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I am a researcher working on electromagnetic field. when solving the PDE equation, this integral about Bessel funtion arises:

\int_{R1}^{R2} x J_1 (sx) dx

where J_1 is the 1th order Bessel function of first kind, and s is a constant, R1 and R2 is integral interval.

I have not found the solution in any literature, and due to my poor background in applied mathematics, I do not know how to integrate it by myself.

Does anybody know this analytical solution?

Thanks very much in advance!

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# How to integrate the following Bessel funtion

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