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<math>
\begin{align}

\int_{1}^{9}\frac{1}{2x}dx = \frac{1}{2}\int_{1}^{9}\frac{1}{x}dx 

&= \frac{1}{2}\ln{|x|}\bigg|_{1}^{9} = \frac{1}{2}\ln{|9|}-\frac{1}{2}\ln{|1|}

&= \ln{|9^{\frac{1}{2}}|}-\ln{|1^{\frac{1}{2}}|} = \ln{3}-0 = \ln{3}


\end {align}
</math>

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