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Using trig identity to simplify?

  1. May 12, 2013 #1
    I have this equation 1/(r^2+l^2)^(3/2) and I need to integrate it quickly. My first thought is using this integral formula 1/(1+x^2)^(3/2)=x/sqrt(1+x^2) but how exactly do I get my equation into that form?
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  3. May 12, 2013 #2

    Simon Bridge

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    $$\int \frac{dr}{(r^2+l^2)^{3/2}}$$

    You are thinking too much of formulas and not enough of algebra.
    What happens if you put r=lx?
  4. May 12, 2013 #3
    I'm not sure what you mean by what happens. Like, do the integral when r^2=l^2*x^2?
  5. May 12, 2013 #4


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    He means "do the substitution and write down what you get".
  6. May 12, 2013 #5
    Ok I do get a right answer doing that way. Im confused though, how can I just sub in lx? I understand if we divide or multiply to shift the variables around but I'm confused on this subbing thing.
  7. May 12, 2013 #6


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    Integration by substitution, the integration technique, as opposed to integration by randomly plugging in other things
  8. May 12, 2013 #7
    Oh I went through it again and its simple u sub nevermind haha.
  9. May 13, 2013 #8

    Simon Bridge

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    (My emphasis.)
    If I said "substitute r=lu" you'd have been fine?

    You have to look for these things ...
    ...the way forward will not normally look like some formula you've memorized.

    Anyway you go there - well done.
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