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Antiderivatives of Logarithmic Functions

Som formulas for computing antiderivatives of logarithmic functions are deduced.

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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