\documentclass{article}
\usepackage{pgfplots}% This uses tikz
\pgfplotsset{compat=newest}% use newest version
\tikzset{My Line Style/.style={smooth, ultra thick, samples=400}}

\begin{document}
\begin{tikzpicture}
\begin{axis}[unbounded coords=discard]
    \addplot[My Line Style, color=blue, domain=0.1:3](\x,{-sqrt(\x)*cos(2*ln(\x))});
\end{axis}
\end{tikzpicture}





\end{document}