Integrate bessel functions with one of the bessel functions reaching a big value

I have two Bessel functions, one J and one I and also and exp(). Read the attached file "erotisi_matlab".

The bessel I is very big and maybe reaches infinity. I tried to convert it as symbolic function and after that to integrate it. I did that but I think it is completely wrong. Here is me code. The a, b and c are constant values. Is it a matter, if the constant values a and c are big values? Could you please help me ?

a = ... ; 
b = ...;
c = ...;
syms r
f = (besselj(0,(a*r)))*(besseli(245662.85*r))*exp(c*r)*r;
vpaintegral(f,r,0,b);

[Walter Roberson]

It would be easier to investigate if you provided values for a, b, c

[Walter Roberson]

One thing that could be important is whether c is positive or negative. If it is positive it would not be surprising to get large values; with negative you at least get a decaying curve that has a chance of having a finite integral.

[Konstantinos Lekkas]

Here is my matlab code in details

U_1_p = 1.542719177353733;
a_1_p = a_1_q = 4.0e-06;
W_1_q = 1.336914125166486;
Konsta = -1.658662526599862; 
D = 40e-06;
syms r
f = (besselj(0,(U_1_p*(r/a_1_p))))*(besseli(0,((W_1_q/a_1_q)-(Konsta/(D-r)))*r))*(exp(Konsta*(D/(D-r))))*r;

vpaintegral(f,r, [0 a_1_p])

[Walter Roberson]

The value produced by vpaintegral() agrees with the calculation in Maple.

[Konstantinos Lekkas]

Actually MATLAB gave me result: 1.266e-12

Is it right ?

[Walter Roberson]

1.2660873190593569*10^(-12) approximately. You cannot more precise than that because of inaccuracies in your floating point constants.

[Konstantinos Lekkas]

Thank you vey much mr Walter Roberson