Suppose, in my research (mathematical) I have a critical step that I need to solve, and, due to various reasons I cannot find decent answer to that step by myself or by contacting friends or colleagues, so that I decide to post a similar but simpler problem to the relevant StackExchange (Math). Now, if someone comes up with a good answer that I can use to further my research, will it be enough to acknowledge the contribution of the author of the answer and citing that particular thread of StackExchange, or do I need to include that person as a coauthor of the paper that I might prepare based on that answer?   I emphasize here that the paper is supposed to be not all about that particular result, there are many other things, and that particular answer is useful, albeit critically, at an intermediate stage of proving some results in the paper. I personally feel that citing and acknowledging the contribution is respectful enough. However, I want to know what the standard norm is.
Sometimes we may ask questions on stack exchange or online forums wherein the response is helpful or even essential to a piece of work that gets published in an academic journal. If this occurs, how should credit be given to those involved in the exchange? Should they all be included as authors? Should a link to the forum be included as a reference in the paper?  Once something is in a stack exchange or forum, it's "published". Perhaps in the future, the current peer review model will transform into people writing blogs and posting in forums and databases. But for now, how might this issue be dealt with while forums, blogs, etc coexist with journals?
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As the goal is to get the installation working, other options are welcome. I tried to install the bin file, but got an error: cannot execute binary file. Evaluate the integral   $$\int\frac{1}{x^2\left(x^4+1\right)^{3/4}}\,dx$$   My Attempt:  Let $x = \frac{1}{t}$. Then $dx = -\frac{1}{t^2}\,dt$. Then the integral converts to   $$ -\int \frac{t^3}{(1+t^4)^{3/4}}\,dt $$  Now Let $(1+t^4) = u$. Then $t^3\,dt = \frac{1}{4}du$. This changes the integral to  $$ \begin{align} -\frac{1}{4}\int t^{-3/4}\,dt &amp;= -u^{1/4}+\mathcal{C}\\ &amp;= -\left(1+t^4\right)^{1/4}+\mathcal{C} \end{align} $$  So we arrive at the solution  $$\int\frac{1}{x^2\left(x^4+1\right)^{3/4}}\,dx = - \left(\frac{1+x^4}{x^4}\right)^{1/4}+\mathcal{C.}$$  Question: Is there any other method for solving this problem? Subject-verb inversion / verb-subject-object -- is this correct? I recently read the following in a schoolbook:     Wrote the researchers, "[...]"   I wonder if this is correct English. 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An example is provided to illustrate:     In how many ways can 4 identical jobs (indistinguishable balls) be distributed among 26 members (urns) without exclusion (since one member can do multiple jobs)?      A sample outcome might be:   $\text{_____________}$   |  A  |  B  |  C  |...|  Z  |    $\text{--------------------}$      $\text{_____________}$   |  o  | oo|    |   |    ||| o  |    $\text{_____________}$   |  A  |  B  |  C  |...  |  Z  |    $\text{--------------------}$      Thus, the question is reduced to, "How many $(26-1+4)$ letter words are there consisting of four circles and $(26-1)$ vertical lines?"  Therefore, the solution is:  $\binom{26-1+4}{4}$   I really don't understand why its $(26-1+4)$.  There's only 26 different spots or "urns" to place the 4 jobs.  Can someone please explain?    I looked through another text to try and understand and I found it explained as such:       There are $\binom{n+r-1}{r-1}$ distinct nonnegative integer valued vectors $(x_1,...,x_r$ satisfying the equation $(x_1 + ... + x_r = x_n$ for $x\ge0$. $\spadesuit$   How in the world are they deriving this?  For distinct positive integers I understand:  Assume I have 8 balls (n=8) and I have 3 urns (r=3): o^o^o^o^o^o^o^o, where o represents  a ball and ^ represents a place holder where an urn could be placed.  For this scenario:     There are $\binom{n-1}{r-1}$ distinct positive integer valued vectors $(x_1,...,x_n)$ satisfying the equation:  $x_1 + ... + x_n = n, x_i&gt;0, i=1,..,r$ $\clubsuit$   It's clear that I could have this specific case ooo|ooo|oo.  Here the bar represents a divide for the urn and you see I have 3 sections.  So that case is clear.  Can anyone please explain this problem to me?  I don't understand the nonnegative integer case.   Also, people who post tend to be crazy smart and explain things very in a complicated manner.  I'd appreciate it if it could be explained in layman's terms as much as possible.   Thank you!!! How do I call functions loaded from a Static Resource JavaScript file? I'd like to put some shared Javascript to Resource file to reuse it between several components. This Javascript is general purpose set of utility functions. However, functions from my resource file are not available from the Components. 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