Answer
\[ = \ln \left| {\sin x} \right| + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\cot \,xdx} \hfill \\
\hfill \\
use\,\,\,\,\cot x = \frac{{\cos x}}{{\sin x}} \hfill \\
\hfill \\
\int_{}^{} {\cot xdx\, = \int_{}^{} {\frac{{\cos x}}{{\sin x}}dx} } \hfill \\
\hfill \\
set\,\,u = \sin x\,\,then\,\,du = \cos xdx \hfill \\
\hfill \\
\int_{}^{} {\frac{{\cos x}}{{\sin x}}\,dx} = \int_{}^{} {\frac{{du}}{u}} \hfill \\
\hfill \\
integrate\,\, \hfill \\
\hfill \\
= \ln \left| u \right| + C \hfill \\
\hfill \\
\,\,u\, = \,\sin \,x\,\,then \hfill \\
\hfill \\
= \ln \left| {\sin x} \right| + C \hfill \\
\end{gathered} \]
