I can't solve integral symbolically [MC15]

[Xonio]

Hello! My name is Ivan and I often use Mathcad 15 at my university.

I've been working on some task recently which involved symbolical calculations in Mathcad.

I faced a problem that one of the integrals just won't solve. I used Mathcad for over a year now and i have no clue how to fix this. Can someone tell me what's wrong?

Thank you in advance!

[Werner_E]

Your integral leads to elliptic integrals of the first and second kind.

Mathcad (muPad) simply is not able to solve that.

Here is Wolfram Alpha with the integral you basically try to calculate:

https://www.wolframalpha.com/input/?i=int+sqrt+%28a%2Bb%2Fx%5E4%29+dx

[Xonio]

I believe if i substitute rho squared for x it would be possible to integrate by parts. May be its possible to somehow simplify it?

[Werner_E]

Unfortunately there is no "trick" to be able to simplify elliptical integrals.

Do you really need a symbolic solution? Of course providing specific values you can get a good numeric solution if you want.