Anti-differentiate by recognition from a supplied derivative
Use the displayed function and supplied derivative
Use exact values throughout
\[F(t)=\left(19\,t - 11\right)^{\frac{2}{3}}\]
\[F'(t)=\frac{2}{3}\,\left(19\,t - 11\right)^{-\frac{1}{3}}\,\left(19\right)\]
\[g(t)=F'(t)\]
Work on the interval where
\[19\,t - 11>0\]