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Homework Help: Is this a trig interval?

  1. Mar 14, 2013 #1
    1. The problem statement, all variables and given/known data
    Evaluate the integral.

    2. Relevant equations
    [itex]\displaystyle\int \frac{1}{x^5 + 5} dx[/itex]

    3. The attempt at a solution

    could i turn this into an x^2 + a^2 --> arctan

    for example: [itex] \frac{1}{x^(5/2)^2 + \sqrt{5}^2} dx [/itex]

    note that is: [itex]x^{5/2}[/itex] squared.
    Last edited: Mar 14, 2013
  2. jcsd
  3. Mar 14, 2013 #2


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    Your thread title says, "Is this a trig interval?" :confused:

    No. If you let u = x5/2, what would du equal, and can you make the substitution work?
  4. Mar 15, 2013 #3
    how would i solve this then?
  5. Mar 15, 2013 #4


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    Wolframalpha gives a very complicated answer, so I'm not sure this integral can be evaluated using the usual analytic methods. Maybe you copied the problem wrong?
  6. Mar 15, 2013 #5


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    One analytic way to do it is to factor x^5+5 completely over the complex numbers and then use partial fractions. Then carefully track how the complex parts cancel. It's a MASSIVE pain in the neck. I could start it but I would probably never finish. Certainly wouldn't assign it as a problem.
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