Integrate the following functions `((x+1)(x+logx)^2)/x`

Explanation

`((x+1)(x+logx)^2)/x`
`(1+1/x)(x+logx)^2`
Let t = x+logx.
Then dt = (1+1/x)dx
therefore `int ((x+1)(x+logx)^2)/x dx = int t^2 dt`
`t^3/3 +c = (x+logx)^3/3 +c`