The question:
Use integration by parts to evaluate the following integral
$\displaystyle \int ln(x) dx$
I'm not sure what to do, since this looks like a single part to me. I'm clearly missing something fundamental here. Thanks.
The general form is
$\displaystyle \int u \, dv = u v - \int v \, du$
Let $\displaystyle u=\ln x$ and $\displaystyle dv=dx$. What does this give you?
Notice that if you work this problem this way, you do not have to know what the integral of $\displaystyle \ln x$ is! Instead you only need to know the derivative of $\displaystyle \ln x$ to compute $\displaystyle du$. That is the reason for using the method.