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The absolute branching ratio of the $K^+ \rightarrow \pi^+\pi^-\pi^+(\gamma)$decay, inclusive of final-state radiation, has been measured using $\sim$17million tagged $K^+$ mesons collected with the KLOE detector at DA$\Phi$NE, theFrascati $\phi$-factory. The result is:  \[ BR(K^+ \rightarrow \pi^+\pi^-\pi^+(\gamma)) = 0.05565 \pm 0.00031_{stat}\pm 0.00025_{syst} \] a factor $\simeq$ 5 more precise with respect to theprevious result. This work completes the program of precision measurements ofthe dominant kaon branching ratios at KLOE.

Measurement of the absolute branching ratio of the $K^+ \rightarrow \pi^+\pi^-\pi^+(\gamma)$ decay with the KLOE detector