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\sqrt[3]{3x-1}\\
\sqrt{x+1}=t\\
\sqrt[3]{3x-1}=\sqrt[3]{3t^2-4}\\
" alt=" \sqrt{x+1}>\sqrt[3]{3x-1}\\
\sqrt{x+1}=t\\
\sqrt[3]{3x-1}=\sqrt[3]{3t^2-4}\\
" align="absmiddle" class="latex-formula">
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\sqrt[3]{3t^2-4}\\
t^3>3t^2-4\\
t^3-3t^2+4>0\\
(t-2)^2(t+1)>0\\
(-1;2) \ U \ (2;+oo)\\
\\
" alt=" t>\sqrt[3]{3t^2-4}\\
t^3>3t^2-4\\
t^3-3t^2+4>0\\
(t-2)^2(t+1)>0\\
(-1;2) \ U \ (2;+oo)\\
\\
" align="absmiddle" class="latex-formula"> теперь ставя заместо

и учитывая ОДЗ
получаем