Question: integrals with Bessel functions

How do I solve

int(int(exp(cos(theta)*sin(phi))*sin(phi), phi = 0 .. Pi), theta = 0 .. 2*Pi)


I think it is equal to

2*Pi*(int(sin(phi)*BesselI(0, sin(phi)), phi = 0 .. Pi))

but Maple also does not solve this integral?


Does anyone know how to solve these integrals (with or withouth Maple)?

Are there other programs that can solve these kinds of integrals?

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