Antiderivatives of Logarithmic Functions

Antiderivative of the Natural Log Function

In this case the technique of Integration by parts works. To this end, define $u = \ln v$ and therefore, $du = \nicefrac{dv}{v}$ .
Also, let $dw = dv$ , so that $w = v$ . Then,

$\begin{eqnarray*} \int \ln v \cdot dv &=& v\cdot \ln v - \int v\cdot\frac{dv}{v} \\ &=& v\cdot \ln v - \int dv \\ &=& v\cdot \ln v - v + C \end{eqnarray*}$

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Antiderivatives of Logarithmic Functions

Som formulas for computing antiderivatives of logarithmic functions are deduced.

Antiderivative of the Natural Log Function