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Antiderivatives & Indefinite Integrals

  1. Apr 11, 2010 #1
    1. The problem statement, all variables and given/known data

    Compute the following integral:



    2. Relevant equations
    none


    3. The attempt at a solution
    x^(1/2)-2(x^2)^(1/3) +1*x^(-1/4)dx =
    (2/3)x^(3/2)-....I don't know this part....+x * (4/3)x^(3/4)
    and this is where I stopped....

    btw sorry I didn't put the symbols and stuff, I'm slow when it comes to technology...
     
    Last edited: Apr 11, 2010
  2. jcsd
  3. Apr 11, 2010 #2
    what level is this at?
     
  4. Apr 11, 2010 #3
    Differential Calculus (calculus 1)
     
  5. Apr 11, 2010 #4
    is this the right integral?

    [tex]\int \frac{x^{\frac{1}{2}}-2\left(x^2+1\right)^{\frac{1}{3}}}{x^{1/4}} \, dx[/tex]
     
  6. Apr 11, 2010 #5

    Cyosis

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    I don't think that integral is going to be possible without special functions.
     
  7. Apr 11, 2010 #6
    O_O special funcitons?
     
  8. Apr 11, 2010 #7

    Cyosis

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    Where did you get get this integral from and what is the question? Finding a 'normal' anti-derivative is not going to happen. So if this is a calculus one exercise there is more to it than you're telling us.
     
  9. Apr 11, 2010 #8
    The question was "Compute the following integral: "
     
  10. Apr 11, 2010 #9

    Cyosis

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    I don't see how you will be able to compute that integral at your level.
     
  11. Apr 11, 2010 #10

    Cyosis

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    I see, while you may think this integral is nearly the same it is in fact much much easier. Just do the division and you get three trivial expressions.
     
  12. Apr 11, 2010 #11
    ok then, what do you think?

    ∫ [x^(1/2) – 2*x^(2/3) +1] * x^(-1/4) dx

    Distribute the x^(-1/4)
    ∫ x^(-1/8) – 2*x^(-1/6) + x^(-1/4) dx

    Solve
    (8/7)x^(7/8) – (12/5)x^(5/6) + (4/3)x^(3/4) + C , I entered that in but it's wrong....
     
    Last edited: Apr 11, 2010
  13. Apr 11, 2010 #12

    Cyosis

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    The method is correct, but the arithmetic is not. For example 1/2-1/4 is not -1/8 and 2/3-1/4 is not -1/6.
     
  14. Apr 11, 2010 #13

    (x^(1/2))(x(-1/4) - (2x^(2/3))(x(-1/4)) + (x(-1/4)) = (x^(1/4)) - (2x^(5/12)+ x^(-1/4)
    x^(1/4)-2x(5/12)+x^(-1/4)
    (4/5)x^(5/4) - (24/17)x^(17/12) +(4/3)x^(3/4) + c

    it's right, thank you :)
     
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