Problems on Techniques of Integration

Use the Integration by Parts. Set

u &=& \ln(x)\\
dv &=& dx\;.


du &=&\displaystyle \frac{1}{x} dx\\
v &=& x\;.


\begin{displaymath}\int \ln(x) dx = x \ln(x) - \int x \frac{1}{x} dx = x \ln(x) - \int dx\end{displaymath}


\begin{displaymath}\int \ln(x) dx = x \ln(x) - x + C\;.\end{displaymath}

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