In this paper, we introduce the integral operator $I_{eta }(p_{1},...,p_{n};alpha _{1},...,alpha _{n})(z)$ of analytic functions with positive real part. The radius of convexity of this integral operator when $eta =1$ is determined. In particular, we get the radius of starlikeness and convexity of the analytic functions with $Releft{ f(z)/zight} >0$ and $Releft{ f^{prime }(z)ight} >0$. Furthermore, we derive sufficient condition for the integral operator $% I_{eta }(p_{1},...,p_{n};alpha _{1},...,alpha _{n})(z),,$to be analytic and univalent in the open unit disc, which leads to univalency of the operators $intlimits_{0}^{z}left( f(t)/tight) ^{alpha }dt$ and $% intlimits_{0}^{z}left( f^{prime }(t)ight) ^{alpha }dt$ .

Keywords: Analytic and univalent functions, Starlike and convex functions, Functions of positive real part, Integral operator