# Integral of Legendre polynomial

1. Dec 11, 2009

### shaun_chou

1. The problem statement, all variables and given/known data
In solving a question I got a problem of solving the following integral. Your comments are appreciated.

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

3. 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 $$\int_{-1}^{1}P_l(x)$$

2. Dec 11, 2009

### gabbagabbahey

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

3. Dec 15, 2009

### shaun_chou

Thanks a lot for your help.