Can you solve this Amazing Fractional Part Integral?

This fractional part integral is solved using integrals, infinite series and riemann zeta function.
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[@ANSACADEMYOFFICIAL]

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1) 5 Most Important Calculus questions for JEE ADVANCED
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[@AdarshRaj-h6u]

Wow sir ,pure love of learning

[@yahyashaikh7151]

Beautiful problem

[@abhishekmali8289]

That was a good problem for JEE Advanced! Please bring more like this.

[@ANSACADEMYOFFICIAL]

Sure! I hope you liked it.

[@notsodope834]

Not saying easy, but it uses the usual/general approach which is used in such question of separating integrals with limits in interval(n, n+1) by fixing the integer part

[@ANSACADEMYOFFICIAL]

Yes, thus I chose this problem so that it could be conveyed to the general audience. This was the 3rd problem in a list of 50+ problems in ascending order of difficulty. Hope you liked it!

[@notsodope834]

@@ANSACADEMYOFFICIAL I loved it. Coz even with jee concepts mixed this can be solved

[@amananshu9942]

What are you pursuing from IITM.?

[@ANSACADEMYOFFICIAL]

BS DS,3rd year. Previously I was at ISI Kolkata.