deletemath.stackexchange.com/q/1050040/23353 (this is one of the most-asked questions on the site, and is a duplicate. The extra visibility for search engines isn't necessary.)
@anorton: I noticed that you have given some flags for merging. I haven't looked at all of them yet, but I think here is a reasonable place to state some thoughts on your requests.
The first group consisting of 1, 2, and 3 (the $\int_0^\infty \frac{dt}{1+t^4}$ trio).
The first question is somewhat thematically different from the other two (already knowing what the integral should be), and so probably shouldn't be merged into either of the others.
While the last two are strikingly similar, the difference in variable causes me to pause. At the very least every answer in one of the questions would have to be altered somehow in order to either (1) state that it comes from a previous question where the integrating variable is $a$ instead of $b$, or (2) to match the integrating variable of the target of the merge.
Also, (3) more-or-less explicitly states that methods from complex analysis are not sought, and one answer in (2) does mention it. (Such a restriction does not appear in (2).)
I'm thinking of leaving each of these as they are, though adding a comment to (3) stating that further answers can be found in the other two.
Crap. Just looked at another one of your merge requests that extends the one described above. Patience.
Okay, 4 is in relation to (2) and (3) as (2) is to (3): different integrating variable, and an answer uses complex analysis. Again, I don't think it's a reasonable candidate for a merge, though, again, linking to it from (3) is probably in order.
I am not sure this question should have been closed as duplicate. Looking for differentiable solutions of Cauchy functional equation is easier task than looking for continuous solutions.
reopen The following question on a combinatoiral sum was voted as a dupe; actually I voted too. But it is not really. I voted to reopen. It has 3 votes to reopen but likely is through review already.
@MartinSleziak I am not sure either; the formulation is a bit unclear: "find df/dx, if it exists" could mean "assume df/dx exists and determine it" or "determine if df/dx exists and also determine it." The later is a dupe the former not, if I see correctly.
re your question: we might wait a while (until that OP's takehome exam is over) and then turn it into the one you had in mind, or at least make the two interpretations explicit.
@quid I have to admit that I was not very happy after receiving a comment about take-home exam. But it is not my duty to police the users. Moreover, they have already seen answer (in fact, several answers). And they still have some work to do. (At least if the question is supposed to be your interpretation. If it is about differentiable functions, the answer is quite close to complete solution.)
@ArthurFischer Thank you for your detailed response. I forgot/overlooked that notational differences are important in merging questions, and the point about complex methods is valid. Maybe those shouldn't be merged. However, I believe my other grouping (the indefinite form of the same integral) all use the same notation ($x$ is the variable of integration) and the OPs don't specify any particular desired methods--those may be better candidates for deletion.
As an aside, I came across that network of questions while doing some searches for the most convoluted "duplicate of" paths on the site. One particular question in this set is four layers deep in "duplicate of" links (the duplicates cover both indefinite and definite forms of the integral). Just thought I'd mention it in case you were wondering why I dug up a set of old questions...