Well, when integrating you should always have d[arg]d[arg], where [arg] is a variable, it's like int∫ is "(" and that is the ")". It's more important because it tell us with which variable you want us to integrate.
In this case it's pretty clear that's xx but as a general rule it's important to specify.
Anyhow, using the property of logarithms we have
intln(x^2)/ln(x^3)dx = int(2ln(x))/(3ln(x))dx = int(2dx)/3 = (2x)/3 + c∫ln(x2)ln(x3)dx=∫2ln(x)3ln(x)dx=∫2dx3=2x3+c
Assuming x in RR, x > 0, x != 1 so as to avoid complex numbers when doing those algebrisms and/or having the function defined in the reals at those points.
