Hiow to evaluate

$\displaystyle \int_0^1{dx \frac{d^{2l-1}}{dx^{2l-1}} \[ (x^2-1)^{2l} \]$

Using the binomial theorem

$\displaystyle \int_0^1{dx \frac{d^{2l-1}}{dx^{2l-1}} \[ \sum_{k=0}^{2l} \frac{(2l)!}{k!(2l-k)!} x^{4l-2k} (-1)^k \]$

l is a non negative integer.

I don't know how to proceed. Is there another way?

Thanks.