I was given a task and it seems this is not a joke. I am shocked and do not even know where to start ...
$$\int \frac{1}{dx}=???$$
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2Maybe they want the integral of $\frac1x$? – Maximilian Janisch Sep 30 '19 at 19:34
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It's trivial.... log|x| +C – Hrackadont Sep 30 '19 at 19:36
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2This is a long shot that only suits if it's meant to be a trick question, but if whoever set it thinks $\int f(x)$ is an acceptable abbreviation for $\int f(x)dx$, it could mean $\int\frac{1}{cx}=\frac1c\ln|x|+C$ with $c=d$ (where $C$ is locally constant, possibly taking different values for $x>0,,x<0$). – J.G. Sep 30 '19 at 19:39
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Who gave the task and where is this from? This may make sense if one is talking about $f(t)=\frac{1}{d\cdot x}$ where $d$ and $x$ are two constants, so $\int f(t),dt=\frac{t}{dx}+C$... If it is a joke, then it is a really bad one. – Sep 30 '19 at 19:42
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1@J.G. Or maybe it was just $$\int \frac{1}{dx}dd=\frac1x\ln|d|+c$$ Who knows that? :) – user Sep 30 '19 at 19:43
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In integral, would it make any sense to write dx as denominator? – Sep 30 '19 at 19:45
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Also: What's this : $\displaystyle\int{\frac{1}{{x}dx}}$ equal if it is a correct formula? – Sep 30 '19 at 19:46
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The joke here. – user Sep 30 '19 at 19:49
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this question is hilarious though – Donlans Donlans Sep 30 '19 at 20:14
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In calculus context, that expression
$$\color{red}{\int \frac{1}{dx}}$$
in completely meaningless indeed the symbol $dx$ we use in the integrals is just a symbol to indicate the variable we are considering for integration. We can't manage it as a number.
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4$dx$ is not just that. Depending on your field, of course. In calculus it is just that, but in both measure theory and differential geometry it has a very specific meaning. At any rate, $\int\frac1{dx}$ is still meaningless. – Arthur Sep 30 '19 at 19:36
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2since you dont need an dx in an Integral you just read it as dx with the constant d and have as an result 1/dln(x)+C – trula Sep 30 '19 at 19:39
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