Simple question, hard answer: Int: SQRT(1+x^2)/SQRT(10-x^3)

[seeker]

Is the following integral evaluatable by means of an anti-derivative?

Int: SQRT(1+x^2)/SQRT(10-x^3)

Obviously, if it is, please be as specific as possible about the procedure.

 

[galactus]

Re: Simple question, hard answer

If you mean is it doable by elementary means, then I don't believe so. Although, something clever may be possible.

 

[seeker]

Galactus (or anyone), what do you mean by the phrase "by elementary means"? Is there a third category, "sophisticated means", in addition to 1)the various well-known techniques of integration--substitution, integration by parts, partial fractions,etc. and 2)numerical approximation? And specifically, is there ANY way, however intricate and tedious, of obtaining an anti-derivative for this particular integral?

 

[galactus]

By elementary means, I mean parts, substitution, etc. The methods we learn in calc class. There are more sophisticated methods using complex analysis and other ways. Let me ponder on it. I am asking others about it. If I have any luck, I will let you know. I ran this through Maple and It wouldn't even give me a closed form.
If it were a definite integral we could work with it by using approximation methods.

 

[galactus]

I ran this through Maple and the Integrator(http://integrals.wolfram.com/index.jsp) and they both say there is no closed form.

If there is, it'll take some fancy footwork.

 

[seeker]

Galactus: I appreciate your zeal and thoroughness in tackling the problem I posed. You're a real asset to those of us in the jungle without a machete. Oh, and thanks for the link to Mathematica. I've already been tickled playing with my new toy.