Non-elementary Integral?

1. Nov 25, 2008

phil ess

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

none

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. Nov 25, 2008

Dick

The function is odd on that interval. f(-x)=-f(x).

Last edited: Nov 25, 2008
3. Nov 25, 2008

lucidicblur

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?

4. Nov 25, 2008

phil ess

For a symmetric function that is odd, the integral on the interval -a to a = 0 !
Thanks guys.