Integral of square of Cosecant function

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$\int {\csc}^2\left(2x+8\right)\; dx$

**Answer**

$\int {\csc}^2\left(2x+8\right)\; dx$

Substitute $u=2x+8$. So, $du =2\; dx$

Or, $\frac{1}{2}\; du = dx$

And, $\int {\csc}^2\left(2x+8\right)\; dx = \frac{1}{2}\int {\csc u}^2 \;du$

$=-\frac{1}{2}\cot u + C$

Substituting back $u=2x+8$

$=-\frac{1}{2} \cot\left(2x+8\right)+C$