Question

Integral of 4(6x-1)^2/3 dx

Answer 1

`\displaystyle\int4(6x-1)^(2/3)\,\mathrm dx`

Let
`y=6x-1`, so that
`\mathrm dy=6\,\mathrm dx\implies\frac{\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(y^(5/3))/(\frac53)+C=\frac23*\frac35y^(5/3)+C=\frac25y^(5/3)+C`

and back-substituting to get this in terms of
`x`, you end up with


`\frac25(6x-1)^(5/3)+C`