Can I move a constant function out of an integral? I have the following integral:
$$\int\exp(2\pi i \Omega t)\beta(\omega_0)d\Omega$$
while $\Omega$ is defined as 
$$\Omega = \omega - \omega_0$$.
$\omega_0$ is handled as a constant value, while $\omega$ is a variable. Now I am not sure if I can move $\beta(\omega_0)$ out of the integral. 


Reason for moving it out: It is a const. value, and never changes.
Reason for doubt: $\omega_0$ is also used in the integration variable $\Omega$. 


Is there a reason not to move $\beta$ out?
Use
$d\Omega=d\omega$ and write the integral explicitly as 

$$
I(\omega_0)=\int d\omega e^{-2\pi i\omega_0 t} e^{2\pi i\omega t}\beta(\omega_0)
$$

now it should be obvious which factors can be pulled out of the integral.
If $ \beta ( \omega_0 )$ is a function of constant $\omega_0$ alone, it can be pulled out of the integral sign.  $ d \omega = d \Omega $ ,  $\omega ,\Omega $ are variables.