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Evaluating an indefinite integral

  1. Nov 13, 2009 #1
    1. The problem statement, all variables and given/known data
    Evaluate the indefinite integral.

    [tex]\int \left({\sqrt[5]{x^5}}-\frac{6}{5 x}+\frac{1}{4 x^{7}} \right) dx[/tex]


    3. The attempt at a solution

    O.k. the only anti-derivative I am having trouble getting is the first one [tex]{\sqrt[5]{x^5}}[/tex].

    I am not sure what formula I would use or how to do it. I looked through the book, but I didn't see anything addressing this. Any help would be appreciated.

    I imagine that it would be easier to write it as [tex](x^{5})^{\frac{1}{5}}[/tex]

    Working through it I get [tex](\frac{x^{6}}{6})^{\frac{1}{5}}[/tex]

    then I am stuck...
     
  2. jcsd
  3. Nov 13, 2009 #2
    Remember that when you raise a power to a power, that by the Law of Exponents the powers multiply. :wink:
     
  4. Nov 13, 2009 #3

    Mark44

    Staff: Mentor

    Simplify first!!
    [tex]\sqrt[5]{x^5}~=~x[/tex]
     
  5. Nov 13, 2009 #4
    Yeah, I can't believe I missed that. So then the anti-derivative should be [tex]\frac{x^{2}}{2}[/tex] + a constant?
     
  6. Nov 13, 2009 #5

    Mark44

    Staff: Mentor

    Yes, but you won't need a constant for each term in the integrand - just one for all three.
     
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