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How to calculate the antiderivative of: [sqrt(t^4 + t^2 + 1)]/(t^2 + 1)

  1. May 29, 2010 #1
    Anybodys knows how to resolve the problem of the subject.
    I am working in it for three hours. I am desperated.

    I have tried all the subtitutions of "Calculus. Schaum. Ayres&Mendelson". Whithout suceeds.

    Thank you.

  2. jcsd
  3. May 29, 2010 #2
    Well, I'm sorry to disappoint you, but it's simply impossible to calculate it. Just try typing it into wolfram alpha, mathematica or whatever: http://integrals.wolfram.com/index.jsp?expr=Sqrt[x^4+%2B+x^2+%2B+1]/(x^2+%2B+1)&random=false

    See what you get? Three different elliptic functions, that are not elementary functions. Hence, this function doesn't have an antiderivative that could be written down using elementary functions only.
  4. May 29, 2010 #3
    Where in your homework is it?
    I mean, can we see the full problem?
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