I can't seem to find a formula for Haar integral
$$ \int_{SU(n)} F(U) d \mu$$
The integration will probably be executed using some parametrization with $n^2 -1$ parameters as I believe $SU(n)$ is related to $S^{d^2 -1}$. What interests me is the most general formula, as I can't seem to find any specifics for $n > 2$. Something that may simplify the concept is the fact, that I want to integrate volumes of balls $$ B(g,\epsilon) = \{ U \in SU(n): |U-g| \leq \epsilon \}. $$
Is there any material on that or could anyone show me a way of building such a measure?
EDIT: $F$ should be such that the result is a volume of a ball in $SU(n)$ . From one source I see that for $SU(2)$ $ F(\theta, \phi, \psi) $ (where $\phi, \psi, \theta$ are Euler angles) is a central function satisfying $F(ghg^{-1}) = F(h)$. That simplifies $F (\theta, \phi, \psi) = F (\phi)$. The exact formula for $F$ is given as 1 if $| \sin \frac{\phi}{2}| < \frac{\epsilon}{2 \sqrt{2}}$, 0 otherwise. $\phi$ is the spectral angle.
You can find a description of the Haar measure on $SU(n)$ in
"Generalized Euler Angle Parametrization for SU(N)" Tilma, Sudarshan
and
"Composite parameterization and Haar measure for all unitary and special unitary groups" Spengler, Huber, Hiesmayr.