Hello,
[tex] \int\limits{ln(x^\frac{1}{3}) } \, dx =\frac{1}{3}*\int\limits{ln(x) } \, dx \\\\
=\frac{1}{3}*(x*ln(x)-x)+C=\frac{x}{3}*(ln(x)-1)+C
[/tex]
Th[tex]\int\limits{ln(x) } \, dx=x*ln(x)- \int\limits{x* \frac{1}{x} \, dx \\\\
=x*ln(x) -x+C[/tex]
The last integration is made by "parties(in french)"
[tex] \int\limits{ln(x)} \, dx =x*ln(x)- \int\limits{x* \frac{1}{x} } \, dx \\\\
=x*ln(x)-x+C
[/tex]
