Integral of square of Cosecant function

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$\int {\csc}^2\left(12x+8\right)\; dx$

**Answer**

$\int {\csc}^2\left(12x+8\right)\; dx$

Substitute $u=12x+8$. So, $du =12\; dx$

Or, $\frac{1}{12}\; du = dx$

And, $\int {\csc}^2\left(12x+8\right)\; dx = \frac{1}{12}\int {\csc u}^2 \;du$

$=-\frac{1}{12}\cot u + C$

Substituting back $u=12x+8$

$=-\frac{1}{12} \cot\left(12x+8\right)+C$