how does the beta function make the total probability of Dirichlet distribution integrate to 1?

Question

the Dirichlet distribution $$Dir(\boldsymbol\mu|\boldsymbol\alpha)=\frac{1}{B(\boldsymbol\alpha)}\prod_K\mu_k^{\alpha_k-1}$$

How is the normalization term $B(\boldsymbol\alpha)$ calculated?
or in other words how can I show that the total probability integrates to 1?

I tried searching relevant textbooks and pages, but they all seem to just put down the equation there directly.

Any help would be appreciated.