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$$\int_{0}^{1}x(1-x^2)^ndx=\frac{1}{2n+2}$$ The book says a simple calculation shows this,but I don't know how to calculate. Maybe it's not simple for me...

Please anyone help.

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2 Answers

up vote 4 down vote accepted

Let $u=1-x^2$. Then $du=-2x\,dx$, and you basically end up integrating $u^n$.

I expect you can now push things through. Please indicate if there is any difficulty.

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Thank you very much! I calculated and got the answer! –  nnnea Nov 29 '12 at 7:52
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actually, it is connected to the Beta function

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This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. –  Stefan Hansen Nov 29 '12 at 9:04
    
...or elaborate a bit what you mean... –  draks ... Nov 29 '12 at 9:32
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