Integration of Legendre Polynomial I need to evaluate the following integral
\begin{equation} \int_{-1}^1 \frac{d^4P_l(x)}{dx^4}P_n(x)dx\end{equation}. Of course the answer I need is in terms of $l$ and $n$. Does anyone have any idea how to proceed?

The facts below should allow you to compute the integral in question in terms of $l$ and $n$: 


*

*The Legendre polynomials $P_0, \dots, P_n$ form a basis for the space of polynomials of degree at most $n$.

*The Legendre polynomials are orthogonal:
$$
\int_{-1}^{1} P_m(x) P_n(x)\,dx = {2 \over {2n + 1}} \delta_{mn}
$$

*$\dfrac{d^4P_l(x)}{dx^4}$ is a polynomial of degree $l-4$ if $l\ge 4$ or the zero polynomial otherwise.
