# Very simple calculation of integral

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

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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