Anti-differentiate by recognition from a supplied derivative
Use the displayed function and supplied derivative
Keep the answer in exact form
\[P(z)=\left(-7\,z - 6\right)^{\frac{2}{3}}\]
\[P'(z)=\frac{2}{3}\,\left(-7\,z - 6\right)^{-\frac{1}{3}}\,\left(-7\right)\]
\[g(z)=-P'(z)\]
Work on the interval where
\[-7\,z - 6>0\]