Determine an integral with legendre polynomials 
Determine the following integral $\int_{-1}^{1}x^2P_{2n-1}(x)dx$

I am unsure how to go about this. I understand that $P_{2n-1}=\frac{1}{2^{2n-1}(2n-1)!}\frac{d^{2n-1}}{dx^{2n-1}}(x^2-1)^{2n-1}$
and $\sum_{n=0}^{\infty}P_n(x)r^n=(1-2rx+r^2)^{-\frac{1}{2}}$
However I am unsure how to relate these to the integral?

Hint: $2n-1$ is odd, and the interval of integration is symmetric around the origin.
