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Simple Integration

  1. Mar 22, 2015 #1
    1. The problem statement, all variables and given/known data
    integrate
    integral.JPG

    2. Relevant equations
    please solve this using methods only like
    1. Substitution
    2.Partial fraction
    3.By Parts

    3. The attempt at a solution
    i have tried all the above three methods mainly using substitution and by parts....
    i have expanded the a^3 - x^3 and then kept the a/2 - x as "p" but still the function doesn't simplify
     
  2. jcsd
  3. Mar 22, 2015 #2
    What context did this appear in? It doesn't appear to have an elementary antiderivative.
     
  4. Mar 22, 2015 #3

    Ray Vickson

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    Science Advisor
    Homework Helper

    The integral is "non-elementary", so cannot be done in terms of a finite expression involving only elementary functions (such as powers, roots, trigonometric functions and their inverses, exponentials and logarithms, etc.). However, it can be expressed in terms of the non-elementary "elliptic functions", or it can be expressed in terms of an infinite series of elementary functions.

    Note: the non-elementary nature of the integral is a theorem that has been proven rigorously. It is not just a matter of somebody not being smart enough to figure out how to do the integral (in finitely many terms and factors of elementary functions); rather, it has been proven to be impossible. So, even if you allow yourself to use a formula taking 10 billion pages to write out in detail, it still would not be the answer to your question!
     
  5. Mar 24, 2015 #4
    ok, fine then....:oldcry:
     
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