How to Solve the Integral of a Legendre Polynomial?

[shaun_chou]

Homework Statement

In solving a question I got a problem of solving the following integral. Your comments are appreciated.

Homework Equations

$$\int_{-1}^{1}xP_l'(x)dx=?$$

The Attempt at a Solution

I tried to solve by integration by parts, i.e.
$$\left{}xP_l(x)\right{|}_{-1}^{1}-\int_{-1}^{1}P_l(x)$$ but I can't get the simple solution to $$\int_{-1}^{1}P_l(x)$$

 

[gabbagabbahey]

Hint: the Legendre polynomials satisfy an orthogonality relationship...

 

[shaun_chou]

Thanks a lot for your help.