I am looking for a closed-form expression for the following integral: $$ I_1 = \int_{0}^{\infty} J_{2m} \left( a x\right) x \dfrac{ e^{-j \sqrt{k^2-x^2} b}}{ \sqrt{k^2-x^2}} \textrm{d} x $$ where $J_{2m}(\cdot)$ is the Bessel function of the first kind and order $2m$, with $m$ integer. A series representation would also be useful.
Other integrals for which I am looking for a closed-form expression are $$ I_2 = \int_{0}^{\infty} { x^{1/2} e^{-a x } J_{2n-1/2}( b x ) J_0 \left( c x \right) \textrm{d} x } $$ and $$ I_3 = \int_{0}^{\infty} { x^{1/2} e^{-a x } J_{2n-1/2}( b x ) J_1 \left( c x \right) \textrm{d} x } $$ where $n$ is an integer.