  We study the distribution of $S$-integral points on $\mathrm{SL}_2$-orbit
closures of binary forms and prove an asymptotic formula for the number of
$S$-integral points of bounded height on $\mathrm{SL}_2$-orbit closures of
binary forms. This extends a result of Duke, Rudnick, and Sarnak. The main
ingredients of the proof are the method of mixing developed by Eskin-McMullen
and Benoist-Oh, Chambert-Loir-Tschinkel's study of asymptotic volume of height
balls, and Hassett-Tschinkel's description of log resolutions of
$\mathrm{SL}_2$-orbit closures of binary forms.
