What is the integral of ln(x)/x?

The Mathematician — Sat, 11 Mar 2023 13:00:27 +0000

The integral of

\ln(x)/x

\frac{1}{2}\ln^2(x) + C

.

Solution. We want to determine the integral of

\ln(x)/x

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

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:

\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*}

Therefore, the integral of

\ln(x)/x

\frac{1}{2}\ln^2(x) + C

ln(x)/x Archives - Epsilonify