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Integration in matlab: Explicit integral could not be found

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H=1,R=1,theta=20;
syms x;
syms alpha;
%sigma=F/(2*pi*R*(alpha-1));
z_desh=((x/alpha*x^2+1-alpha)^2-1)^-.5
beta=(sin(theta)+(sin(theta)*sin(theta)+4*alpha*(alpha-1)))/2*alpha
eq=int(z_desh,x,4,1)
when i run the above code en error show like: Warning: Explicit integral could not be found. How to solve this.?
Thanks

Accepted Answer

Walter Roberson
Walter Roberson on 8 Dec 2012
First thing to do is heck whether the x/alpha*x^2 is really what you meant. If it was, why not say x^3/alpha ?
Next, check whether you really want to integrate from 4 down to 1, instead of from 1 to 4.
Thirdly, check why you define beta but then do not use it in what is being integrated.
If your integral is exactly as shown, then there is no readily available analytic form for it. A small number of values of alpha lead to analytic forms; the others do not.
  8 Comments
Walter Roberson
Walter Roberson on 8 Dec 2012
My code is in Maple, using a facility of Maple that does not translate directly into the MuPAD Symbolic Toolbox
What I determined in the end is that you had better use numeric integration and something like fsolve(), instead of trying to use symbolic integration.
When you do your fsolve(), do not use an alpha less than 1: it is not difficult to demonstrate that alpha between 0 and 1 will generate integrals involving complex values.

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