Integrate[SphericalBesselJ[1,k*r]*Exp[-a*r]*r^2,{r,0,∞}]

Manipulate[Plot[{Re[(r/((((r^2)+(((1+I*t))^2)))^2))],Im[(r/((((r^2)+(((1+I*t))^2)))^2))]},{r,0,10},PlotRange->{{0,10},{-0.3,0.5}},Frame->True],{t,0,10}]

Manipulate[Plot[r^2*((Abs[(r/((((r^2)+(((1+I*t))^2)))^2))])^2),{r,0,10},PlotRange->{{0,10},{-0.01,0.1}},Frame->True],{t,0,10}]

rad[x_,y_]:=Sqrt[x^2+y^2];
ct[x_,y_]:=y/Sqrt[x^2+y^2];

Manipulate[DensityPlot[Abs[((rad[x,y]*ct[x,y])/(((((rad[x,y])^2)+(((1+I*t))^2)))^2))],{x,-10,10},{y,-10,10},PlotPoints->30],{t,0,10}]