Is there a "more easier" way to integrate by parts? I found a photo from Facebook (now removed) with the following content:

When integrating by parts, students often struggle with how to break up the original integrand into $u$ and $dv$. $\color{blue}{\rm LIATE}$ is an acronym that is often used to determine which part of the integrand should become $u$. Here's how it works: let $u$ be the function from the original integrand that shows up on the list below.

*

*Logarithmic functions e.g. $(\ln x)$

*Inverse trigonometric functions e.g. $(\tan^{-1}x)$

*Algebraic functions e.g. $(x^{3} + x - 2)$

*Trigonometric functions e.g. $(\cos x)$

*Exponential functions e.g. $(e^{x})$
In general, we want to let $u$ be a function whose derivative $du$ is both relatively simple and compatible with $v$. Logarithmic and inverse trigonometric functions appear first in the list because their derivatives are algebraic, so if $v$ is algebraic, $v\,du$ is algebraic and an integration with "weird" functions is transformed into one that is completely algebraic. Note that the LIATE approach does not always work, but in many cases it can be helpful.

I tried to use this approach on a relatively simple integral, which is
$$\int (\ln x)^{2}\,dx.$$
I am quite confused whether $u$ should be $\ln x$ or $(\ln x)^{2}$. Is there a more refined way to integrate by parts?

Edit to avoid confusion: I found the antiderivative of $(\ln x)^{2}$, but I am asking for an "easier" way.

The idea here is that we have something we don't know how to integrate,  but maybe taking derivatives makes it simple.   We don't know an easy integral for $\ln (x)$,  so we make $u=(\ln x)^2$   We also want $dv$ something easy to integrate.  Again,  the only option here for something easy to integrate is $dx$
