`int ((3+ ln\ 2x)^3)/(x) dx`

Let

u = 3 + ln 2x

We can expand out the log term on the right hand side as follows:

3 + ln 2x = 3 + ln 2 + ln x

Now the first 2 terms on the right are constants (whose derivative equals zero) and the derivative of the natural log of x is `1/x`.

Then `du = 1/x dx`.

`int(3+ln\ 2x)^3/(x)dx`

`=int u^3 du`

`=(u^4)/(4)+K`

`=((3+ln\ 2x)^4)/(4)+K`