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Heavy integral

  1. Aug 12, 2007 #1
    Try to solve this integral:

    [tex]I=\int \frac{\sqrt{\sqrt{x^4+1}-x^2}}{x^4+1}\,{\rm dx}[/tex]
     
  2. jcsd
  3. Aug 12, 2007 #2

    dextercioby

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    Subbing [itex]x^2 =\sinh t [/itex] will give you something like this

    [tex] I=\int \frac{\sqrt{\coth t -1}}{\cosh t}{}dt [/tex]

    Feed it now to Mathematica. There's about 50% chances it will return a complicated expression in terms of elliptic integrals.
     
  4. Aug 12, 2007 #3
    Nice substitution, I managed to solve it now.
    Thanks
     
  5. Aug 12, 2007 #4

    dextercioby

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    Apparently the integral is expressible in terms of elementary functions.
     
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