% !TeX TXS-program:compile = txs:///pdflatex

\documentclass[margin=5mm]{standalone}
\usepackage[nonpgfplots]{tkz-grapheur}

\begin{document}

\begin{GraphiqueTikz}[x=12cm,y=2.4cm,Xmin=-0.1,Xmax=1.1,Xgrille=0.1,Xgrilles=0.025,Ymin=-0.5,Ymax=3,Ygrille=0.5,Ygrilles=0.1]
	%axes et grille
	\TracerAxesGrilles*[Police=\small,Elargir=0mm,Origine]{-0.1,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1}{-0.5,0.5,1,1.5,2,2.5}
	%tracés
	\begin{scope}
		\clip (0,0) rectangle (1,{exp(1)}) ;
		\foreach \k in {1,2,3,10,20,30}{%
			\TracerCourbe[Couleur=darkgray,Debut=0,Fin=1]{x^\k*exp(x)}
		}
	\end{scope}
	%textes
	\foreach \k/\absCk in {1/0.16,2/0.4,3/0.56,10/0.8,20/0.88,30/0.98}{%
		\draw[darkgray] (\absCk,0.45) node {$\mathcal{C}_{k}$} ;
	}
\end{GraphiqueTikz}

\end{document}