How do you solve the integral of ln(x)

This will use the process of integration by parts.

First, notice that ln(x)=ln(x)*1.

So, the integral of ln(x) is the integral of ln(x)1. The process of integration by parts is;  int(v^du/_dx)dx=vu - int(^dv/_dx*u)dx.

Set ln(x)=v, 1=^du/_dx, so int(ln(x)*1)dx = ln(x)x - int(¹/_xx)dx = xln(x)-int(1)dx = xln(x)-x+constant.

And you're done!