue that another question does, but the answers to the original question is sufficiently outdated, should the new question still be closed as a duplicate? 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My guess is wget -c [previous options used] [url] and run it in the same working directory as the file were downloaded to. I'd like to show that the class of all limit ordinals, LIM, is cofinal in the class of all ordinals ON.  I thought that I could do this by contradiction and assume that it wasn't cofinal in ON. Then there is an $\alpha \in$ ON such that for all $\beta \in $ LIM: $\beta &lt; \alpha$, i.e. $\beta \in \alpha$ and hence LIM $\subset \alpha$.  This means that LIM is a set so we can consider $\bigcup$ LIM. Then we have $\beta &lt; \bigcup$ LIM for all $\beta \in$ LIM by definition of $\bigcup$ LIM. So LIM $\subseteq \bigcup$ LIM.   $\bigcup$ LIM is either a limit or a successor ordinal.  If it is a limit ordinal then $\bigcup$ LIM $\in$ LIM and by transitivity of ON, $\bigcup$ LIM $\subseteq$ LIM, so $LIM = \bigcup$ LIM in this case which would mean that $\bigcup$ LIM $\in$ LIM $= \bigcup$ LIM which would be a contradiction because sets cannot contain themselves. Hence $\bigcup$ LIM cannot be a limit ordinal.  If $\bigcup$ LIM is a successor ordinal then $\bigcup$ LIM = $\beta \cup \{&#160;\beta \}$ for some $\beta \in $ ON.  Now I'm not sure how to proceed from here. I'm also not sure about whether I'm on the right track with this proof because I think there should be a shorter way  to prove this.  Thanks for your help. Placing a single algorithm in two columns So I tried a few different answers that I found here, and I feel that this is possibly a duplicate question, but everything I have tried from the other solutions hasn't worked.  Basically I am trying to bake a material to a texture that will be used in Unity, but every test gives me a black background image.  In the image below, the top image texture is the mask (black and white, white being the leaves), and the bottom image texture is the colour. How to perform Stream functions on an Iterable?