$\int_{0}^{1}x(1-x^2)^ndx=\frac{1}{2n+2}$ 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.
$\int_{0}^{1}x(1-x^2)^ndx=\frac{1}{2n+2}$ 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.
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.
actually, it is connected to the Beta function