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?

I want to compute Hankel transforms with Maple.

I have noticed that Maple uses a different Hankel transform than the one in e.g. Bracewell (p335).

Maple computes

Integral{f(t)*Jn(s*t)*sqrt(s*t)dt, t:0->inf},

while I want to compute

Integral{f(t)*Jn(s*t)*t dt, t:0->inf}.

How can I compute the Hankel transform below with Maple?

Hello,

I am new to Maple. I am trying to solve a big integral, but I cannot solve it using Maple.

The problem boils down to this integral:

int(exp(x*cos(theta)+y*sin(theta)), theta=0..2*Pi)

The solution of this integral is:

2*Pi*BesselI(0, sqrt(x*x+y*y))

How can I get Maple to solve these integrals?