Integral of Cotangent function

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$\int \cot\left(15x+6\right)\; dx$

**Answer**

$\int \cot\left(15x+6\right)\; dx$

Substitute $u=15x+6$. So, $du =15\; dx$

Or, $\frac{1}{15}\; du = dx$

And, $\int \cot\left(15x+6\right)\; dx = \frac{1}{15}\int \cot u \;du$

$=\frac{1}{15}\ln \left|\sin u\right| + C$

Substituting back $u=15x+6$

$=\frac{1}{15}\ln \left| \sin\left(15x+6\right)\right|+C$