Question

Integrate? `int((log(1+x))^3)/(2x)dx`

Answer 1

What I see is that `1/x` is the derivative of `lnx`, so I would rewrite this in terms of `ln(u)`.

`log(1+x) = (ln(1+x))/(ln 10)`

As a result:

`=> int (log(1+x))^3/(2x)dx = 1/(2(ln10)^3) int (ln(1+x))^3/xdx`

This has no elementary exact solution, and this is as far as we can go. Had it been `2(1+x)` instead, then this would be doable via `u` substitution.