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: Evasive integral substitution

  1. Oct 29, 2008 #1
    I am staring at an integral of the form

    [tex]
    \int \frac{sin(at)}{(1 + bsin^{2}(at))^{1/2}} dt
    [/tex]

    which I have generated for myself (in attempting to model the behaviour of a particle in an oscillating field). I can't see a sensible substitution to try, at present. I could hunt down a standard integral, perhaps, but I suspect something obvious is evading me...

    Any hints? Also, any suggestions for brushing up on solving integrals of this sort? I'm a bit rusty :-)

    Cheers!
     
  2. jcsd
  3. Oct 29, 2008 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It's sin that makes this complicated, isn't it? That seems the obvious place to start.
     
  4. Oct 29, 2008 #3

    Mark44

    Staff: Mentor

    This might be useful: Change 1 + b*sin^2(at) into 1 + b*(1 - cos^2(at) = 1 + b - b*cos^2(at).

    You could then use the substitution u = cos(at), du = -a*sin(at)dt.

    Then your integral would be roughly du/(A - bu^2)^(1/2), and you might be able to find that in a table of integrals or, failing that, apply a trig substitution.

    Anyway, that's the direction I would go as a start.
     
  5. Oct 30, 2008 #4
    A good suggestion. Thank you. It will end up with an arc sin of a cos, I think, but perhaps that can be rewritten more elegantly...
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook