What is the integration of (logx)3?

Answer 1

You mean log base 3?

log_3 x = ln x / ln 3 by the logarhithm rules, where ln is the natural log.
So all you have to do is integrate ln x, and the 1 / ln 3 you can just drag along (it's a constant)

Answer 2

if it's the integration of (log X)^3, I think you can integrate by parts, that should do the trick