What is the antiderivative of #1/[x(ln(x^3))]#?
(You can get this by the chain rule, or more simply, by noting that
This integral can be evaluated by substitution:
Upon substitution, the integral becomes:
Another way to proceed:
# = 1/3 int 1/(xln(x)) dx#
It looks different, but what is the difference?
# = 1/3(ln3 + ln abs lnx)+C#
# = 1/3ln3 + 1/3 ln abs lnx+C#
So the difference between the expressions is a constant.
The two general answers simply have different