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**maths4prasad****Member**- Registered: 2013-08-15
- Posts: 3

the problem is to prove that -∫(-1 to 1) u^(n-1)(x) u^(n+1)(x)dx = (-1)^n ∫(-1 to 1)u(x)u^(2n)(x)dx

here (n-1),(n+1),(2n) are n th derivatives and u(x) = (x²-1)^n

plz help me to prove above problem...

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,636

Hi;

You should latex these so they are readable.

This is a good online latex creator. It uses pull down menus and produces perfect latex every time.

http://latex.codecogs.com/editor.php

That is the LHS of your question. Refresh my memory, which polynomials are u(x)?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**maths4prasad****Member**- Registered: 2013-08-15
- Posts: 3

thanks for replying..

that problem u interpreted is correct, and u(x)=\left(x^2-1)^n

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,636

Hi;

So the whole question looks like this:

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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