Solving Explicit integral in symbolic form

Hi all,

I am solving an integral brom beta (which is function of dimensionless alpha) to 1. The function f has x variable and alpha constant. I am trying this with symbolic method. I am expecting solution in terma of alpha. Theta is known. I have followed previous discussions but still I am getting error as 'Explicit integral could not be found'

Please help

     clear;clc;

     syms alpha positive;
     syms x;

     theta = 0  ;

     beta = (sin (theta) + sqrt( (sin(theta).^2) + (4.*alpha.*(alpha -          1) )  ) ./(2.*alpha))
     a = beta;
     b = 1;

     f =( (x/((alpha.*x.*x)+1-alpha)).^2 -1).^(-1/2)

     int(f,x,a,b)

Answer 1

[Walter Roberson]

Can you restrict alpha even further than just "positive" ? The indefinite integral has a number of different cases, sensitive to the value of alpha, and when one tries to use that particular "a", a symbolic division by 0 is created that makes it difficult to resolve the definite integral.

The treatment with unknown alpha also introduces possibly-spurious imaginary quantities.

[Amit Kadam]

You are right if and only if alpha is more than 1 I will get some answer but I don't know how to code such condition? The software is new to me and difficult to find information. Can you help me?

[Walter Roberson]

Use assume() to provide an assumption (if you have a new enough MATLAB)

You might also have to provide an assumption on the value of "a"; in particular whether it is greater than "b" or not (it turns out to be less than 1 except at the limit)

I have an expression for the integral, but I have my system working to see if there is a nicer form for it. It involves the elliptic functions.

[Amit Kadam]

Thanks Walter, I can not access matlab now. I m sure this will work.

[Walter Roberson]

I would not count on MuPAD being able to handle the elliptic integrals, but it might be able to.

My system is still trying to find a nicer expression for the integral. So far no meaningful simplifications, other than finding a way to rewrite the single occurrence of EllipticK in terms of EllipticE and EllipticF... not sure if that counts :-(