Decompose into Partial Fraction. Image Added. I really had no idea how to write these questions out without copying and pasting them onto here, so I am sorry for that..I hope adding a picture is fine. I would appreciate any kind of help, and if you dont mind suggesting a useful website, or video that can explain these problems to me. Thank you
Integration by partial fractions; how and why does it work? Could someone take me through the steps of decomposing  $$\frac{2x^2+11x}{x^2+11x+30}$$ into partial fractions?   More generally, how does one use partial fractions to compute integrals $$\int\frac{P(x)}{Q(x)}\,dx$$ of rational functions ($P(x)$ and $Q(x)$ are polynomials) ?    This question is asked in an effort to cut down on duplicates. See .  Also see .
How do I configure internet connection for Terminal on Ubuntu 14.04? I've installed on Ubuntu 14.04 and with I've Broadband connection setup, Browser connection is OK,  but Terminal not connection via internet, when command type "sudo apt-get update" by terminal then showing me Error, see screenshot, How I can fix this ? Ubuntu 16.04 multitouch gestures Why am I still getting a password prompt with ssh with public key authentication? I'm working from the URL I found here:    My ssh client is Ubuntu 64 bit 11.10 desktop and my server is Centos 6.2 64 bit. I have followed the directions. I still get a password prompt on ssh.  I'm not sure what to do next. Solving of a seperable differential equation show that $a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$ let $a,b,c&gt;0$. Show that   $$a^2+b^2+c^2+2abc+3\ge (1+a)(1+b)(1+c)$$   By the $$(1+a)(1+b)(1+c)=1+a+b+c+ab+bc+ac+abc$$ it is suffient to show  $$a^2+b^2+c^2+abc+2\ge a+b+c+ab+bc+ac$$ How? I can't write Chinese characters in edited posts, but OP could when posting On sites with new responsive theme, word wrap on long titles breaks in the middle of a word For sites that have the new responsive theme enabled, where the "Ask Question" button is in line with the question title on question pages, the word wrap on long titles is not working correctly.  It will break a word across two lines.  Here is an  from Personal Finance and Money:  Maximum width, left nav hidden:   Narrow width:   This is also happening on beta sites.  Here is an  on Sports:    These screenshots were all taken on Firefox, but I am seeing the same problems in Chrome and Internet Explorer.  One more example: Power of a generator generates the group iff this power is coprime to the group order. Let $\langle g\rangle$ be a cyclic group of order $n$. Suppose $1\leq q \leq n-1$, I want to show that $g^q$ generates $\langle g\rangle$ if and only if $\gcd(n,q)=1$.  Suppose $g^q$ generates $\langle g\rangle$, then   $$ 1,g^q,g^{2q},...,g^{(n-1)q} $$  are all distinct and $g^{nq}=1$, since $n$ is the order of the group. Note that this is the lowest multiple of $q$ for which this is the case. Therefore $\operatorname{lcm}(q,n)=qn$ and it follows that $q$ and $n$ are coprime.  On the other hand, if $\gcd(q,n)=1$, then $\operatorname{lcm}(q,n)=qn$, we have $g^{nq}=1$ and hence all of  $$ 1,g^q,g^{2q},...,g^{(n-1)q} $$  are distinct again and $g^q$ is a generator.  Is my proof correct at all and is there maybe a more elegant argument? Show the two fields are not isomorphic Let $p,q,r$ be prime integers with $q\neq r$. Let $\sqrt[p]q$ denote any root of $x^p-q$ and $\sqrt[p]r$ denote any root of $x^p-r$. Please show that $\mathbb{Q}(\sqrt[p]q)\neq\mathbb{Q}(\sqrt[p]r)$.  By Eisenstein we know the two polynomials are irreducible and so they are minimal polynomials and both have degree $p$. "Stack Overflow requires external JavaScript from another domain" message For example i have the domainname buyhouse.com The keywords "buy house new york"  buyhouse.com/new-york/   buyhouse.com/buy-house-new-york/   Whats the best url option for SEO? When creating presentations in , those little symbols that you can click on and will take you to different parts of your presentation are automatically included on your slides.  I don't like that, but decided not to try and change it for now. The problem is that when I gave my presentation to my supervisor to revise, the first thing he did was cross the symbols out in red, meaning: take this out!  What should I do? Is there an easy command to get rid of those symbols or do I have to change the theme of my presentation to get rid of the symbols? What is this icon depicting a phone and Wi-Fi together? Detecting start bit in software UART I'm experimenting with writing a software UART on my microcontroller using GPIO pins. This is to temporarily add a UART channel on a project until we get the new design implemented that uses a uC with more UART ports.  What I'm having difficulty with is correctly detecting a start bit in a serial stream. The source of the stream is external and doesn't care when my device powers up. So it's very likely that my device will power on and start seeing data bits in the middle of a byte transmission. Undoubtedly, that will cause my software UART to read erroneous values, as it won't be able to tell the difference between a start bit and any other high-to-low transition.  Is this an inevitable issue with a UART channel? Or is there some clever trick that the uC manufacturers use in their hardware UARTs? Constructing a continuous function whose graph seems 'special' I've been reading through Zorich's "Analysis I" book recently, and I came across this nice little exercise.  Let $f: [0,1]\to \mathbb R$ be a continuous function such that $f(0)=f(1)$. Show that    for any $n\in \mathbb N$ there exists a horizontal closed interval of length $\frac 1n$ with endpoints on the graph of this function; if the number $\ell$ is not of the form $\frac 1n$ there exists a function of this form on whose graph one cannot inscribe a horizontal chord of length $\ell$.   The first part can be proven like this: Consider $g: [0,(n-1)/n] \to \mathbb R$ given by $g(x) = f(x) - f(x+1/n)$. Then   $$\sum_{k=0}^{n-1} g(k/n) = 0$$  and therefore either all of these points are zero or there exists both a point where $g$ is positive and a point where $g$ is negative. By continuity, there must then also be a point where $g = 0$. So we are done.  Now, the second statement seemed rather counterintuitive, and I have given it some time now, but don't see a counterexample for $\ell &lt; 1/2$.  (For $\ell &gt; 1/2$ the function $f(x) = \sin(2\pi x)$ will do.)  Can anyone help me out?  Cheers, Turning off and on images in figures Is it possible to prevent the contents of a figure from being rendered? I have a large book document, and to speed up compiling while working on a draft, I would like to have some way of ignoring the content of the images, but ensuring that the figure size remains.  In several cases I am using a line like:  \includegraphics[width=\linewidth]{figure.pdf}     so I do not know the actual size of the image. Norman Window Optimization How to create csv files in controller method from list I want to create csv files from lists and send an email attaching them, how to do that in a controller method? Term for words like Snowmageddon, Nipplegate and even cheeseburger? Ubuntu halts after few seconds of starting and nothing works command, virtual terminal, GUI