How to Solve the Scalar Density Integral in Spherical Coordinates?

[Korbid]

hi!

i need to solve this integral:

$\rho_s=\int (m/\omega)e^{-\omega/T}d{\vec k}$
where $\omega=\sqrt{m^2+{\vec k}}$ is the dispersion relation, T is the temperature of the system and m the mass of a particle

Thank you!

 

[mfb]

How do you add a scalar to a vector?

If k would be a scalar, the derivative of $e^{-\omega / T}$ looks promising.

 

[Korbid]

Sorry! I was wrong!

$\omega = \sqrt{m^2 + \vec{k}^2}$

However, i still can't solve it.

 

[mfb]

Did you try spherical coordinates?