\(\displaystyle\int4(6x-1)^{2/3}\,\mathrm dx\)
Let \(y=6x-1\), so that \(\mathrm dy=6\,\mathrm dx\implies\dfrac{\mathrm dy}6=\mathrm dx\). Then
\(\displaystyle\int4(6x-1)^{2/3}\,\mathrm dx=\int\frac46y^{2/3}\,\mathrm dy\)
Simplifying and applying the power rule gives
\(\displaystyle\frac23\frac{y^{5/3}}{\frac53}+C=\frac23\times\frac35y^{5/3}+C=\frac25y^{5/3}+C\)
and back-substituting to get this in terms of \(x\), you end up with
\(\dfrac25(6x-1)^{5/3}+C\)
