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Imposible Integral?

  1. Jun 26, 2012 #1
    1. The problem statement, all variables and given/known data

    I have to find the definite integral of: [itex]\int\left(\sqrt[3]{1-x^{7}}-\sqrt[7]{1-x^{3}}\right)dx[/itex] with bounds [0,1]

    2. The attempt at a solution

    I know that this can be done with hypergeometric functions, but I ca't use them because "we haven't seem them yet", so I have to do this with "everyday" integration tools. The only thing I was told was that I have to start with a substitution and the last part would be a cyclical integral, which tells me that I probably have to also use integration by parts in the middle.

    I'm not asking for someone to give me the answer right away, I just need a starting point/mini-guide to help me get to the answer on my own, although I'm grateful with any kind of help (: Thanks!
     
    Last edited: Jun 27, 2012
  2. jcsd
  3. Jun 27, 2012 #2
    Which substitutions have you tried so far?
     
  4. Jun 27, 2012 #3
    u= x7, x3, 1-x3, 1-x7
     
  5. Jun 27, 2012 #4

    Curious3141

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    Homework Helper

    Sure that's not a definite integral with bounds of [0,1]?

    Because there's a neat trick to immediately and trivially evaluate it in that case. See my earlier post in this thread: https://www.physicsforums.com/showthread.php?t=571323
     
  6. Jun 27, 2012 #5
    Wow, that's a really nice trick. :approve:
     
  7. Jun 27, 2012 #6

    It is!!! Sorry, I thought I put the bounds on the integral. I'm new here so I probably didn't do it right...fixed the post (: and thanks for that trick!
     
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