TITLE: Integrating $\ln x$ by parts
QUESTION [6 upvotes]: I am asked to integrate by parts $\int \ln(x) dx$. But I'm at a loss isn't there supposed to be two functions in the integral for you to be able to integrate by parts?

REPLY [3 votes]: Just a good point: Wherever you have $$\int p(x)\ln(x)dx$$ in which $p(x)$ is an integrable function; you can use the integration by parts as follows: $$u=\ln(x),~~dv=p(x)dx$$ such that $$\int udv=uv-\int vdu$$