Integral of Cotangent function

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$\int \cot\left(5x-10\right)\; dx$

**Answer**

$\int \cot\left(5x-10\right)\; dx$

Substitute $u=5x-10$. So, $du =5\; dx$

Or, $\frac{1}{5}\; du = dx$

And, $\int \cot\left(5x-10\right)\; dx = \frac{1}{5}\int \cot u \;du$

$=\frac{1}{5}\ln \left|\sin u\right| + C$

Substituting back $u=5x-10$

$=\frac{1}{5}\ln \left| \sin\left(5x-10\right)\right|+C$