Thanks, smallphi. if there is only this integral, Mathematica can compute it. but, this integral is a part of a triple integral. The triple integral is:
A(r,z,R1,R2,Z1,Z2)=(u*I/2)int_{Z1}^{Z2} int_{R1}^{R2} int_{0}^{inf} r' J_1(s*r') J_1(s*r) exp(-s*abs(z-z')) ds dr' dz'
As r' and z' are...