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Help on this integral

  1. Aug 2, 2009 #1
    how can i integrate this expression

    dx/sqrt(x^2+r^2)

    in books i found just the answer,but i need the solution step by step

    can you help me?
     
  2. jcsd
  3. Aug 2, 2009 #2

    arildno

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    Now, let x=ru, where u is your new variable.

    Try and simplify after this substitution of variables what you get as your integrand!
     
  4. Aug 2, 2009 #3
    after simplifying i got this

    du/sqrt(u^2+1)

    but still i can not see the solution
     
  5. Aug 2, 2009 #4

    jgens

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    If you don't recognize that integral, another useful substitution might be: x = r * sinh(u). Or, if you're unfamiliar with the hyperbolic functions, try the trigonometric substitution: x = r * tan(u).
     
    Last edited: Aug 2, 2009
  6. Aug 2, 2009 #5
    hyperbolic functions are a little complicated for me so i will try x=r*tan(u)
     
  7. Aug 2, 2009 #6

    jgens

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    That's the more difficult substitution, but alright!
     
  8. Aug 2, 2009 #7
    i tried x=r.tan(u) substitution and i got what i want.
    thanks...
     
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