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Primitive of x/sqrt(4+x^4)

  1. Nov 6, 2006 #1
    I know that tu solve this primitive we have tu use the substitution method,but I think that none of the rules that should be used apply to this!The problem is, to use the substitution: x=a/b sen t we should have the function in the format (sqrt(a^2 - b^2*x^2)),but instead of a x^2 I have a x^4.
    I'm studying for an exam about primitives I'm having tomorrow and I really could use some help on this!
    Thanks in advance for the reply!
  2. jcsd
  3. Nov 6, 2006 #2


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    Let u = x^2
    du/dx = 2x
    du = 2xdx

    Hence 1/2 Integral (1/ Root( u^2 + 4) ) du
    Which is a inverse hyperbolic integral.
  4. Nov 6, 2006 #3


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    Make the substitution [itex] x^2 =t [/itex].

  5. Nov 6, 2006 #4
    Now that i look at the primitive,I think it's not necessary to make substitutions...Multyplying the fraction by 1/4 it could be something like: 1/4*x/sqrt(1/4 + (1/4x)^4),which in turn would loook like: 1/4primitive x/sqrt(1/4 + (1/2x^2)2).Since it's no the form f'/sqrt(1-f^2) , the primitive of the function would be: 1/4arcsen(1/2x^2).
    Could this be solved this way?
    Thanks in advance for the reply!^_^
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