**Solution.**We want to determine the integral of \ln(x)/x:

\begin{align*} \int \frac{\ln(x)}{x} dx. \end{align*}

\begin{align*} \int \frac{\ln(x)}{x} dx &= \int u du \\ &= \frac{1}{2}u^2 + C \\ &= \frac{1}{2}\ln^2(x) + C. \end{align*}

Skip to content
## What is the integral of ln(x)/x?

The integral of \ln(x)/x is \frac{1}{2}\ln^2(x) + C.

**Solution.** We want to determine the integral of \ln(x)/x:
We will use the substitution method. Let u = \ln(x), then we know from here that du = \frac{1}{x}dx. So we get the following:
Therefore, the integral of \ln(x)/x is \frac{1}{2}\ln^2(x) + C.

\begin{align*} \int \frac{\ln(x)}{x} dx. \end{align*}