A Frusterating Double-Integral

1. Apr 7, 2010

Joshk80k

1. The problem statement, all variables and given/known data

Integrate:

$$\int \int \frac{1}{[(x_1-x_2)^2+a^2 ]^1^/^2} dx_1 dx_2$$

(The bounds on the first integral are [-L/2, L/2] and the second integral's bounds are the same.)

2. Relevant equations

N/A

3. The attempt at a solution

I stared at this problem long and hard, and was hoping to use some sort of a trigonometric substitution, but nothing came to mind. I have a suspicion that I might need integral tables to solve this problem, but I might be jumping the gun on this.

I feel like the 'a' variable is throwing a real wrench in the system. If anyone could maybe nudge me in the right direction (if this is solvable without consulting a table) I'd be very appreciative.

2. Apr 7, 2010

Cyosis

To get rid of the a we could use a substitution x1-x2=a f(u). This would allow you to move the a in front of the integral sign. We then have a relation of the form 1/sqrt(f(u)^2+1). Now you can find a trigonometric or hyperbolic function for f(u) that obeys f(u)^2+1=g(u)^2. Do you know which one?