bessel_i (2, %i*x) or bessel_i(2, x) with integrate --> noun form

bessel_i(2, z) apparently doesn't have an
integration rule for integrate?

(%i1) load(nint);
(%o1) "c:/work2/nint.mac"

------------------
bessel_i  examples
------------------------

order 1 numerical:  ok:

(%i2) integrate (bessel_i(1,%i*x),x,1,10000);
(%o2) %i*bessel_i(0,10000*%i)-%i*bessel_i(0,%i)
(%i3) f(%);
(%o3) -0.77229384691136*%i

order 1 symbolic: ok:

(%i16) integrate(bessel_i(1,x),x);
(%o16) -bessel_i(0,x)

(%i17) integrate(bessel_i(1,%i*x),x);
(%o17) %i*bessel_i(0,%i*x)

*but*
order 2 numerical: * noun form:*

(%i4) integrate (bessel_i(2,%i*x),x,1,3);
(%o4) 'integrate(bessel_i(2,%i*x),x,1,3)

order 2 symbolic: noun form:

(%i14) integrate(bessel_i(2,x),x);
(%o14) 'integrate(bessel_i(2,x),x)

(%i15) integrate(bessel_i(2,%i*x),x);
(%o15) 'integrate(bessel_i(2,%i*x),x)

order 2 symbolic, imag. arg:  noun form

(%i5) integrate (bessel_i(2,%i*x),x,a,b);
(%o5) 'integrate(bessel_i(2,%i*x),x,a,b)

order 1 symbolic, imag. arg:  ok

(%i6) integrate (bessel_i(1,%i*x),x,a,b);
(%o6) %i*bessel_i(0,%i*b)-%i*bessel_i(0,%i*a)

order 2 symbolic, real arg:  noun form

(%i7) integrate (bessel_i(2,x),x,a,b);
(%o7) 'integrate(bessel_i(2,x),x,a,b)

-------------------
bessel_j example:
------------------------

(%i8) integrate (bessel_j(2,x),x,a,b);
(%o8) hypergeometric([3/2],[5/2,3],-b^2/4)*b^3/24
       -hypergeometric([3/2],[5/2,3],-a^2/4)*a^3/24

-------------------------
bessel_y example:
--------------------------

(%i9) integrate (bessel_y(2,x),x,a,b);
(%o9) ((%pi*struve_h(0,b)*bessel_y(1,b)+%pi*struve_h(-1,b)*bessel_y(0,b))*b
       -4*bessel_y(2,b))
       /2
       -((%pi*struve_h(0,a)*bessel_y(1,a)+%pi*struve_h(-1,a)*bessel_y(0,a))*a
        -4*bessel_y(2,a))
        /2

So the case of bessel_i appears anomalous.

bessel_i  orders 3 and 4:

(%i10) integrate (bessel_i(3,%i*x),x,1,3);
(%o10) 'integrate(bessel_i(3,%i*x),x,1,3)

(%i11) integrate (bessel_i(4,%i*x),x,1,3);
(%o11) 'integrate(bessel_i(4,%i*x),x,1,3)

(%i12) integrate (bessel_i(3,%i*x),x,1,b);
(%o12) 'integrate(bessel_i(3,%i*x),x,1,b)

(%i13) integrate (bessel_i(4,%i*x),x,a,b);
(%o13) 'integrate(bessel_i(4,%i*x),x,a,b)

    Ted