A RIDICULOUSLY AWESOME INTEGRAL: int sin(x)/sinh(x) from 0 to infinity

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Our guest for today's show is Math Vader. May the complex force be with you!

Daniel's solution:

Series expansion for the cotangent function:
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Me: What happened to your voice?

Maths505: Math is one hell of a drug, man.

manthing
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Contour Integral works for me here but I do like this power series stuff too!

Vader doing integrals, that’s good content.

SuperSilver
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Didn't know Darth Vader loved maths so much
Especially integrals

kartikeyasaxena
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Really liked your work divining the expression for the series!

rk
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What about int (sin^2(x)/sinh^2(x))dx?

АлексейШубин-нй
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You came to Math hell's room. Let the game begin.

smarthumanism
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That's one serious series. Kudos!

TheMartinbowes
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great video and awesome integral indeed, but what happened to the audio lmao

arturstolf
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Ha ha. My sound card has a bunch of voices too. Fun switch. Great integral.

AB-nuwe
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I brute-forced the sum through equating it to sum 1/(k^2+1) for natural k, minus its even k terms, or 1/(4k^2+1). Both can be solved using the digamma function

taterpun
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jejejeje te amo math 505 la verdad que aqui si aprendo matamaticas e ingles al mismo tiempo... estas labrando personas matematicas...yo tambien quisiera mostrarle a la comunidad latina como pensar mas alla en las matematicas y no limitarse....como tu.... quizas lo haga en español😁

felipealonsoobandolopez
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This is the furthest I’ve gotten through a problem on this channel. I just didn’t know how to rewrite the sum

hifriend
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I reduced that integral to exactly that infinite sum and didn't know what to do next. This is unbelievably beautiful solution.

bushwalker
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Its over Anakin i have the high ground

zawadulhoque
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Could you have used the geometric series route in the cos/cosh integral instead of the Beta function route?

Mephisto
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Okay but why is Jigsaw making math videos.

Anyone else excited for Saw X?

DanTheManHibiki
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It can be solved using contour integration

Anonymous-Indian..
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I spy with my little eye a geometric series. :D

Edit: vindicated at 1:49 !

emanuellandeholm
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This is such a great method. I was impressed when im(integrand) just became Sigma(1/(odd^2 + 1)) ❤️🎃❤️🎃❤️🎃

IndranilBiswas_
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Sounds like you have gas real bad; time for some bicarbonate soda!

thomasblackwell