Integral of Cotangent function

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$\int \cot\left(13x-8\right)\; dx$

**Answer**

$\int \cot\left(13x-8\right)\; dx$

Substitute $u=13x-8$. So, $du =13\; dx$

Or, $\frac{1}{13}\; du = dx$

And, $\int \cot\left(13x-8\right)\; dx = \frac{1}{13}\int \cot u \;du$

$=\frac{1}{13}\ln \left|\sin u\right| + C$

Substituting back $u=13x-8$

$=\frac{1}{13}\ln \left| \sin\left(13x-8\right)\right|+C$