Closed Form of a really difficult Integral

I became very interested in the closed form for the following Integral:\[\]\[\int_{0}^{\Large\frac{\pi}{2}}\frac{1}{(1+x^2)(1+\tan x)}\,\mathrm dx\] \[\]No known \(exact\) Closed Form for this Integral exists so far (well not to my knowledge at least). However, I thought I would post it as members of the community might be interested in finding its Closed Form. \[\] Happy solving!

Note by Ishan Dasgupta Samarendra
3 years, 8 months ago

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@Azhaghu Roopesh M @Shashwat Shukla @Raghav Vaidyanathan @Trevor Arashiro @everybodyinterested!

Ishan Dasgupta Samarendra - 3 years, 8 months ago

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Please don't mass @mention too many people at once. I'm fine with you @mentioning me but but please keep it to a maximum of 4 people at once. Those 4 will feel more inclined to respond in that case.

Trevor Arashiro - 3 years, 8 months ago

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Really sorry for doing that.

Ishan Dasgupta Samarendra - 3 years, 8 months ago

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have you tried this

Soumya Dubey - 3 years, 8 months ago

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Yeah, but that's an \(approximate\) form. By the way, I hope I'm not breaking a rule by hoping to get people interested in finding and exact Closed Form. If I am, I'll delete it immediately.

Ishan Dasgupta Samarendra - 3 years, 8 months ago

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@Ishan Dasgupta Samarendra The closed form of the above integral can only be found by an excellent approximation, as said by tunk-fey araiawan.i provided the link for furthur details and assumption about the problem, as soon as anyone comes up with a solution to your doubt,i will immediately remove the link.

and no , dont delete the note, i am okay with it.

Soumya Dubey - 3 years, 8 months ago

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Could you please remove the reference to that problem? This is because some people might use what will perhaps appear subsequently in a manner which would not do justice to that problem.

Ishan Dasgupta Samarendra - 3 years, 8 months ago

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You mean this?

Kartik Sharma - 3 years, 8 months ago

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