A RIDICULOUSLY AWESOME FRACTIONAL TRIGONOMETRIC INTEGRAL!!!

WOW!!!
WHAT AN INTEGRAL!!!
Adding trigonometry to the fractional part mix was definitely an awesome idea.
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[@manstuckinabox3679]

BRO THIS WAS FREAKING INSANE! each move was so unexpected lol! thank you for reminding me that I skippped the infinite product chapter from my complex analysis book.

[@jonsmith8579]

Thank you Maths 505 for solving the integrals

[@mikecaetano]

Logging the product to obtain a series was a really nice touch.

[@martiribapons]

Simply brilliant!!

[@user-nt7cg6ok6f]

Your channel is like a breath of fresh air for me)

[@cristoduke8953]

Love these interesting integrals

[@Mephisto707]

Beautiful result indeed!

[@slavinojunepri7648]

This is so cool, my goodness!

[@vicentepoblete6627]

brilliant example of the fractional part

[@MrWael1970]

Really Smart solution. Thank you.

[@palestinemorocco1920]

Amazing ❤

[@fartoxedm5638]

did pretty the same with the original remainder function and bunch of telescoping sums and limits, but yours looks much cleaner!

[@Maths_3.1415]

Nice integrals bro 🎉

[@krishgarg2806]

I was able to get to the ln series by myself, and thats where I got stuck. amazing integral!

[@monikaherath7505]

OMG I almost did this myself except I made the mistake of thinking you could telescope it instantly (mistaking the initial k as a constant) getting pi/2 -1/2 ln2, although I felt intuitivey that it was wrong lol thanks for the proper solution I feel I'm improving just by watching your vids

[@cicik57]

right it is standard strategy when you have floor function integral_, worth to remember

[@nimrodkadish]

So cool! Now do the same integral, just with the integrand being {cotx}, please

[@hyperpsych6483]

It took me a solid few seconds to realize why you chose that particular decimal 😂

[@suvosengupta4657]

Thats some legit example for floor function

[@nickruffmath]

Great solution from start to finish! Loved the sinh result for log..reminds me of using the sin version and taking the logarithmic derivative to get a cotangent generating series for even values of the Zeta function.