\displaystyle\lim_{a\to 0}\int_{\ln{a}}^{\ln{1/3}}\frac{dt}{t^{4/3}}=-3\lim_{a\to 0 } \frac{1}{\sqrt[3]{t}} |_{\ln{a}}^{\ln{1/3}}=\dots=\frac{-3}{\sqrt[3]{\ln{(3^{-1})}}}=\frac{3}{\sqrt[3]{\ln{3}}}