Mathematica: Integration of Bessel Function & Exponent Function & Trigonometric Function

I have an integral with the form

Int[k_]:=Integrate[Exp[-x]xSin[x]BesselJ[0,k*x],{x,0,10}]

where BesselJ[0,kr] is the modified Bessel function of the first kind.

Now i can't get the directly answer from Mathematica..

I want to get the curve of Int[k], maybe a approximate is also acceptable..What can I do then?

Since the function doesn't have an antiderivative, your best bet is to numerically integrate. Example:

Int[k_] := NIntegrate[Exp[-x] x Sin[x] BesselJ[0, k x], {x, 0, 10}]
Plot[Int[k], {k, -5, 5}]

PS: I have edited your question, as you had some typos. You cannot use I as the symbol (it messes the complex i), and also when defining a function have to use := instead of =.