# 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.
Your support is truly a huge encouragement.
Every subscriber and every like are wholeheartedly appreciated.

• Luc De Graaf 19 days ago

Hey 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

• spar 4 months ago

Isnt it +-sqrt(8)?

• santhanam krishnan bhaskar 2 months ago

Explanation 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 Kondamudi 4 months ago +1

Great solve!!!!!

• Vaidhyanathan A 5 months ago +1

What a beautiful problem,and how simple logics are used too,great,thank you sir..

• Rishi Sarkar 6 months ago

this guy is a mad genius

• Meh ! 8 months ago +8

Interesting stuff!
Your accent sounds little bit like blackpenredpen XD

• Michael Empeigne 8 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 unmastered 8 months ago

Can you upload more tricky u sub

• The unmastered 8 months ago

I love this so much

• magnifecent 8 months ago +2

• Jonathan Liu 8 months ago +1

Wasn't the problem originally asking for "all possible values of k?"

• magnifecent 8 months ago

It was, however he meant it to say "largest value of k"

• Jonathan Liu 8 months ago

Magic!

• Easy Mathematics 8 months ago +6

Very tricky and nice solution.
I guess this should be the most elegant solution. Beautiful. :)

• petre Tepner 8 months ago +3

• Nicholas Leclerc 8 months ago

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

• Andrés Robles 8 months ago +1

K no puede ser negativo también?

• Just Weird 8 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

• δτ 8 months ago

Why is 2034 the largest possible value of k?

• δτ 8 months ago +2

@Jia Ming
Ah, ok.

• Jia Ming 8 months ago +4

The integral evaluates to -sqrt(8) for another value of k. That value is approx -6091.9754

• δτ 8 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 Nguyen 8 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 Datau 8 months ago

What Is The App he use ?

• Jeff Ahn 8 months ago +2

Just wtf man

• Rot 8 months ago +3

Mind blown

• Parth Pawar 8 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 Snow 8 months ago +37

you are the most craziest person on the youtube...

• Ben Burdick 8 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 SZN 8 months ago

Thanks

• PRAKHAR AGARWAL 8 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!!

• Thanks you

• Smokie Bear 🔴🔵 8 months ago +3

I knew my explanation was pretty close.

• Duran Chen 8 months ago

second

• Joshua Cohen 8 months ago +2

First