result =
syms nu x
result = int(besselj(nu, x), x, 0, 4*sym(pi))
Bessel J is a family of functions, distinguished by the ν value. You cannot get much of a result unless you specify the ν value you want to work with.
result0 = int(besselj(0, x), x, 0, 4*sym(pi))
vpa(result0)