Integrating a function without u-substitution?

Question

I'm trying to figure out how to Integrate a function like that without the use of $u-$substitution. Would really appreciate some help here!

$$\int\ln^2 x\,dx$$

Thanks in advance!

Answer 1

Integrate by parts: $$\int \ln^2 x\,dx = x\ln^2 x-\int 2\ln x\,dx = x\ln^2 x-2\left(x\ln x-x+C\right), C \in \mathbb{R}.$$