On univalence of integrals of $(F')^{\lambda}$ and Bloch functions

In this note we estimate a constant $C_{\alpha}$, connected with the Bloch class $\mathcal{B}$ and the universal linear invariant families $U_{\alpha}$. Moreover, we estimate the radius of the biggest disc such that for all its elements $\lambda$ the integral of $(h')^{\lambda}$ is univalent for all $h\in U_{\alpha}$.