Symbolic Integration, how to count when int can not compute?

I have an unusual function with several symbolic parameters,that contains integral. I am trying to fit this function later to experimental data and acquire those parameteres. I tried to use 'integral', but it requires a function without any symbolic variables. Then I tried 'int', but the integral is too complicated and even after 30 mins I get no result- 'busy'. Is there any other method for integral solving?

Function looks like this-

photo and below it there are 4 parameters that we look for, all besides Ri which is our 'x' We know re, ri and Ri as Data of course. R=sqrt(Ri^2+ri^2+r^2)

For the clarity of this post I put the code in my second post.

[Andrew Newell]

It would be easier to answer this question if you showed us the function.

[Artur]

Any suggested solution to this function ?

Answer 1

[Sean de Wolski]

Use the curve fitting app ( cftool ) or lsqcurvefit to fit to the data finding those coefficients.

The use of a symbolic integral here does not sound necessary.

http://www.mathworks.com/help/releases/R2014b/curvefit/curve-fitting.html

http://www.mathworks.com/help/releases/R2014b/optim/nonlinear-least-squares-curve-fitting.html

[Artur]

/Could you please check the function problem and code for more precise answer as we have already tried those apps and they can't compute at all or do it wrong.

Answer 2

[Artur]

1. We can not use the tool as we are not able to put the integral function as a function to fit.

2. Trying to solve this function first by using 'int' to get the final equation gives an obviously wrong result that contains complex number, which also can not be put into this app.

3.Lsqcurve fitting function can not contain symbolic numbers, so we can not use it.

4. We don't care that much about accuracy of our result so we tried to calculate it numerically using 'for loop', but even though the result was too complicated for app to handle.

The raw function contains double integral, 1 integral, 4 symbolic parameters that we are looking for.

Answer 3

[Artur]

 syms Mse r rb Rik Mc mii gammai Ri %symboliczne dane   %podmieniac sane            subs(integer,Ri,RiT(1,i));

 R=sqrt(Ri^2+ri^2+r^2); %

 %  integer 3 Mse

 integer3=int((sqrt(Ri^2+ri^2+r^2)-r)/r,r); %dzialczy

 c=subs(integer3,r,re);

 d=subs(integer3,r,ri);

 integer3calc=c-d;

 integer3calc=vpa(integer3calc,4);

 %integer2 wewn

 tic;   

 integer2=int((R-rb)/rb*(gammai*r/ri/((rb-mii*r/ri)^2+(gammai^2/4*r^2/ri^2))),rb);

 integer2=vpa(integer2,4);

 e=subs(integer2,rb,R);

 f=subs(integer2,rb,r);

 integer2calc=e-f;

integer2calc=vpa(integer2calc,4);

toc; 

q=0;

integer1calc=0;

for i=ri:((re-ri)/5):re;

     integer1temp=subs(integer2calc,r,i);

    integer1calc=integer1calc+integer1temp*(re-ri)/5;

    q=q+1 

end

 integer1calc=vpa(integer1calc,4);

% sumowanie ogolne

 TensionCo=Mc/2/pi*integer1calc;

 TensionSe=Mse*integer3calc;

 Tension=TensionCo+TensionSe;

 Tension=vpa(Tension,4);

tic toc shows that the second integral it countrs for about 10 mins