I want to derive equation 3.26 from jackson's book, classical electrodynamics.
$(2l+1)\int_{0}^{1}P_l(x)dx=(-\frac{1}{2})^{(l-1)/2}\dfrac{(2l+1)(l-2)!!}{2(\dfrac{l+1}{2})!}$
where l is odd, using the Rodrigues formula
$P_l(x)=\dfrac{l}{2^l l!}\dfrac{d^l}{dx^l}(x^2-1)^l$
I have tried a direct substitution
\begin{split} (2l+1)\int_{0}^{1}P_l(x)dx&=(2l+1)\int_{0}^{1}\dfrac{l}{2^l l!}\dfrac{d^l}{dx^l}(x^2-1)^ldx\\ &=\dfrac{(2l+1)l}{2^l l!}\int_o^1 \dfrac{d^l}{dx^l} \sum_{k=0}^{l}(-1)^k\binom{l}{k}x^{2(l-k)}dx \end{split}
But I don't know how to continue from here, can you give me some hints?