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Fraction of integrals with different variables

  1. Jan 10, 2012 #1
    how would one evaluate this without using trig substitution? Is it possible to make one integral out of this?

    {int[(y^2 + a1^2)^-1]dy +c1}/{int[(x^2 + a2^2)^-1]dx +c2} +c3

    the numbers behind the 'a's and 'c's are supposed to be subscripts.

    Also, how would one deal with this:

    {int[(y^2 + a1^2)^-1]dy +c1}/(a tan{int[(x^2 + a2^2)^-1]dx +c2}) +c3


    Please advise
     
  2. jcsd
  3. Jan 10, 2012 #2

    CompuChip

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    You can use the standard integral
    [tex]\int \frac{1}{1 + x^2} \, dx = \tanh(x)[/tex]
    and a "normal" (non-trig) substitution, and then you can do them separately.
     
  4. Jan 10, 2012 #3

    Char. Limit

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    That doesn't seem right. Isn't that integral tan(x)+C, and not tanh(x)+C?
     
  5. Jan 10, 2012 #4
    Or rather atan(x)+C...
     
  6. Jan 10, 2012 #5

    Char. Limit

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    Touche.
     
  7. Jan 10, 2012 #6

    CompuChip

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    Heh, double fail :-)
    I knew it was something with tan and an extra letter! Thanks micromass :)
     
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