# Solution 71: Forcing the u-Substitution to Work

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**Published on Dec 20, 2018**- We modify the given expression such that a well-chosen u-sub instantly finishes the problem.

Congratulations to Nicholas Patel, aby p, Parth Pawar, adandap, JiaMing Lim, Nitro Zox, Evyatar Baranga, Rishav Gupta, Peter, and Kostas Jelo for successfully solving the last week's math challenge question! Nicholas Patel was the first person to solve the question.

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Luc De Graaf19 days agoHey man, I love this vid, but I don't understand why you need to set the exponent of the derivative of x^2n equal to 2018-n

spar4 months agoIsnt it +-sqrt(8)?

santhanam krishnan bhaskar2 months agoExplanation for that given at the beginning of the video. Anyways I will say it again. Since when k increases the integrand increases, the maximum value of k will occur at the maximum value of the integrand, which being equal to +8 is larger than when being equal to -8.

Aditya Kondamudi4 months ago^{+1}Great solve!!!!!

Vaidhyanathan A5 months ago^{+1}What a beautiful problem,and how simple logics are used too,great,thank you sir..

Rishi Sarkar6 months agothis guy is a mad genius

Meh !8 months ago^{+8}Interesting stuff!

Your accent sounds little bit like blackpenredpen XD

Agfd4 months ago^{+1}Not at all, in my opinion

Erik Arteaga5 months ago^{+3}His accent sounds similar *isn't it?*

Vincent William Rodriguez7 months agolol agreed

Michael Empeigne8 months ago^{+1}Prove this following : if the bases are in arithmetic progression, and the exponent, n, is odd; then the expression is divisible by the sum of the bases.

Written mathematically:

[ a^n + ( a + d )^n + ( a + 2d)^n + ........ + ( a + ( r - 1 )*d )^n ] is divisible by r* [ 2a + ( r - 1 )*d ] / 2.

The unmastered8 months agoCan you upload more tricky u sub

The unmastered8 months agoI love this so much

magnifecent8 months ago^{+2}can you try math olympiad?

Jonathan Liu8 months ago^{+1}Wasn't the problem originally asking for "all possible values of k?"

magnifecent8 months agoIt was, however he meant it to say "largest value of k"

Jonathan Liu8 months agoMagic!

Easy Mathematics8 months ago^{+6}Very tricky and nice solution.

I guess this should be the most elegant solution. Beautiful. :)

petre Tepner8 months ago^{+3}Do you remember to put your socks on before your shoes?

Nicholas Leclerc8 months ago"Nicholas Patel", huh, an "h" like me... you copycat ! (; p)

Andrés Robles8 months ago^{+1}K no puede ser negativo también?

Just Weird8 months ago^{+1}I tried both methods of Usub. Then thought I can try to make it its derivative and use that...though didn't know how. Thanks

δτ8 months agoWhy is 2034 the largest possible value of k?

δτ8 months ago^{+2}@Jia Ming

Ah, ok.

Jia Ming8 months ago^{+4}The integral evaluates to -sqrt(8) for another value of k. That value is approx -6091.9754

δτ8 months ago^{+1}Right, the function is given, so this manipulation gives the solution.

My question was dumb.

Thanks, anyway.

But should 2034 then not be also the only solution?

Minh Cong Nguyen8 months ago^{+1}if k>2034 then AUC of the curve is bigger than sqrt(8) (because the function is strictly increasing in respect of k). So 2034 is the largest possible value of k

Taufiqurrahman Datau8 months agoWhat Is The App he use ?

Jeff Ahn8 months ago^{+2}Just wtf man

Rot8 months ago^{+3}Mind blown

Parth Pawar8 months ago^{+1}Amazing! Hey but what about that work done by spring analogy somebody did in the comments, I would like to know more about that!

Jon Snow8 months ago^{+37}you are the most craziest person on the youtube...

AndreiRomanul2 months ago*r / e n g r i s h*

Also, yeah.

Omar Omy5 months agodaaamn

Ben Burdick8 months ago^{+4}Well, I'm proud I at least tried this one. It was quite interesting; I would love a problem similar to this in the future.

Zyloh SZN8 months agoThanks

PRAKHAR AGARWAL8 months ago^{+4}Great question with a mind blowing explanations!!!

Never thought a solution could be made by forcing it and that it could be approached this way...

Thanks Sir!!

زين العابدين ماجد8 months agoThanks you

زين العابدين ماجد8 months ago@Yassar Mandouri

هههههه صار

Yassar Mandouri8 months agoزين العابدين ماجد

يلحبيب

Thanks you

او

Thank you

هاي for اشطبها بعد اذن شواربك

Smokie Bear 🔴🔵8 months ago^{+3}I knew my explanation was pretty close.

Duran Chen8 months agosecond

Joshua Cohen8 months ago^{+2}First