Is substitution a good strategy when I have to integrate a natural log? For example, I have the integral ∫xln(x^2)dx. Would it be better to use parts?

So far, I have tried: u= x^2 

I came up with the new integral of 1/2∫ln(u)du...
I am not sure what the next step is
To solve 
$$\int\ln(u) \,du$$
a common trick is to treat the integral as 
$$\int 1 \cdot \ln(u) \, du$$
and use integration by part. 
So 
$$\int 1 \cdot \ln(u) \, du = u \ln(u)+\int 1\cdot \,du = u\ln(u)+u +C. $$
To solve 
$$\int\ln(u) \,du$$
a common trick is to treat the integral as 
$$\int 1 \cdot \ln(u) \, du$$
and use integration by part. 
So 
$$\int 1 \cdot \ln(u) \, du = u \ln(u)+\int 1\cdot \,du = u\ln(u)+u +C. $$