$\displaystyle \int{\ln{x} \ dx}$

= $\displaystyle \int{\ln{x}(1) \ dx}$ //pull out a '1'

= $\displaystyle \ln{x}(x) - \int{\frac{1}{x}x}$ //use integration by parts

= $\displaystyle x\ln{x} - \int{1}$

= $\displaystyle x\ln{x} - x$

= $\displaystyle x(\ln{x} - 1)$

Is pulling out a 1 in the first step a legitimate method when using integration by parts, or is it just a coincidence that it works? Thanks!