I want to integrate the dirac delta function in the following expression: $$f(\vec{k}_L) = N(k_L)\frac{K*}{X*^2} \int d^3\vec{k}_s \int d^2\vec{l} \frac{P1(k_s)}{P2(k_s)*C} g(\vec{k}_s) T(\vec{l}) \delta^3(\vec{k}_L + \vec{k}_s + \frac{\vec{l}}{X*}) $$
I was wondering how to do this with some of the functions depending on $\vec{k}_s$ and some just on $k_s$ and not a standard form of the dirac delta function (like $\delta^3(\vec{x}-\vec{a})$). An other thing I know is that $k_L << k_s$. How can I integrate this delta function?