1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integration-Problem with substitution

  1. Nov 12, 2009 #1
    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. jcsd
  3. Nov 12, 2009 #2


    Staff: Mentor

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

    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 [itex]\theta[/itex] = r/p.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook