Antiderivatives of Logarithmic Functions

In this case, let: $v = \ln u$ , so that $dv = \nicefrac{du}{u}$ . Rewrite the antiderivative as follows:

$\begin{equation*} \int \frac{du}{u\,\ln u} = \int \frac{1}{\ln u}\cdot \frac{du}{u} = \ln\left\vert \ln |u| \right\vert + C \end{equation*}$

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