# Integration-Problem with substitution

1. Nov 12, 2009

### jameson2

1. The problem statement, all variables and given/known data
I have reached this integration from a mechanics problem about small angle scattering. t= (2pa/mv^2)*(int from p to infinity) [r*dr]/[((b^2 +r^2)^(3/2))(sqrt(r^2 - p^2))]

2. Relevant equations

3. The attempt at a solution
I know that there should be a substitution that will make this an easy problem, but I can't find it. I've tried the simple ones like let y=r^2, or y=b^2 + r^2, but they didn't get me anywhere.

2. Nov 12, 2009

### Staff: Mentor

For further reference, here is your integral in a more readable form:
$$\frac{2pa}{mv^2}\int_{r = p}^{\infty}\frac{r~dr}{(b^2 + r^2)^{3/2}\sqrt{r^2 - p^2}}$$

You might try an ordinary substitution of u = r2 - p2, but I'm not sure that will do you much good. Next I would try a trig substitution, sec $\theta$ = r/p.