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How to calculate the integral $$\int\frac{\tan x}{x+\sin x}\mathrm dx\;\;?$$

I use a website called integral of the day, all the previous ones have answers, but today I cannot find an answer for it and no online calculators can do it either. It comes from this website: https://www.sammserver.com/iotd/ , but as it is the next day it has changed now.

Charlie43
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    Welcome to [math.se] SE. Take a [tour]. You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an [edit]): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance. – Another User Feb 06 '23 at 21:54
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    this is an interesting problem, please edit your question adding your effort otherwise it'll be closed and we can't answer as it's against the EoQS – Sine of the Time Feb 06 '23 at 22:04
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    related https://math.stackexchange.com/questions/906633/evaluating-the-integral-int-12-fracx-tan-xx-sin-xdx?noredirect=1 – Sine of the Time Feb 06 '23 at 22:06
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    I do not think there is an antiderivative in terms of functions we usually use, elementary or nonelementary. Would you mind linking the site you got this from? – Captain Chicky Feb 06 '23 at 22:30
  • @Moo if you have maple I think it’s worth a shot trying that as well. Unfortunate I don’t so rip – Captain Chicky Feb 06 '23 at 22:38
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    Do you have any reason to believe that this integral can be calculated in terms of known functions? – jjagmath Feb 07 '23 at 04:21
  • @jjagmath, all the previous ones I have seen are able to be done like that, so I thought this one may be able to. – Charlie43 Feb 07 '23 at 22:07
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    @CaptainChicky, I linked the website, but it's changed now because it is an integral of the day. – Charlie43 Feb 07 '23 at 22:07
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    @SineoftheTime I don't see how you would attempt this integral. Where can you put in 'effort'? There's no suitable substitution, a reasonable way to conduct integration by parts, or any other method. – phi-rate Feb 08 '23 at 02:51
  • @chroma I agree with you, in fact was a piece of advice because many user are very strict regarding this matter (you can see the 3 downvotes). I did not flag the question, but I was just telling the OP to add more details because otherwise the question may be closed (it happened to me :( ). – Sine of the Time Feb 08 '23 at 16:13

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