Question

What is the integral ln x^1/3 dx.

Answer 1

Hello,


`\int\limits{ln(x^(1)/(3)) } \, dx =(1)/(3)*\int\limits{ln(x) } \, dx \\\\ =(1)/(3)*(x*ln(x)-x)+C=(x)/(3)*(ln(x)-1)+C`
Th
`\int\limits{ln(x) } \, dx=x*ln(x)- \int\limits{x* (1)/(x) \, dx \\\\ =x*ln(x) -x+C`

The last integration is made by "parties(in french)"


`\int\limits{ln(x)} \, dx =x*ln(x)- \int\limits{x* (1)/(x) } \, dx \\\\ =x*ln(x)-x+C`