the integral of the Bessel function in Matlab

I try to calculate the integral of the Bessel function in Matlab

syms r a b k 
assume(a>0)
assume(k>0 & k<1)
L=int(log(r)*(besselj(0,a*r)+b*bessely(0,a*r)),r,k,1)

L = 

but I have this error (Invalid limits given : (k, 1)) i.e. I have a problem in log(r) but the k checks (0<k<1) I don't know how to set this condition (0<k<1) in Matlab to get the correct result.

how can I calculate this integral with this condition?

Answer 1

[Torsten]

Seems there is no analytical solution for this integral (see MATLAB output above).

Give values to the variables and use numerical integration:

a = 1;
b = 2;
k = 0.5;
L = integral(@(r)log(r).*(besselj(0,a*r)+b*bessely(0,a*r)),k,1)

L = -0.0605

[mery]

I don't need the numerical values of this integral, I'need just the symbolic values

[Torsten]

I'need just the symbolic values

What can't be done, can't be done.

[mery]

L = Integrate[Log[r]*(BesselJ[0,a*r]+b*BesselY[0,a*r]),{r,k,1},

Assumptions->{0<k<1,a>0}]

it is possible on matimaticas,we add this condition ( Assumptions->{0<k<1,a>0}).

but I don't know how I can do it in Matlab?

it's the same?

[Torsten]

Then why don't you just copy the MATHEMATICA solution to MATLAB ?

One copy-paste suffices.

[mery]

I did it but without a result, I still have an error I don't know why

[Torsten]

What error ? You now have an expression for L that you can directly insert instead of

L = int(log(r)*(besselj(0,a*r)+b*bessely(0,a*r)),r,k,1)