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syms nu x
result = int(besselj(nu, x), x, 0, 4*sym(pi))
result = 
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))
result0 = 
vpa(result0)
ans = 
0.8340841018533418306979596564232

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