Evaluate: `int(2)^(2)^(2)^x\ \ 2^2^x\ \ 2^x\ dx`

Explanation

`int ((2^2)^2)^x dx`
Let `2^x=t`
`=>(dt)/(dx)=2^x ln 2`
`=>2^x dx=(dt)/(ln 2)`
`=>(2^2)^t 2^t(dt)/(ln 2)`
let `2^t=m`
`=>(dm)/(dt)=2^t ln 2`
`=>2^t dt=(dm)/(ln 2)`
`int(2^mdm)/(ln 2)^2`
`=2^m/(ln 2)^3`
`=(((2^2)^2)^x)/(ln 2)^3+c`