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The principal goal of this paper is to extend the classical problem of findthe values of $\alpha\in \C$ for which the mappings, either$F_\alpha(z)=\int_0^z(f(\zeta)/\zeta)^\alpha d\zeta$ or$f_\alpha(z)=\int_0^z(f'(\zeta))^\alpha d\zeta$ are univalent, whenever $f$belongs to some subclasses of univalent mappings in $\D$, but in the case ofharmonic mappings, considering the \textit{shear construction} introduced byClunie and Sheil-Small in \cite{CSS}.

A new approach for the univalence of certain integral of harmonic mappings