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Non-elementary Integral?

  1. Nov 25, 2008 #1
    1. The problem statement, all variables and given/known data

    Solve the integral of x2sin(x) / (1+x6) from -pi/2 to pi/2.

    2. Relevant equations


    3. The attempt at a solution

    Well Im supposed to do this using the substitution method, so I tried:

    u = x2
    du = 2x dx which doesn't cancel out any terms

    u = 1+x6
    du = 6x5 dx which again doesn't cancel anything out

    u = sin(x)
    du = cox(x) dx useless also

    Is this possible with substitution? I seem to have tried every option for u. Is there another way to do this? (without taylor series and stuff like that)

    Thanks for the help!

    Also, I tried doing this integral on the computer, and it said it cannot be solved because it is probably a "non-elementary integral", hence the title of the thread.
  2. jcsd
  3. Nov 25, 2008 #2


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    The function is odd on that interval. f(-x)=-f(x).
    Last edited: Nov 25, 2008
  4. Nov 25, 2008 #3
    I had a similar question earlier. The result is a whole bunch of sine and cosine integrals and imaginary parts. I don't understand how one would do this, but go ahead and put it in the integrator (mathematica) and check the answer out. What level is this for?
  5. Nov 25, 2008 #4
    For a symmetric function that is odd, the integral on the interval -a to a = 0 !
    Thanks guys.
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