Non-elementary Integral: Solving x^2sin(x)/(1+x^6) using Substitution Method

[phil ess]

Homework Statement

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

Homework Equations

none

The Attempt at a Solution

Well I am 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.

 

[Dick]

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

 

[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?

 

[phil ess]

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