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Homework Help: How to solve this root integral

  1. Feb 18, 2009 #1
    i tried this:
    [tex]
    \int \frac{1-\sqrt{x+1}}{1+\sqrt[3]{x+1}}=\int \frac{1-\sqrt{x+1}}{1+\sqrt[3]{x+1}}*\frac{1+\sqrt{x+1}}{1+\sqrt{x+1}}*\frac{1-\sqrt[3]{x+1}+(x+1)^{\frac{3}{2}}}{1-\sqrt[3]{x+1}+(x+1)^{\frac{3}{2}}}
    [/tex]
    but when i got read of 2 roots i got another two roots which are more complicated
    ??
     
  2. jcsd
  3. Feb 18, 2009 #2

    tiny-tim

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    Science Advisor
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    Hi transgalactic! :smile:

    Hint: substitute! :wink:
     
  4. Feb 18, 2009 #3
    i tried t=(x+1)^1/3
    but it creates anoted roots in the dt
    ??
     
  5. Feb 18, 2009 #4

    tiny-tim

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    Science Advisor
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    uhh? :confused:

    dx = … ?

    anyway, (x+1)1/6 might be easier.
     
  6. Feb 18, 2009 #5
    but i dont have members of 1/6 power
    ??
     
  7. Feb 18, 2009 #6

    Mark44

    Staff: Mentor

    Sure you do. a^(1/2) = a^(1/6)^3, and b^(1/3) = b^(1/6)^2.
     
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