Please for some help with this integration problem.

i.e.

integral ((a x^4 + b x^2 + c)^–½) dx

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- May 27th 2006, 06:44 PMeulinatorIntegration Help
Please for some help with this integration problem.

i.e.

integral ((a x^4 + b x^2 + c)^–½) dx - May 27th 2006, 07:24 PMThePerfectHacker
Are you certain it is not,

?? - May 27th 2006, 07:31 PMchancey
I havn't done any intergration yet, but what I remember from calculus is to rationalise the denominator

Don't know if that helps... - May 27th 2006, 08:28 PMeulinator
Thanks for the rationalize approach. I will look into that.

The problem is based on predicting the rotation of a solid body after any given time. As far as I know there is no yet found solution. The integration is done numerically on a computer. I am desparately trying to get a theoretical formula. Alas, I am not that great with integration; I am at GCE A-level.

The equation is actually correctly stated. - May 27th 2006, 08:32 PMThePerfectHacker
Maybe there reason why it is done numerically is because it cannot be precisely computed!

There are cases like that so do not be supprised. - May 27th 2006, 08:48 PMeulinatorQuote:

Originally Posted by**ThePerfectHacker**

I actually broke down the numerical method into this itegration and a matrix inverse. I expect that this approach have been attempted before, and hoped against.

Thanks for your expertise. - May 27th 2006, 11:22 PMeulinatornew equation form
I have a broken down the original equation using partial fractions

Using the roots of a quadratic equation, let

and

Therefore becomes

Trying pratial fractions,

Therefore

When then and

Likewise

So the original becomes

Expanding to avoid imaginary values

The new form is

How can this proceed further? I noticed that it does not fall exactly in the arcsin value for the integral - May 28th 2006, 04:11 AMtopsquark
Don't quote me on this.

I don't have my book with me at the moment, but the integral in question (I think!) appears in my Mechanics book. If I remember correctly, the integral can be reduced to an elliptic integral. They have no closed form.

-Dan - May 28th 2006, 11:07 AMThePerfectHackerQuote:

Originally Posted by**topsquark**

But as far as my post #5 is correct. That is why they used numerical methods. - May 28th 2006, 05:19 PMeulinator
The equation was not correct :( due to the ± issue of the square root. I will try to re-formulate the equation keeping the sign in mind. Consequently, the result I gave in post one would be rather unsolvable.

I also looked at Elliptic Integral and Jacobian Elliptic Functions. I could not follow Closed Form.

You are right:**This integral form is done in numerical methods.** - June 3rd 2006, 01:09 AMchancey
I don't know if your still working on it, but maybe this may help The Integral Calculator

- June 7th 2006, 12:57 AMeulinatorQuote:

Originally Posted by**chancey**

Thanks. - June 15th 2006, 01:39 PMeulinator
I think that I finally understand the

*closed form*and the*ellipsoid*concept

Firstly, the first equation is not of a 'function' therefore the area under the graph would not be closed, and to explain it more vividly: the eqution is that of an ellipse!

EDIT: I think that the arctan integral is only valid for a range of x<1

Well, I did the equation for this over, if any is interested in helping. I am putting it in the Advance Topics section.