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Homework Help: Help with Integral

  1. May 4, 2009 #1
    I am trying to work out the integral that takes the form:

    [tex]I=\int \frac{x\, dx}{(a^2+x^2)^{3/2}} [/tex]

    I cannot find it in a table, so I am trying By Parts.

    Letting [itex]dv=x\,dx[/itex] and letting [itex]u=(a^2+x^2)^{-3/2}[/itex]

    proves to be futile since I just wind up with a similar integral again, it turns into a vicious cycle

    Letting [itex]u=x[/itex] and [itex](a^2+x^2)^{-3/2}\, dx[/itex] again leaves me with another integral that is not in a table, that is, I get

    [tex]I=\frac{x^2}{a^2\sqrt{a^2+x^2}}-\int\frac{x\, dx}{a^2\sqrt{a^2+x^2}}[/tex]

    Is there a better way? Or should I Integrate by Parts again?

    This is annoying. It is just an "intermediate step" in a Griffiths E&M problem. :grumpy:
  2. jcsd
  3. May 4, 2009 #2


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    It might not be in the table because it's so simple. Just substitute u=(a^2+x^2).
  4. May 4, 2009 #3
    Well. Aren't you a smarty-pants. :biggrin:

    Cannot believe I missed that.

    Where is that :commits Sepuku: emoticon?

    Oh... and thanks!
  5. May 4, 2009 #4
    Hey T-T I like Dick's u-substitution. It's really quick. :smile:

    I have actually never used a trig substitution. I will probably post back here in a while as I would like to learn.

    For now, I am finishing up my E&M.

    Thanks! :smile:
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