Mathematics

The key is recognizing that $\ln(5x) = \ln(5) + \ln(x)$, which splits this into a constant plus a familiar logarithm. You already know how to integrate $\ln(x)$ using integration by parts (where $u = \ln(x)$ and $dv = dx$), and $\ln(5)$ is just a constant multiplier. This decomposition transforms an unfamiliar integral into one you can handle with a standard technique.

The key is recognizing that $\ln(5x) = \ln(5) + \ln(x)$, which splits this into a constant plus a familiar logarithm. You already know how to integrate $\ln(x)$ using integration by parts (where $u = \ln(x)$ and $dv = dx$), and $\ln(5)$ is just a constant multiplier. This decomposition transforms an unfamiliar integral into one you can handle with a standard technique.