How Do You Integrate a Cubic Polynomial with a Complex Radicand?

[flash]

Hi
I'm trying to integrate
$$\int (-40x^3 + 38.4x^2 - 13.288x + 1.98072)\sqrt{14400x^4 - 18432x^3 + 9087.36x^2 - 2041.0368x+ 177.570944}dx$$
The way I thought I could do it was express the first part (the cubic) in terms of the derivative of the second and do it by substitution. Unfortunately it doesn't work.
Not totally sure that it can be done at all.

Thanks for any help!

 

[Dick]

No, I don't think you are going to be able to integrate that in closed form. But there are simple numerical methods to consider like Simpson's rule.

 

[Kummer]

You can painfully do it by elliptic intehrals. But how did you arrive at this problem?

 

[nicktacik]

I put it into maple, and the answer cannot be expressed with elementary functions (and the answer is about 19 lines!)

 

[flash]

Ok thanks people. I found the answer numerically. I arrived at the problem when trying to evaluate the surface of revolution of the cubic function.

 

[Gib Z]

How did you evaluate an indefinite integral numerically :(

 

[flash]

Haha it was a definite integral, just didn't bother with the notation :-)