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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
2 years ago

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You mean this? Kartik Sharma · 2 years ago

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Comment deleted May 19, 2015

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@Ishan Dasgupta Samarendra I'll delete this link as soon as you see it for the same reason as what I mentioned to Soumya. Just tell me when you see it, please. Ishan Dasgupta Samarendra · 2 years ago

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@Ishan Dasgupta Samarendra 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 · 2 years ago

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@Trevor Arashiro Really sorry for doing that. Ishan Dasgupta Samarendra · 2 years ago

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@Ishan Dasgupta Samarendra have you tried this Soumya Dubey · 2 years ago

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@Soumya Dubey 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 · 2 years ago

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@Soumya Dubey 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 · 2 years 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 · 2 years ago

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