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I don't like memorizing

  1. Feb 26, 2009 #1
    does anybody know how to derive this integral???

    [tex] \int \frac{dx}_{\sqrt{x^2 + a^2}} [/tex] [tex] = ln(x+ \sqrt{x^2 + a^2}) [/tex]
     
    Last edited: Feb 26, 2009
  2. jcsd
  3. Feb 26, 2009 #2

    Dick

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    Looks like you already took it, wrongly. Looks more to me like an arctan. Some things are worth memorizing. Not all, but some.
     
  4. Feb 26, 2009 #3
    corrections are made above.
     
  5. Feb 26, 2009 #4

    Dick

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    The easy way is to use hyperbolic functions. Substitute x=a*sinh(t). Then figure out what the arcsinh function looks like by solving a quadratic. Otherwise a trig substitution like x=a*tan(t).
     
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