Strategies for Evaluating Elliptic Integrals

[cepheid]

Homework Statement

Can you give me a strategy or get me started in the right direction?

I need to evaluate:

$$\int_{x_1}^{x_2} (E-\alpha |x|^{\nu})^{\frac{1}{2}} \,dx$$

Homework Equations

$$\nu > 0$$

x1 and x2 are known in terms of E, alpha, and nu

The Attempt at a Solution

 

[cepheid]

okay I fixed a crucial mistake (forgetting the dx). I wonder if that will help, now that you know what variable I'm supposed to be integrating wrt.

 

[dextercioby]

For arbitrary $\nu$ it's typically an elliptic integral.